,transcriber's ,note3 ,in this          
plain-text rendering1  4'4 means        
therefore  alpha1 beta1 4441 ,alpha1    
,beta1 444 for ,greek symbols           
,,deductive ,,logic  ,,by  ,,st4        
,,george ,,stock1 ,m4,a4  ,,pembroke    
,,college1 ,,oxford     ,,preface4  ,one
 critic1 who was kind enough to look at 
this book in manuscript1 recommended me 
to abandon the design of ,publishing it1
 on the ground that my logic was too    
like all other logics2 another suggested
 to me to cut out a considerable amount 
of new matter4 ,the latter advice ,i    
have followed2 the former has encouraged
 me to hope that ,i shall not be        
considered guilty of wanton innovation4 
,the few novelties which ,i have        
ventured to retain will1 ,i trust1 be   
regarded as legitimate extensions of    
received lines of teaching4  ,my object 
has been to produce a work which should 
be as thoroughly representative of the  
present state of the logic of the       
,oxford ,schools as any of the          

text-books of the past4 ,the qualities  
which ,i have aimed at before all others
 have been clearness and consistency4   
,for the task which ,i have taken upon  
myself ,i may claim one                 
qualification--that of experience2 since
 more than seventeen years have now     
elapsed since ,i took my first pupil in 
logic for the ,honour ,school of        
,moderations1 and during that time ,i   
have been pretty continuously engaged in
 studying and teaching the subject4  ,in
 acknowledging my obligations to        
previous writers ,i must begin with     
,archbishop ,whately1 whose writings    
first gave me an interest in the        
subject4 ,the works of ,mill and        
,hamilton have of course been freely    
drawn upon4 ,i have not followed either 
of those two great writers exclusively1 
but have endeavoured to assimilate what 
seemed best in both4 ,to ,professor     
,fowler ,i am under a special debt4 ,i  
had not the privilege of personal       
teaching from him in logic1--as ,i had  

in some other subjects2 but his book    
fell into my hands at an early period in
 my mental training1 and was so         
thoroughly studied as to have become a  
permanent part of the furniture of my   
mind4 ,much the same may be said of my  
relation to the late ,professor         
,jevons's ,elementary ,lessons in       
,logic4  ,two other books1 which ,i feel
 bound to mention with special emphasis1
 are ,hansel's edition of ,aldrich and  
,mc,cosh's ,laws of ,discursive         
,thought4 ,if there be added to the     
foregoing ,watts's ,logic1 ,thomson's   
,outlines of the ,laws of ,thought1     
,bain's ,deductive ,logic1 ,jevons's    
,studies in ,deductive ,logic and       
,principles of ,science1 ,bradley's     
,principles of ,logic1 ,abbott's        
,elements of ,logic1 ,walker's edition  
of ,murray1 ,ray's ,text-book of        
,deductive ,logic1 and ,weatherley's    
,rudiments of ,logic1 ,i think the list 
will be exhausted of modern works from  
which ,i am conscious of having         

borrowed4 ,but1 not to forget the sun1  
while thanking the manufacturers of     
lamps and candles1 ,i should add that ,i
 have studied the works of ,aristotle   
according to the measure of my time and 
ability4  ,this work has had the great  
advantage of having been revised1 while 
still in manuscript1 by ,mr4 ,alfred    
,robinson1 ,fellow of ,new ,college1 to 
whom ,i cannot sufficiently express my  
obligation4 ,i have availed myself to   
the full of the series of criticisms    
which he was kind enough to send me4 ,as
 some additions have been made since    
then1 he cannot be held in anyway       
responsible for the faults which less   
kindly critics may detect4  ,for the    
examples at the end ,i am mainly        
indebted to others1 and to a large      
extent to my ingenious friend1 the ,rev4
 ,w4 ,j4 ,priest of ,merton ,college4   
,my thanks are due also to my friend and
 former pupil1 ,mr4 ,gilbert ,grindle1  
,scholar of ,corpus1 who has been at the
 pains to compose an index1 and to      

revise the proofs as they passed through
 the press4  ,and last1 but not least1  
,i must set on record my gratitude to   
,commander ,r4 ,a4 ,stock1 ,r4,n41 one  
of ,her ,majesty's ,knights of ,windsor1
 without whose brotherly aid this work  
might never have been written1 and would
 certainly not have assumed exactly its 
present shape4  ,,oxford1  ,october #bb1
 #ahhh4     ,,contents4  ,,preface4     
,,introduction1  #a-ef4  ,,part ,i4 ,of 
,terms1  #eg-aga4    ,,chap4 ,i4 ,of the
 ,term as distinguished from other      
words1  #eg-gf4    ,,ii4 ,of the        
,division of ,things1  #gg-he4    ,,iii4
 ,of the ,divisions of ,terms1  #hf-afe4
    ,,iv4 ,of the ,law of ,inverse      
,variation of ,extension and ,intension1
    #aff-aga4  ,,part ,,ii4 ,of         
,propositions1  #agb-ahe4    ,,chap4 ,i4
 ,of the ,proposition as distinguished  
from other ,sentences1    #agb-ahe4     
,,ii4 ,of the ,copula1  #ahf-bja4       
,,iii4 ,of the ,divisions of            
,propositions1  #bjb-bgc4    ,,iv4 ,of  

the ,distribution of ,terms1  #bgd-bid4 
,v4 ,of the ,quantification of the      
,predicate1  #bie-cab4    ,,vi4 ,of the 
,heads of ,predicables1  #cac-cdf4      
,,vii4 ,of ,definition1  #cdg-chd4      
,,viii4 ,of ,division1  #che-dbe4       
,,part ,,iii4 ,of ,inferences1          
#dbf-hhd4    ,,chap4 ,i4 ,of ,inferences
 in general1  #dbf-dda4    ,,ii4 ,of    
,deductive ,inferences1  #ddb-ddh4      
,,iii4 ,of ,opposition1  #ddi-dgh4      
,,iv4 ,of ,conversion1  #dgi-die4    ,v4
 ,of ,permutation1  #dif-ejb4    ,,vi4  
,of ,compound ,forms of ,immediate      
,inference1  #ejc-ecb4    ,,vii4 ,of    
,other ,forms of ,immediate ,inference1 
#ecc-eci4    ,,viii4 ,of ,mediate       
,inferences or ,syllogisms1  #edj-eeg4  
,,ix4 ,of ,mood and ,figure1  #eeh-efh4 
,x4 ,of the ,canon of ,reasoning1       
#efi-eha4    ,,xi4 ,of the ,general     
,rules of ,syllogism1  #ehb-eih4        
,,xii4 ,of the ,determination of the    
,legitimate ,moods of ,syllogism1       
#eii-fje4    ,,xiii4 ,of the ,special   

,rules of the ,four ,figures1  #fjf-fbj4
    ,,xiv4 ,of the ,determination of the
 ,moods that are valid in the ,four     
,figures1  #fba-fcb4    ,,xv4 ,of the   
,special ,canons of the ,four ,figures1 
#fcc-fdg4    ,,xvi4 ,of the ,special    
,uses of the ,four ,figures1  #fdh-fee4 
,,xvii4 ,of the ,syllogism with ,three  
,figures1  #fef-fff4    ,,xviii4 ,of    
,reduction1  #ffg-gjj4    ,,xix4 ,of    
,immediate ,inference as applied to     
,complex ,propositions1    #gja-gcj4    
,,xx4 ,of ,complex ,syllogisms1         
#gca-gdc4    ,,xxi4 ,of the ,reduction  
of the ,partly ,conjunctive ,syllogism1 
#gdd-geb4    ,,xxii4 ,of the ,partly    
,conjunctive ,syllogism regarded as all 
,immediate   ,inference1  #gec-gei4     
,,xxiii4 ,of the ,disjunctive           
,syllogism1  #gfj-gfe4    ,,xxiv4 ,of   
the ,reduction of the ,disjunctive      
,syllogism1  #gff-gfi4    ,,xxv4 ,of the
 ,disjunctive ,syllogism regarded as an 
,immediate   ,inference1  #ggj-ggg4     
,,xxvi4 ,of the ,mixed ,form of ,complex

 ,syllogism1  #ggh-gie4    ,,xxvii4 ,of 
the ,reduction of the ,dilemma1         
#gif-gig4    ,,xxviii4 ,of the ,dilemma 
regarded as an ,immediate ,inference1   
#gih1gii4    ,,xxix4 ,of ,trains of     
,reasoning1  #hjj-hbf4    ,,xxx4 ,of    
,fallacies1  #hbg-hhd4  ,,exercises4    
,,index4     ,,introduction4   #a4      
,,logic is divided into two branches1   
namely--    7#a7 ,inductive1    7#b7    
,deductive4   #b4 ,the problem of       
inductive logic is to determine the     
actual truth or falsity of propositions3
 the problem of deductive logic is to   
determine their relative truth or       
falsity1 that is to say1 given such and 
such propositions as true1 what others  
will follow from them4   #c4 ,hence in  
the natural order of treatment inductive
 logic precedes deductive1 since it is  
induction which supplies us with the    
general truths1 from which we reason    
down in our deductive inferences4   #d4 
,it is not1 however1 with logic as a    
whole that we are here concerned1 but   

only with deductive logic1 which may be 
defined as ,the ,science of the ,formal 
,laws of ,thought4   #e4 ,in order fully
 to understand this definition we must  
know exactly what is meant by 'thought1'
 by a 'law of thought1' by the term     
'formal1' and by 'science4'   #f4       
,thought1 as here used1 is confined to  
the faculty of comparison4 ,all thought 
involves comparison1 that is to say1 a  
recognition of likeness or unlikeness4  
#g4 ,the laws of thought are the        
conditions of correct thinking4 ,the    
term 'law1' however1 is so ambiguous    
that it will be well to determine more  
precisely in what sense it is here used4
   #h4 ,we talk of the 'laws of the     
land' and of the 'laws of nature1' and  
it is evident that we mean very         
different things by these expressions4  
,by a law in the political sense is     
meant a command imposed by a superior   
upon an inferior and sanctioned by a    
penalty for disobedience4  ,but by the  
'laws of nature' are meant merely       

certain uniformities among natural      
phenomena2 for instance1 the 'law of    
gravitation' means that every particle  
of matter does invariably attract every 
other particle of matter in the         
universe4   #i4 ,the word 'law' is      
transferred by a metaphor from one of   
these senses to the other4 ,the effect  
of such a command as that described     
above is to produce a certain amount of 
uniformity in the conduct of men1 and   
so1 where we observe uniformity in      
nature1 we assume that it is the result 
of such a command1 whereas the only     
thing really known to us is the fact of 
uniformity itself4   #aj4 ,now in which 
of these two senses are we using the    
term 'laws of thought'8 ,the laws of the
 land1 it is plain1 are often violated1 
whereas the laws of nature never can be 
so ,footnote3 ,there is a sense in which
 people frequently speak of the laws of 
nature being violated1 as when one says 
that intemperance or celibacy is a      
violation of the laws of nature1 but    

here by 'nature' is meant an ideal      
perfection in the conditions of         
existence44 ,can the laws of thought be 
violated in like manner with the laws of
 the land8 ,or are they inviolable like 
the laws of nature8   #aa4 ,in          
appearance they can be1 and manifestly  
often are violated-for how else could   
error be possible8 ,but in reality they 
can not4 ,no man ever accepts a         
contradiction when it presents itself to
 the mind as such3 but when reasoning is
 at all complicated what does really    
involve a contradiction is not seen to  
do so2 and this sort of error is further
 assisted by the infinite perplexities  
of language4   #ab4 ,the laws of thought
 then in their ultimate expression are  
certain uniformities which invariably   
hold among mental phenomena1 and so far 
they resemble the laws of nature3 but in
 their complex applications they may be 
violated owing to error1 as the laws of 
the land may be violated by crime4      
#ac4 ,we have now to determine the      

meaning of the expression 'formal laws  
of thought4'   #ad4 ,the distinction    
between form and matter is one which    
pervades all nature4 ,we are familiar   
with it in the case of concrete things4 
,a cup1 for instance1 with precisely the
 same form1 may be composed of very     
different matter-gold1 silver1 pewter1  
horn or what not8   #ae4 ,similarly in  
every act of thought we may distinguish 
two things--    7#a7 the object thought 
about1    7#b7 the way in which the mind
 thinks of it4  ,the first is called the
 ,matter2 the second the ,form of       
,thought4   #af4 ,now ,formal1 which is 
another name for ,deductive ,logic1 is  
concerned only with the way in which the
 mind thinks1 and has nothing to do with
 the particular objects thought about4  
#ag4 ,since the form may be the same1   
whilst the matter is different1 we may  
say that formal logic is concerned with 
the essential and necessary elements of 
thought as opposed to such as are       
accidental and contingent4 ,by          

'contingent' is meant what holds true in
 some cases1 but not in others4 ,for    
instance1 in the particular case of     
equilateral triangles it is true to say1
 not only that 'all equilateral         
triangles are equiangular1' but also    
that 'all equiangular triangles are     
equilateral4' ,but the evidence for     
these two propositions is independent4  
,the one is not a formal consequence of 
the other4 ,if it were1 we should be    
able to apply the same inference to all 
matter1 and assert generally that if all
 ,a is ,b1 all ,b is ,a1 which it is    
notorious that we cannot do4   #ah4 ,it 
remains now for the full elucidation of 
our definition to determine what is     
meant by 'science4'   #ai4 ,the question
 has often been discussed whether logic 
is a science or an art4 ,the answer to  
it must depend upon the meaning we      
assign to these terms4   #bj4 ,broadly  
speaking1 there is the same difference  
between ,science and ,art as there is   
between knowing and doing4    ,science  

is systematized knowledge2   ,art is    
systematized action4   ,science is      
acquired by study2   ,art is acquired by
 practice4   #ba4 ,now logic is         
manifestly a branch of knowledge1 and   
does not necessarily confer any         
practical skill4 ,it is only the right  
use of its rules in thinking which can  
make men think better4 ,it is therefore1
 in the broad sense of the terms1 wholly
 a science and not at all an art4   #bb4
 ,but this word 'art1' like most others1
 is ambiguous1 and is often used1 not   
for skill displayed in practice1 but for
 the knowledge necessary thereto4 ,this 
meaning is better conveyed by the term  
'practical science4'   #bc4 ,science is 
either speculative or practical4 ,in the
 first case we study merely that we may 
know2 in the latter that we may do4     
,anatomy is a speculative science2      
,surgery is a practical science4  ,in   
the first case we study the human frame 
in order that we may understand its     
structure2 in the second that we may    

assist its needs4 ,whether logic is a   
speculative or a practical science      
depends entirely upon the way in which  
it is treated4 ,if we study the laws of 
thought merely that we may know what    
they are1 we are making it a speculative
 science2 if we study the same laws with
 a view to deducing rules for the       
guidance of thought1 we are making it a 
practical science4   #bd4 ,hence logic  
may be declared to be both the science  
and the art of thinking4 ,it is the art 
of thinking in the same sense in which  
grammar is the art of speaking4         
,grammar is not in itself the right use 
of words1 but a knowledge of it enables 
men to use words correctly4 ,in the same
 way a knowledge of logic enables men to
 think correctly1 or at least to avoid  
incorrect thoughts4 ,as an art logic may
 be called the navigation of the sea of 
thought4   #be4 ,the laws of thought are
 all reducible to the three following   
axioms1 which are known as ,the ,three  
,fundamental ,laws of ,thought4    7#a7 

,the ,law of ,identity--      ,whatever 
is1 is2    or1 in a more precise form1  
,every ,a is ,a4    7#b7 ,the ,law of   
,contradiction--      ,nothing can both 
be and not be2     ,nothing can be ,a   
and not ,a4    7#c7 ,the ,law of        
,excluded ,middle--      ,everything    
must either be or not be2               
,everything is either ,a or not ,a4     
#bf4 ,each of these principles is       
independent and self-evident4   #bg4 ,if
 it were possible for the law of        
identity to be violated1 no violation of
 the law of contradiction would         
necessarily ensue3 for a thing might    
then be something else1 without being   
itself at the same time1 which latter is
 what the law of contradiction militates
 against4 ,neither would the law of     
excluded middle be infringed4 ,for1 on  
the supposition1 a thing would be       
something else1 whereas all that the law
 of excluded middle demands is that it  
should either be itself or not4 ,a would
 in this case adopt the alternative of  

being not ,a4   #bh4 ,again1 the        
violation of the law of contradiction   
does not involve any violation of the   
law of identity3 for a thing might in   
that case be still itself1 so that the  
law of identity would be observed1 even 
though1 owing to the law of             
contradiction not holding1 it were not  
itself at the same time4 ,neither would 
the law of excluded middle be infringed4
 ,for a thing would1 on the supposition1
 be both itself and not itself1 which is
 the very reverse of being neither4     
#bi4 ,lastly1 the law of excluded middle
 might be violated without a violation  
of the law of contradiction3 for we     
should then have a thing which was      
neither ,a nor not ,a1 but not a thing  
which was both at the same time4        
,neither would the law of identity be   
infringed4 ,for we should in this case  
have a thing which neither was nor was  
not1 so that the conditions of the law  
of identity could not exist to be       
broken4 ,that law postulates that       

whatever is1 is3 here we have a thing   
which never was to begin with4   #cj4   
,these principles are of so simple a    
character that the discussion of them is
 apt to be regarded as puerile4         
,especially is this the case with regard
 to the law of identity4 ,this principle
 in fact is one of those things which   
are more honoured in the breach than in 
the observance4 ,suppose for a moment   
that this law did not hold--then what   
would become of all our reasoning8      
,where would be the use of establishing 
conclusions about things1 if they were  
liable to evade us by a ,protean change 
of identity8   #ca4 ,the remaining two  
laws supplement each other in the       
following way4 ,the law of contradiction
 enables us to affirm of two exhaustive 
and mutually exclusive alternatives1    
that it is impossible for both to be    
true2 the law of excluded middle        
entitles us to add1 that it is equally  
impossible for both to be false4 ,or1 to
 put the same thing in a different form1

 the law of contradiction lays down that
 one of two such alternatives must be   
false2 the law of excluded middle adds  
that one must be true4  #cb4 ,there are 
three processes of thought    7#a7      
,conception4    7#b7 ,judgement4    7#c7
 ,inference or ,reasoning4   #cc4       
,conception1 which is otherwise known as
 ,simple ,apprehension1 is the act of   
forming in the mind the idea of         
anything1 e4g4 when we form in the mind 
the idea of a cup1 we are performing the
 process of conception4   #cd4          
,judgement1 in the sense in which it is 
here used ,footnote3 ,sometimes the term
 'judgement' is extended to the         
comparison of nameless                  
sense-impressions1 which underlies the  
formation of concepts4 ,but this amounts
 to identifying judgement with thought  
in general4  may be resolved into       
putting two ideas together in the mind1 
and pronouncing as to their agreement or
 disagreement1 e4g4 we have in our minds
 the idea of a cup and the idea of a    

thing made of porcelain1 and we combine 
them in the judgement--',this cup is    
made of porcelain4'   #ce4 ,inference1  
or ,reasoning1 is the passage of the    
mind from one or more judgements to     
another1 e4g4 from the two judgements   
',whatever is made of porcelain is      
brittle1' and ',this cup is made of     
porcelain1' we elicit a third judgement1
 ',this cup is brittle4'   #cf4         
,corresponding to these three processes 
there are three products of thought1    
viz4    7#a7 ,the ,concept4    7#b7 ,the
 ,judgement4    7#c7 ,the ,inference4   
#cg4 ,since our language has a tendency 
to confuse the distinction between      
processes and products1 ,footnote3 ,e4g4
 ,we have to speak quite                
indiscriminately of ,sensation1         
,imagination1 ,reflexion1 ,sight1       
,thought1 ,division1 ,definition1 and so
 on1 whether we mean in any case a      
process or a product4 it is the more    
necessary to keep them distinct in      
thought4 ,strictly we ought to speak of 

conceiving1 judging and inferring on the
 one hand1 and1 on the other1 of the    
concept1 the judgement and the          
inference4  ,the direct object of logic 
is the study of the products rather than
 of the processes of thought4 ,but1 at  
the same time1 in studying the products 
we are studying the processes in the    
only way in which it is possible to do  
so4  ,for the human mind cannot be both 
actor and spectator at once2 we must    
wait until a thought is formed in our   
minds before we can examine it4 ,thought
 must be already dead in order to be    
dissected3 there is no vivisection of   
consciousness4 ,thus we can never know  
more of the processes of thought than   
what is revealed to us in their         
products4   #ch4 ,when the three        
products of thought are expressed in    
language1 they are called respectively  
7#a7 ,the ,term4    7#b7 ,the           
,proposition4    7#c7 ,the ,inference4  
#ci4 ,such is the ambiguity of language 
that we have already used the term      

'inference' in three different          
senses--first1 for the act or process of
 inferring2 secondly1 for the result of 
that act as it exists in the mind2 and1 
thirdly1 for the same thing as expressed
 in language4  ,later on we shall have  
to notice a further ambiguity in its    
use4   #dj4 ,it has been declared that  
thought in general is the faculty of    
comparison1 and we have now seen that   
there are three products of thought4 ,it
 follows that each of these products of 
thought must be the result of a         
comparison of some kind or other4       
,the concept is the result of comparing 
attributes4   ,the judgement is the     
result of comparing concepts4   ,the    
inference is the result of comparing    
judgements4   #da4 ,in what follows we  
shall1 for convenience1 adopt the       
phraseology which regards the products  
of thought as clothed in language in    
preference to that which regards the    
same products as they exist in the mind 
of the individual4 ,for although the    

object of logic is to examine thought   
pure and simple1 it is obviously        
impossible to discuss it except as      
clothed in language4 ,accordingly the   
three statements above made may be      
expressed as follows--    ,the term is  
the result of comparing attributes4     
,the proposition is the result of       
comparing terms4   ,the inference is the
 result of comparing propositions4      
#db4 ,there is an advantage attending   
the change of language in the fact that 
the word 'concept' is not an adequate   
expression for the first of the three   
products of thought1 whereas the word   
'term' is4 ,by a concept is meant a     
general notion1 or the idea of a class1 
which corresponds only to a common term4
 ,now not only are common terms the     
results of comparison1 but singular     
terms1 or the names of individuals1 are 
so too4   #dc4 ,the earliest result of  
thought is the recognition of an        
individual object as such1 that is to   
say as distinguished and marked off from

 the mass of its surroundings4 ,no doubt
 the first impression produced ,upon the
 nascent intelligence of an infant is   
that of a confused whole4 ,it requires  
much exercise of thought to distinguish 
this whole into its parts4 ,the         
completeness of the recognition of an   
individual object is announced by       
attaching a name to it4 ,hence even an  
individual name1 or singular term1      
implies thought or comparison4 ,before  
the child can attach a meaning to the   
word 'mother1' which to it is a singular
 term1 it must have distinguished       
between the set of impressions produced 
in it by one object from those which are
 produced in it by others4  ,thus1 when 
,vergil says    ,incipe1 parve puer1    
risu cognoscere matrem1  he is exhorting
 the beatific infant to the exercise of 
the faculty of comparison4   #dd4 ,that 
a common term implies comparison does   
not need to be insisted upon4 ,it is    
because things resemble each other in   
certain of their attributes that we call

 them by a common name1 and this        
resemblance could not be ascertained    
except by comparison1 at some time and  
by some one4 ,thus a common term1 or    
concept1 is the compressed result of an 
indefinite number of comparisons1 which 
lie wrapped up in it like so many       
fossils1 witnessing to prior ages of    
thought4   #de4 ,in the next product of 
thought1 namely1 the proposition1 we    
have the result of a single act of      
comparison between two terms2 and this  
is why the proposition is called the    
unit of thought1 as being the simplest  
and most direct result of comparison4   
#df4 ,in the third product of thought1  
namely1 the inference1 we have a        
comparison of propositions either       
directly or by means of a third4 ,this  
will be explained later on4 ,for the    
present we return to the first product  
of thought4   #dg4 ,the nature of       
singular terms has not given rise to    
much dispute2 but the nature of common  
terms has been the great battle-ground  

of logicians4 ,what corresponds to a    
singular term is easy to determine1 for 
the thing of which it is a name is there
 to point to3 but the meaning of a      
common term1 like 'man' or 'horse1' is  
not so obvious as people are apt to     
think on first hearing of the question4 
#dh4 ,a common term or class-name was   
known to medival logicians under the    
title of a ,universal2 and it was on the
 question ',what is a ,universal #g'    
that they split into the three schools  
of ,realists1 ,nominalists1 and         
,conceptualists4 ,here are the answers  
of the three schools to this question in
 their most exaggerated form--   #di4   
,universals1 said the ,realists1 are    
substances having an independent        
existence in nature4   #ej4 ,universals1
 said the ,nominalists1 are a mere      
matter of words1 the members of what we 
call a class having nothing in common   
but the name4   #ea4 ,universals1 said  
the ,conceptualists1 exist in the mind  
alone1 ,they are the conceptions under  

which the mind regards external objects4
   #eb4 ,the origin of pure ,realism is 
due to ,plato and his doctrine of       
'ideas'2 for ,idealism1 in this sense1  
is not opposed to ,realism1 but         
identical with it4 ,plato seems to have 
imagined that1 as there was a really    
existing thing corresponding to a       
singular term1 such as ,socrates1 so    
there must be a really existing thing   
corresponding to the common term 'man4' 
,but when once the existence of these   
general objects is admitted1 they swamp 
all other existences4 ,for individual   
men are fleeting and transitory--subject
 to growth1 decay and death--whereas the
 idea of man is imperishable and        
eternal4 ,it is only by partaking in the
 nature of these ideas that individual  
objects exist at all4   #ec4 ,pure      
,nominalism was the swing of the        
pendulum of thought to the very opposite
 extreme2 while ,conceptualism was an   
attempt to hit the happy mean between   
the two4   #ed4 ,roughly it may be said 

that the ,realists sought for the answer
 to the question ',what is a            
,universal8' in the matter of thought1  
the ,conceptualists in the form1 and the
 ,nominalists in the expression4   #ee4 
,a full answer to the question ',what is
 a ,universal8' will bring in something 
of the three views above given1 while   
avoiding the exaggeration of each4 ,a   
,universal is a number of things that   
are called by the same name2 but they   
would not be called by the same name    
unless they fell under the same         
conception in the mind2 nor would they  
fall under the same conception in the   
mind unless there actually existed      
similar attributes in the several       
members of a class1 causing us to regard
 them under the same conception and to  
give them the same name4 ,universals    
therefore do exist in nature1 and not   
merely in the mind of man3 but their    
existence is dependent upon individual  
objects1 instead of individual objects  
depending for their existence upon them4

 ,aristotle saw this very clearly1 and  
marked the distinction between the      
objects corresponding to the singular   
and to the common term by calling the   
former ,primary and the latter          
,secondary ,existences4 ,rosinante and  
,excalibur are primary1 but 'horse' and 
'sword' secondary existences4   #ef4 ,we
 have seen that the three products of   
thought are each one stage in advance of
 the other1 the inference being built   
upon the proposition1 as the proposition
 is built upon the term4 ,logic         
therefore naturally divides itself into 
three parts4    ,the ,first ,part of    
,logic deals with the ,term2   ,the     
,second ,part deals with the            
,proposition2   ,the ,third ,part deals 
with the ,inference4      ,,part        
,i4--,,of ,,terms4     ,,chapter #a4    
,of the ,term as distinguished from     
other words4    #eg4 ,the word 'term'   
means a boundary4   #eh4 ,the subject   
and predicate are the two terms1 or     
boundaries1 of a proposition4 ,in a     

proposition we start from a subject and 
end in a predicate 7 #ahb-d71 there     
being nothing intermediate between the  
two except the act of pronouncing as to 
their agreement or disagreement1 which  
is registered externally under the sign 
of the copula4  ,thus the subject is the
 'terminus a quo1' and the predicate is 
the 'terminus ad quem4'   #ei4 ,hence it
 appears that the term by its very name 
indicates that it is arrived at by an   
analysis of the proposition4 ,it is the 
judgement or proposition that is the    
true unit of thought and speech4 ,the   
proposition as a whole is prior in      
conception to the terms which are its   
parts3 but the parts must come before   
the whole in the synthetic order of     
treatment4   #fj4 ,a term is the same   
thing as a name or noun4   #fa4 ,a name 
is a word1 or collection of words1 which
 serves as a mark to recall or transmit 
the idea of a thing1 either in itself or
 through some of its attributes4   #fb4 
,nouns1 or names1 are either            

,substantive or ,adjective4  ,a ,noun   
,substantive is the name of a thing in  
itself1 that is to say1 without         
reference to any special attribute4     
#fc4 ,a ,noun ,adjective is a name which
 we are entitled to add to a thing1 when
 we know it to possess a given          
attribute4   #fd4 ,the ,verb1 as such1  
is not recognised by logic1 but is      
resolved into predicate and copula1 that
 is to say1 into a noun which is        
affirmed or denied of another1 plus the 
sign of that affirmation or denial4     
',the kettle boils' is logically        
equivalent to ',the kettle is boiling1' 
though it is by no means necessary to   
express the proposition in the latter   
shape4 ,here we see that 'boils' is     
equivalent to the noun 'boiling'        
together with the copula 'is1' which    
declares its agreement with the noun    
'kettle4' ',boiling' here is a noun     
adjective1 which we are entitled to add 
to 'kettle1' in virtue of certain       
knowledge which we have about the       

latter4 ,being a verbal noun1 it is     
called in grammar a participle1 rather  
than a mere adjective4 ,the word        
'attributive' in logic embraces both the
 adjective and participle of grammar4   
#fe4 ,in grammar every noun is a        
separate word3 but to logic1 which is   
concerned with the thought rather than  
with the expression1 it is indifferent  
whether a noun1 or term1 consists of one
 word or many4 ,the latter are known as 
'many-worded names4' ,in the following  
passage1 taken at random from ,butler's 
,analogy--',these several observations1 
concerning the active principle of      
virtue and obedience to ,god's commands1
 are applicable to passive submission or
 resignation to his will'--we find the  
subject consisting of fourteen words1   
and the predicate of nine4 ,it is the   
exception rather than the rule to find a
 predicate which consists of a single   
word4  ,many-worded names in ,english   
often consist of clauses introduced by  
the conjunction 'that1' as ',that       

letters should be written in strict     
conformity with nature is true'3 often  
also of a grammatical subject with one  
or more dependent clauses attached to   
it1 as    ',he who fights and runs away1
    ,will live to fight another day4'   
#ff4 ,every term then is not a word1    
since a term may consist of a collection
 of words4 ,neither is every word a     
term4 ',over1' for instance1 and        
'swiftly1' and1 generally1 what are     
called particles in grammar1 do not by  
themselves constitute terms1 though they
 may be employed along with other words 
to make up a term4   #fg4 ,the notions  
with which thought deals involve many   
subtle relations and require many nice  
modifications4  ,language has           
instruments1 more or less perfect1      
whereby such relations and modifications
 may be expressed4 ,but these subsidiary
 aids to expression do not form a notion
 which can either have something        
asserted of it or be asserted itself of 
something else4   #fh4 ,hence words are 

divided into three classes--    7#a7    
,categorematic2    7#b7                 
,syncategorematic2    7#c7              
,acategorematic4   #fi4 ,a              
,categorematic word is one which can be 
used by itself as a term4   #gj4 ,a     
,syncategorematic word is one which can 
help to form a term4   #ga4 ,an         
,acategorematic word is one which can   
neither form1 nor help to form1 a term  
,footnote3 ,comparatively few of the    
parts of speech are categorematic4      
,nouns1 whether substantive or          
adjective1 including of course pronouns 
and participles1 are so1 but only in    
their nominative cases1 except when an  
oblique case is so used as to be        
equivalent to an attributive4  ,verbs   
also are categorematic1 but only in     
three of their moods1 the ,indicative1  
the ,infinitive1 and the ,potential4    
,the ,imperative and ,optative moods    
clearly do not convey assertions at all1
 while the ,subjunctive can only figure 
as a subordinate member of some         

assertion4 ,we may notice1 too1 that the
 relative pronoun1 unlike the rest1 is  
necessarily syncategorematic1 for the   
same reason as the subjunctive mood4 ,of
 the remaining parts of speech the      
article1 adverb1 preposition1 and       
conjunction can never be anything but   
syncategorematic1 while the interjection
 is acategorematic1 like the vocative   
case of nouns and the imperative and    
optative moods of verbs1 which do not   
enter at all into the form of sentence  
known as the proposition44   #gb4       
,categorematic literally means          
'predicable4'  ',horse1' 'swift1'       
'galloping' are categorematic4 ,thus we 
can say1 ',the horse is swift1' or ',the
 horse is galloping4'  ,each of these   
words forms a term by itself1 but 'over'
 and 'swiftly' can only help to form a  
term1 as in the proposition1 ',the horse
 is galloping swiftly over the plain4'  
#gc4 ,a term then may be said to be a   
categorematic word or collection of     
words1 that is to say1 one which can be 

used by itself as a predicate4   #gd4   
,to entitle a word or collection of     
words to be called a term1 it is not    
necessary that it should be capable of  
standing by itself as a subject4 ,many  
terms which can be used as predicates   
are incapable of being used as subjects3
 but every term which can be used as a  
subject 7with the doubtful exception of 
proper names7 can be used also as a     
predicate4 ,the attributives 'swift' and
 'galloping' are terms1 quite as much as
 the subject 'horse1' but they cannot   
themselves be used as subjects4   #ge4  
,when an attributive appears to be used 
as a subject1 it is owing to a          
grammatical ellipse4 ,thus in ,latin we 
say ',boni sapientes sunt1' and in      
,english ',the good are wise1' because  
it is sufficiently declared by the      
inflexional form in the one case1 and by
 the usage of the language in the other1
 that men are signified4 ,it is an      
accident of language how far adjectives 
can be used as subjects4 ,they cease to 

be logical attributives the moment they 
are so used4   #gf4 ,there is a sense in
 which every word may become            
categorematic1 namely1 when it is used  
simply as a word1 to the neglect of its 
proper meaning4 ,thus we can            
say--',swiftly is an adverb4' ',swiftly'
 in this sense is really no more than   
the proper name for a particular word4  
,this sense is technically known as the 
'suppositio materialis' of a word4      
,,chapter ,,ii4  ,of the ,division of   
,things4    #gg4 ,before entering on the
 divisions of terms it is necessary to  
advert for a moment to a division of the
 things whereof they are names4   #gh4  
,by a 'thing' is meant simply an object 
of thought--whatever one can think      
about4   #gi4 ,things are either        
,substances or ,attributes4  ,attributes
 may be sub-divided into ,qualities and 
,relations4                      ,thing 
,substance                              
,attribute                              
,quality                    ,relation   

#hj4 ,a ,substance is a thing which can 
be conceived to exist by itself4 ,all   
bodies are material substances4 ,the    
soul1 as a thinking subject1 is an      
immaterial substance4   #ha4 ,an        
,attribute is a thing which depends for 
its existence upon a substance1 e4g4    
greenness1 hardness1 weight1 which      
cannot be conceived to exist apart from 
green1 hard1 and heavy substances4      
#hb4 ,a ,quality is an attribute which  
does not require more than one substance
 for its existence4 ,the attributes just
 mentioned are qualities4 ,there might  
be greenness1 hardness1 and weight1 if  
there were only one green1 hard and     
heavy substance in the universe4   #hc4 
,a ,relation is an attribute which      
requires two or more substances for its 
existence1 e4g4 nearness1 fatherhood1   
introduction4   #hd4 ,when we say that a
 substance can be conceived to exist by 
itself1 what is meant is that it can be 
conceived to exist independently of     
other substances4 ,we do not mean that  

substances can be conceived to exist    
independently of attributes1 nor yet out
 of relation to a mind perceiving them4 
,substances1 so far as we can know them1
 are only collections of attributes4    
,when therefore we say that substances  
can be conceived to exist by themselves1
 whereas attributes are dependent for   
their existence upon substances1 the    
real meaning of the assertion reduces   
itself to this1 that it is only certain 
collections of attributes which can be  
conceived to exist independently2       
whereas single attributes depend for    
their existence upon others4 ,the       
colour1 smoothness or solidity of a     
table cannot be conceived apart from the
 extension1 whereas the whole cluster of
 attributes which constitutes the table 
can be conceived to exist altogether    
independently of other 'such clusters4  
,we can imagine a table to exist1 if the
 whole material universe were           
annihilated1 and but one mind left to   
perceive it4 ,apart from mind1 however1 

we cannot imagine it3 since what we call
 the attributes of a material substance 
are no more than the various modes in   
which we find our minds affected4   #he4
 ,the above division of things belongs  
rather to the domain of metaphysics than
 of logic3 but it is the indispensable  
basis of the division of terms1 to which
 we now proceed4     ,,chapter ,,iii4   
,of the ,division of ,terms4    #hf4    
,the following scheme presents to the   
eye the chief divisions of terms4       
,term     ,division of terms according  
to their place in thought4              
,subject-,term       ,attributive       
according to the kind of thing          
signified4       ,abstract              
,concrete      according to ,quantity in
 ,extension4       ,singular            
,common      according to ,quality4     
,positive       ,privative              
,negative      according to number of   
meanings4       ,univocal               
,equivocal      according to number of  
things involved in the name4            

,absolute       ,relative      according
 to number of quantities4               
,connotative       ,non-connotative     
,subject-term and ,attributive4    #hg4 
,by a ,subject-term is meant any term   
which is capable of standing by itself  
as a subject1 e4g4 'ribbon1' 'horse4'   
#hh4 ,attributives can only be used as  
predicates1 not as subjects1 e4g4       
'cherry-coloured1' 'galloping4' ,these  
can only be used in conjunction with    
other words 7syncategorematically7 to   
make up a subject4 ,thus we can say ',a 
cherry-coloured ribbon is becoming1' or 
',a galloping horse is dangerous4'      
#hi4 ,attributives are contrivances of  
language whereby we indicate that a     
subject has a certain attribute4 ,thus1 
when we say ',this paper is white1' we  
indicate that the subject 'paper'       
possesses the attribute whiteness4      
,logic1 however1 also recognises as     
attributives terms which signify the    
non-possession of attributes4           
',not-white' is an attributive equally  

with 'white4'   #ij4 ,an ,attributive   
then may be defined as a term which     
signifies the possession1 or            
non-possession1 of an attribute by a    
subject4   #ia4 ,it must be carefully   
noticed that attributives are not names 
of attributes1 but names of the things  
which possess the attributes1 in virtue 
of our knowledge that they possess them4
 ,thus 'white' is the name of all the   
things which possess the attribute      
whiteness1 and 'virtuous' is a name2 not
 of the abstract quality1 virtue1       
itself1 but of the men and actions which
 possess it4 ,it is clear that a term   
can only properly be said to be a name  
of those things whereof it can be       
predicated4 ,now1 we cannot intelligibly
 predicate an attributive of the        
abstract quality1 or qualities1 the     
possession of which it implies4 ,we     
cannot1 for instance1 predicate the term
 'learned' of the abstract quality of   
learning3 but we may predicate it of the
 individuals1 ,varro and ,vergil4       

,attributives1 then1 are to be regarded 
as names1 not of the attributes which   
they imply1 but of the things in which  
those attributes are found4   #ib4      
,attributives1 however1 are names of    
things in a less direct way than that in
 which subject-terms may be the names of
 the same things4 ,attributives are     
names of things only in predication1    
whereas subject-terms are names of      
things in or out of predication4 ,the   
terms 'horse' and ',bucephalus' are     
names of certain things1 in this case   
animals1 whether we make any statement  
about them or not3 but the terms 'swift'
 and 'fiery' only become names of the   
same things in virtue of being          
predicable of them4 ,when we say        
',horses are swift' or ',bucephalus was 
fiery1' the terms 'swift' and 'fiery'   
become names respectively of the same   
things as 'horse' and ',bucephalus4'    
,this function of attributives as names 
in a secondary sense is exactly         
expressed by the grammatical term 'noun 

adjective4' ,an attributive is not      
directly the name of anything4 ,it is a 
name added on in virtue of the          
possession by a given thing of a certain
 attribute1 or1 in some cases1 the      
non-possession4   #ic4 ,although        
attributives cannot be used as subjects1
 there is nothing to prevent a          
subject-term from being used as a       
predicate1 and so assuming for the time 
being the functions of an attributive4  
,when we say ',socrates was a man1' we  
convey to the mind the idea of the same 
attributes which are implied by the     
attributive 'human4'  ,but those terms  
only are called attributives which can  
never be used except as predicates4     
#id4 ,this division into ,subject-terms 
and ,attributives may be regarded as a  
division of terms according to their    
place in thought4 ,attributives1 as we  
have seen1 are essentially predicates1  
and can only be thought of in relation  
to the subject1 whereas the subject is  
thought of for its own sake4            

,abstract and ,concrete ,terms4    #ie4 
,an ,abstract ,term is the name of an   
attribute1 e4g4 whiteness ,footnote3    
,since things cannot be spoken of except
 by their names1 there is a constantly  
recurring source of confusion between   
the thing itself and the name of it4    
,take for instance 'whiteness4' ,the    
attribute whiteness is a thing1 the word
 'whiteness' is a term41 multiplication1
 act1 purpose1 explosion4   #if4 ,a     
,concrete ,term is the name of a        
substance1 e4g4 a man1 this chair1 the  
soul1 ,god4   #ig4 ,abstract terms are  
so called as being arrived at by a      
process of ,abstraction4 ,what is meant 
by ,abstraction will be clear from a    
single instance4 ,the mind1 in          
contemplating a number of substances1   
may draw off1 or abstract1 its attention
 from all their other characteristics1  
and fix it only on some point1 or       
points1 which they have in common4      
,thus1 in contemplating a number of     
three-cornered objects1 we may draw away

 our attention from all their other     
qualities1 and fix it exclusively upon  
their three-corneredness1 thus          
constituting the abstract notion of     
'triangle4' ,abstraction may be         
performed equally well in the case of a 
single object3 but the mind would not   
originally have known on what points to 
fix its attention except by a comparison
 of individuals4   #ih4 ,abstraction too
 may be performed upon attributes as    
well as substances4 ,thus1 having by    
abstraction already arrived at the      
notion of triangle1 square1 and so on1  
we may fix our attention upon what these
 have in common1 and so rise to the     
higher abstraction of 'figure4' ,as     
thought becomes more complex1 we may    
have abstraction on abstraction and     
attributes of attributes4 ,but1 however 
many steps may intervene1 attributes may
 always be traced back to substances at 
last4 ,for attributes of attributes can 
mean at bottom nothing but the          
co-existence of attributes in1 or in    

connection with1 the same substances4   
#ii4 ,we have said that abstract terms  
are so called1 as being arrived at by   
abstraction3 but it must not be inferred
 from this statement that all terms     
which are arrived at by abstraction are 
abstract4 ,if this were so1 all names   
would be abstract except proper names of
 individual substances4  ,all common    
terms1 including attributives1 are      
arrived at by abstraction1 but they are 
not therefore abstract terms4 ,those    
terms only are called abstract1 which   
cannot be applied to substances at all4 
,the terms 'man' and 'human' are names  
of the same substance of which ,socrates
 is a name4 ,humanity is a name only of 
certain attributes of that substance1   
namely those which are shared by others4
 ,all names of concrete things then are 
concrete1 whether they denote them      
individually or according to classes1   
and whether directly and in themselves1 
or indirectly1 as possessing some given 
attribute4   #ajj4 ,by a 'concrete      

thing' is meant an individual ,substance
 conceived of with all its attributes   
about it4  ,the term is not confined to 
material substances4 ,a spirit conceived
 of under personal attributes is as     
concrete as plum-pudding4   #aja4 ,since
 things are divided exhaustively into   
substances and attributes1 it follows   
that any term which is not the name of a
 thing capable of being conceived to    
exist by itself1 must be an abstract    
term4 ,individual substances can alone  
be conceived to exist by themselves3 all
 their qualities1 actions1 passions1 and
 inter-relations1 all their states1 and 
all events with regard to them1         
presuppose the existence of these       
individual substances4 ,all names       
therefore of such things as those just  
enumerated are abstract terms4 ,the term
 'action1' for instance1 is an abstract 
term4 ,for how could there be action    
without an agent8 ,the term 'act' also  
is equally abstract for the same reason4
 ,the difference between 'action' and   

'act' is not the difference between     
abstract and concrete1 but the          
difference between the name of a process
 and the name of the corresponding      
product4 ,unless acts can be conceived  
to exist without agents they are as     
abstract as the action from which they  
result4   #ajb4 ,since every term must  
be either abstract or concrete1 it may  
be asked--,are attributives abstract or 
concrete8 ,the answer of course depends 
upon whether they are names of          
substances or names of attributes4 ,but 
attributives1 it must be remembered1 are
 never directly names of anything1 in   
the way that subject-terms are2 they are
 only names of things in virtue of being
 predicated of them4 ,whether an        
attributive is abstract or concrete1    
depends on the nature of the subject of 
which it is asserted or denied4 ,when we
 say ',this man is noble1' the term     
'noble' is concrete1 as being the name  
of a substance3 but when we say ',this  
act is noble1' the term 'noble' is      

abstract1 as being the name of an       
attribute4   #ajc4 ,the division of     
terms into ,abstract and ,concrete is   
based upon the kind of thing signified4 
,it involves no reference to actual     
existence4 ,there are imaginary as well 
as real substances4 ,logically a centaur
 is as much a substance as a horse4     
,terms4    #ajd4 ,a ,singular ,term is a
 name which can be applied1 in the same 
sense1 to one thing only1 e4g4 ',john1' 
',paris1' 'the capital of ,france1'     
'this pen4'   #aje4 ,a ,common ,term is 
a name which can be applied1 in the same
 sense1 to a class of things1 e4g4      
'man1' 'metropolis1' 'pen4'  ,in order  
that a term may be applied in the same  
sense to a number of things1 it is      
evident that it must indicate attributes
 which are common to all of them4 ,the  
term ',john' is applicable to a number  
of things1 but not in the same sense1 as
 it does not indicate attributes4       
#ajf4 ,common terms are formed1 as we   
have seen already 7 #ii71 by            

abstraction1 i4 e4 by withdrawing the   
attention from the attributes in which  
individuals differ1 and concentrating it
 upon those which they have in common4  
#ajg4 ,a class need not necessarily     
consist of more than two things4 ,if the
 sun and moon were the only heavenly    
bodies in the universe1 the word        
'heavenly body' would still be a common 
term1 as indicating the attributes which
 are possessed alike by each4   #ajh4   
,this being so1 it follows that the     
division of terms into singular and     
common is as exhaustive as the preceding
 ones1 since a singular term is the name
 of one thing and a common term of more 
than one4 ,it is indifferent whether the
 thing in question be a substance or an 
attribute2 nor does it matter how       
complex it may be1 so long as it is     
regarded by the mind as one4   #aji4    
,since every term must thus be either   
singular or common1 the members of the  
preceding divisions must find their     
place under one or both heads of this   

one4  ,subject-terms may plainly fall   
under either head of singular or common3
 but attributives are essentially common
 terms4  ,such names as 'green1'        
'gentle1' 'incongruous' are applicable1 
strictly in the same sense1 to all the  
things which possess the attributes     
which they imply4   #aaj4 ,are abstract 
terms then1 it may be asked1 singular or
 common8 ,to this question we           
reply--,that depends upon how they are  
used4 ,the term 'virtue1' for instance1 
in one sense1 namely1 as signifying     
moral excellence in general1 without    
distinction of kind1 is strictly a      
singular term1 as being the name of one 
attribute3 but as applied to different  
varieties of moral excellence--justice1 
generosity1 gentleness and so on--it is 
a common term1 as being a name which is 
applicable1 in the same sense1 to a     
class of attributes4 ,similarly the term
 'colour1' in a certain sense1 signifies
 one unvarying attribute possessed by   
bodies1 namely1 the power of affecting  

the eye1 and in this sense it is a      
singular term3 but as applied to the    
various ways in which the eye may be    
affected1 it is evidently a common term1
 being equally applicable to red1 blue1 
green1 and every other colour4 ,as soon 
as we begin to abstract from attributes1
 the higher notion becomes a common term
 in reference to the lower4 ,by a       
'higher notion' is meant one which is   
formed by a further process of          
abstraction4 ,the terms 'red1' 'blue1'  
'green1' etc41 are arrived at by        
abstraction from physical objects2      
'colour' is arrived at by abstraction   
from them1 and contains nothing1 but    
what is common to all4 ,it therefore    
applies in the same sense to each1 and  
is a common term in relation to them4   
#aaa4 ,a practical test as to whether an
 abstract term1 in any given case1 is   
being used as a singular or common term1
 is to try whether the indefinite       
article or the sign of the plural can be
 attached to it4 ,the term 'number1' as 

the name of a single attribute of       
things1 admits of neither of these      
adjuncts3 but to talk of 'a number' or  
'the numbers1 two1 three1 four1' etc41  
at once marks it as a common term4      
,similarly the term 'unity' denotes a   
single attribute1 admitting of no shades
 of distinction3 but when a writer      
begins to speak of 'the unities' he is  
evidently using the word for a class of 
things of some kind or other1 namely1   
certain dramatical proprieties of       
composition4    ,proper ,names and      
,designations4    #aab4 ,singular terms 
may be subdivided into ,proper ,names   
and ,designations4   #aac4 ,a ,proper   
,name is a permanent singular term      
applicable to a thing in itself2 a      
,designation is a singular term devised 
for the occasion1 or applicable to a    
thing only in so far as it possesses    
some attribute4   #aad4 ',homer' is a   
proper name2 'this man1' 'the author of 
the ,iliad' are designations4   #aae4   
,the number of things1 it is clear1 is  

infinite4  ,for1 granting that the      
physical universe consists of a definite
 number of atoms--neither one more nor  
one less--still we are far from having  
exhausted the possible number of things4
 ,all the manifold material objects1    
which are made up by the various        
combinations of these atoms1 constitute 
separate objects of thought1 or things1 
and the mind has further an indefinite  
power of conjoining and dividing these  
objects1 so as to furnish itself with   
materials of thought1 and also of fixing
 its attention by abstraction upon      
attributes1 so as to regard them as     
things1 apart from the substances to    
which they belong4   #aaf4 ,this being  
so1 it is only a very small number of   
things1 which are constantly obtruding  
themselves upon the mind1 that have     
singular terms permanently set apart to 
denote them4 ,human beings1 some        
domestic animals1 and divisions of time 
and place1 have proper names assigned to
 them in most languages1 e4g4 ',john1'  

',mary1' ',grip1' ',january1' ',easter1'
 ',belgium1' ',brussels1' 'the ,thames1'
 ',ben-,nevis4' ,besides these1 all     
abstract terms1 when used without       
reference to lower notions1 are of the  
nature of proper names1 being           
permanently set apart to denote certain 
special attributes1 e4g4 'benevolence1' 
'veracity1' 'imagination1'              
'indigestibility1 'retrenchment4'       
#aag4 ,but the needs of language often  
require a singular term to denote some  
thing which has not had a proper name   
assigned to it4 ,this is effected by    
taking a common term1 and so limiting it
 as to make it applicable1 under the    
given circumstances1 to one thing only4 
,such a limitation may be effected in   
,english by prefixing a demonstrative or
 the definite article1 or by appending a
 description1 e4g4 'this pen1' 'the     
sofa1' 'the last rose of summer4' ,when 
a proper name is unknown1 or for some   
reason1 unavailable1 recourse may be had
 to a designation1 e4g4 'the honourable 

member who spoke last but one4'         
,collective ,terms4    #aah4 ,the       
division of terms into singular and     
common being1 like those which have     
preceded it1 fundamental and exhaustive1
 there is evidently no room in it for a 
third class of ,collective ,terms4 ,nor 
is there any distinct class of terms to 
which that name can be given4 ,the same 
term may be used collectively or        
distributively in different relations4  
,thus the term 'library1' when used of  
the books which compose a library1 is   
collective2 when used of various        
collections of books1 as the ,bodleian1 
,queen's library1 and so on1 it is      
distributive1 which1 in this case1 is   
the same thing as being a common term4  
#aai1 ,the distinction between the      
collective and distributive use of a    
term is of importance1 because the      
confusion of the two is a favourite     
source of fallacy4  ,when it is said    
',the plays of ,shakspeare cannot be    
read in a day1' the proposition meets   

with a very different measure of        
acceptance according as its subject is  
understood collectively or              
distributively4 ,the word 'all' is      
perfectly ambiguous in this respect4 ,it
 may mean all together or each          
separately--two senses which are        
distinguished in ,latin by 'totus' or   
'cunctus1' for the collective1 and      
'omnis' for the distributive use4       
#abj4 ,what is usually meant however    
when people speak of a collective term  
is a particular kind of singular term4  
#aba4 ,from this point of view singular 
terms may be subdivided into ,individual
 and ,collective1 by an ,individual     
,term being meant the name of one       
object1 by a ,collective ,term the name 
of several considered as one4 ',this    
key' is an individual term2 'my bunch of
 keys' is a collective term4   #abb4 ,a 
collective term is quite as much the    
name of one thing as an individual term 
is1 though the thing in question happens
 to be a group4 ,a group is one thing1  

if we choose to think of it as one4 ,for
 the mind1 as we have already seen1 has 
an unlimited power of forming its own   
things1 or objects of thought4 ,thus a  
particular peak in a mountain chain is  
as much one thing as the chain itself1  
though1 physically speaking1 it is      
inseparable from it1 just as the chain  
itself is inseparable from the earth's  
surface4  ,in the same way a necklace is
 as much one thing as the individual    
beads which compose it4   #abc4 ,we have
 just seen that a collective term is the
 name of a group regarded as one thing3 
but every term which is the name of such
 a group is not necessarily a collective
 term4 ',london1' for instance1 is the  
name of a group of objects considered as
 one thing4 ,but ',london' is not a     
collective term1 whereas 'flock1'       
'regiment1' and 'senate' are4 ,wherein  
then lies the difference8 ,it lies in   
this--that flock1 regiment and senate   
are groups composed of objects which    
are1 to a certain extent1 similar1      

whereas ,london is a group made up of   
the most dissimilar objects--streets and
 squares and squalid slums1 fine        
carriages and dirty faces1 and so on4   
,in the case of a true collective term  
all the members of the group will come  
under some one common name4 ,thus all   
the members of the group1 flock of      
sheep1 come under the common name       
'sheep1' all the members of the group   
'regiment' under the common name1       
'soldier1' and so on4   #abd4 ,the      
subdivision of singular terms into      
individual and collective need not be   
confined to the names of concrete       
things4 ,an abstract term like          
'scarlet1' which is the name of one     
definite attribute1 may be reckoned     
'individual1' while a term like 'human  
nature1' which is the name of a whole   
group of attributes1 would more fitly be
 regarded as collective4   #abf4 ,the   
main division of terms1 which we have   
been discussing1 into singular and      
collective1 is based upon their         

,quantity in ,extension4 ,this phrase   
will be explained presently4   #abf4 ,we
 come now to a threefold division of    
terms into ,positive1 ,privative and    
,negative4 ,it is based upon an implied 
two-fold division into positive and     
non-positive1 the latter member being   
subdivided into ,privative and          
,negative4                     ,term    
,positive                               
,non-,positive                          
,privative                   ,negative  
,if this division be extended1 as it    
sometimes is1 to terms in general1 a    
positive term must be taken to mean only
 the definite1 or comparatively         
definite1 member of an exhaustive       
division in accordance with the law of  
excluded middle 7 #be74 ,thus           
',socrates' and 'man' are positive1 as  
opposed to 'not-,socrates' and          
'not-man4'   #abg4 ,the chief value of  
the division1 however1 and especially of
 the distinction drawn between privative
 and negative terms1 is in relation to  

attributives4  ,from this point of view 
we may define the three classes of terms
 as follows3  ,a ,positive ,term        
signifies the presence of an attribute1 
e4g43 'wise1' 'full4'  ,a ,negative     
,term signifies merely the absence of an
 attribute1 e4g4 'not-wise1' 'not-full4'
  ,a ,privative ,term signifies the     
absence of an attribute in a subject    
capable of possessing it1 e4g4 'unwise1'
 'empty'4 ,footnote3 ,a privative term  
is usually defined to mean one which    
signifies the absence of an attribute   
where it was once possessed1 or might   
have been expected to be present1 e4g4  
'blind4' ,the utility of the slight     
extension of meaning here assigned to   
the expression will1 it is hoped1 prove 
its justification4   #abh4 ,thus a      
privative term stands midway in meaning 
between the other two1 being partly     
positive and partly negative--negative  
in so far as it indicates the absence of
 a certain attribute1 positive in so far
 as it implies that the thing which is  

declared to lack that attribute is of   
such a nature as to be capable of       
possessing it4 ,a purely negative term  
conveys to the mind no positive         
information at all about the nature of  
the thing of which it is predicated1 but
 leaves us to seek for it among the     
universe of things which fail to exhibit
 a given attribute4  ,a privative term1 
on the other hand1 restricts us within a
 definite sphere4 ,the term 'empty'     
restricts us within the sphere of things
 which are capable of fulness1 that is1 
if the term be taken in its literal     
sense1 things which possess extension in
 three dimensions4   #abi4 ,a positive  
and a negative term1 which have the same
 matter1 must exhaust the universe      
between them1 e4g4 'white' and          
'not-white1' since1 according to the law
 of excluded middle1 everything must be 
either one or the other4 ,to say1       
however1 that a thing is 'not-white' is 
merely to say that the term 'white' is  
inapplicable to it4 ',not-white' may be 

predicated of things which do not       
possess extension as well as of those   
which do4 ,such a pair of terms as      
'white' and 'not-white1' in their       
relation to one another1 are called     
,contradictories4   #acj4 ,contrary     
terms must be distinguished from        
contradictory4 ,contrary terms are those
 which are most opposed under the same  
head4 ,thus 'white' and 'black' are     
contrary terms1 being the most opposed  
under the same head of colour4          
',virtuous' and 'vicious' again are     
contraries1 being the most opposed under
 the same head of moral quality4   #aca4
 ,a positive and a privative term in the
 same matter will always be contraries1 
e4g4 'wise' and 'unwise1' 'safe' and    
'unsafe'3 but contraries do not always  
assume the shape of positive and        
privative terms1 but may both be        
positive in form1 e4g4 'wise' and       
'foolish1' 'safe' and 'dangerous4'      
#acb4 ,words which are positive in form 
are often privative in meaning1 and vice

 vers4 ,this is the case1 for instance1 
with the word 'safe1' which connotes    
nothing more than the absence of danger4
 ,we talk of a thing involving 'positive
 danger' and of its being 'positively   
unsafe' to do so and so4 ',unhappy1' on 
the other hand1 signifies the presence  
of actual misery4 ,similarly in ,latin  
'inutilis' signifies not merely that    
there is no benefit to be derived from a
 thing1 but that it is positively       
injurious4 ,all such questions1 however1
 are for the grammarian or              
lexicographer1 and not for the logician4
 ,for the latter it is sufficient to    
know that corresponding to every term   
which signifies the presence of some    
attribute there may be imagined another 
which indicates the absence of the same 
attribute1 where it might be possessed1 
and a third which indicates its absence1
 whether it might be possessed or not4  
#acc4 ,negative terms proper are formed 
by the prefix 'not-' or 'non-1' and are 
mere figments of logic4 ,we do not in   

practice require to speak of the whole  
universe of objects minus those which   
possess a given attribute or collection 
of attributes4 ,we have often occasion  
to speak of things which might be wise  
and are not1 but seldom1 if ever1 of all
 things other than wise4   #acd4 ,every 
privative attributive has1 or may have1 
a corresponding abstract term1 and the  
same is the case with negatives3 for the
 absence of an attribute1 is itself an  
attribute4 ,corresponding to 'empty1'   
there is 'emptiness'2 corresponding to  
'not-full' there may be imagined the    
term 'not-fulness4'   #ace4 ,the        
contrary of a given term always involves
 the contradictory1 but it involves     
positive elements as well4  ,thus       
'black' is 'not-white1' but it is       
something more besides4 ,terms which1   
without being directly contrary1 involve
 a latent contradiction1 are called     
,repugnant1 e4g4  'red' and 'blue4' ,all
 terms whatever which signify attributes
 that exclude one another may be called 

,incompatible4   #acf4 ,the preceding   
division is based on what is known as   
the ,quality of terms1 a positive term  
being said to differ in quality from a  
non-positive one4    ,univocal and      
,equivocal ,terms4    #acg4 ,a term is  
said to be ,univocal1 when it has one   
and the same meaning wherever it occurs4
 ,a term which has more than one meaning
 is called ,equivocal4 ',jam-pot1'      
'hydrogen' are examples of univocal     
terms2 'pipe' and 'suit' of equivocal4  
#ach4 ,this division does not properly  
come within the scope of logic1 since it
 is a question of language1 not of      
thought4 ,from the logician's point of  
view an equivocal term is two or more   
different terms1 for the definition in  
each sense would be different4   #aci4  
,sometimes a third member is added to   
the same division under the head of     
,analogous ,terms4 ,the word 'sweet1'   
for instance1 is applied by analogy to  
things so different in their own nature 
as a lump of sugar1 a young lady1 a     

tune1 a poem1 and so on4 ,again1 because
 the head is the highest part of man1   
the highest part of a stream is called  
by analogy 'the head4' ,it is plainly   
inappropriate to make a separate class  
of analogous terms4  ,rather1 terms     
become equivocal by being extended by   
analogy from one thing to another4      
,absolute and ,relative ,terms4    #adj4
 ,an ,absolute term is a name given to a
 thing without reference to anything    
else4   #ada4 ,a ,relative term is a    
name given to a thing with direct       
reference to some other thing4   #adb4  
',hodge' and 'man' are absolute terms4  
',husband' 'father1' 'shepherd' are     
relative terms4 ',husband' conveys a    
direct reference to 'wife1' 'father' to 
',child1' 'shepherd' to 'sheep4' ,given 
one term of a relation1 the other is    
called the correlative1 e4g4 'subject'  
is the correlative of 'ruler1' and      
conversely 'ruler' of 'subject4' ,the   
two terms are also spoken of as a pair  
of correlatives4   #adc4 ,the           

distinction between relative and        
absolute applies to attributives as well
 as subject-terms4 ',greater1' 'near1   
'like1' are instances of attributives   
which everyone would recognise as       
relative4   #add4 ,a relation1 it will  
be remembered1 is a kind of attribute1  
differing from a quality in that it     
necessarily involves more substances    
than one4 ,every relation is at bottom a
 fact1 or series of facts1 in which two 
or more substances play a part4 ,a      
relative term connotes this fact or     
facts from the point of view of one of  
the substances1 its correlative from    
that of the other4 ,thus 'ruler' and    
'subject' imply the same set of facts1  
looked at from opposite points of view4 
,the series of facts itself1 regarded   
from either side1 is denoted by the     
corresponding abstract terms1 'rule 'and
 'subjection4'   #ade4 ,it is a nice    
question whether the abstract names of  
relations should themselves be          
considered relative terms4              

,difficulties will perhaps be avoided by
 confining the expression 'relative     
term' to names of concrete things4      
',absolute1' it must be remembered1 is a
 mere negative of 'relative1' and covers
 everything to which the definition of  
the latter does not strictly apply4 ,now
 it can hardly be said that 'rule' is a 
name given to a certain abstract thing  
with direct reference to some other     
thing1 namely1 subjection4 ,rather      
'rule' and 'subjection' are two names   
for identically the same series of      
facts1 according to the side from which 
we look at them4 ',ruler' and 'subject1'
 on the other hand1 are names of two    
distinct substances1 but each involving 
a reference to the other4   #adf4 ,this 
division then may be said to be based on
 the number of things involved in the   
name4    ,connotative and               
,non-,connotative ,terms4    #adg4      
,before explaining this division1 it is 
necessary to treat of what is called the
 ,quantity of ,terms4    ,quantity of   

,terms4    #adh4 ,a term is possessed of
 quantity in two ways--    7#a7 ,in     
,extension2    7#b7 ,in ,intension4     
#adi4 ,the ,extension of a term is the  
number of things to which it applies4   
#aej4 ,the ,intension of a term is the  
number of attributes which it implies4  
#aea4 ,it will simplify matters to bear 
in mind that the intension of a term is 
the same thing as its meaning4 ,to take 
an example1 the term 'man' applies to   
certain things1 namely1 all the members 
of the human race that have been1 are1  
or ever will be3 this is its quantity in
 extension4 ,but the term 'man' has also
 a certain meaning1 and implies certain 
attributes--rationality1 animality1 and 
a definite bodily shape3 the sum of     
these attributes constitutes its        
quantity in intension4   #aeb4 ,the     
distinction between the two kinds of    
quantity possessed by a term is also    
conveyed by a variety of expressions    
which are here appended4  ,extension    
breadth  compass  application           

denotation4  ,intension  depth          
comprehension  implication  connotation4
  ,of these various expressions1        
'application' and 'implication' have the
 advantage of most clearly conveying    
their own meaning4 ',extension' and     
'intension1' however1 are more usual2   
and neither 'implication' nor           
'connotation' is quite exact as a       
synonym for 'intension4' 7 #afd47       
#aec4 ,we now return to the division of 
terms into connotative and              
non-connotative4   #aed4 ,a term is said
 to connote attributes1 when it implies 
certain attributes at the same time that
 it applies to certain things distinct  
therefrom4 ,footnote3 ,originally       
'connotative' was used in the same sense
 in which we have used 'attributive1'   
for a word which directly signifies the 
presence of an attribute and indirectly 
applies to a subject4 ,in this1 its     
original sense1 it was the subject which
 was said to be connoted1 and not the   
attribute4   #aee4 ,a term which        

possesses both extension and intension1 
distinct from one another1 is           
connotative4   #aef4 ,a term which      
possesses no intension 7if that be      
possible7 or in which extension and     
intension coincide is non-connotative4  
#aeg4 ,the subject-term1 'man1' and its 
corresponding attributive1 'human1' have
 both extension and intension1 distinct 
from one another4 ,they are therefore   
connotative4 ,but the abstract term1    
'humanity1' denotes the very collection 
of attributes1 which was before connoted
 by the concrete terms1 'man' and       
'human4' ,in this case1 therefore1      
extension and intension coincide1 and   
the term is non-connotative4   #aeh4    
,the above remark must be understood to 
be limited to abstract terms in their   
singular sense4 ,when employed as common
 terms1 abstract terms possess both     
extension and intension distinct from   
one another4 ,thus the term 'colour'    
applies to red1 blue1 and yellow1 and at
 the same time implies 7i4e4 connotes71 

the power of affecting the eye4   #aei4 
,since all terms are names of things1   
whether substances or attributes1 it is 
clear that all terms must possess       
extension1 though the extension of      
singular terms is the narrowest         
possible1 as being confined to one      
thing4   #afj4 ,are there then any terms
 which possess no intension8 ,to ask    
this1 is to ask--,are there any terms   
which have absolutely no meaning8 ,it is
 often said that proper names are devoid
 of meaning1 and the remark is1 in a    
certain sense1 true4 ,when we call a    
being by the name 'man1' we do so       
because that being possesses human      
attributes1 but when we call the same   
being by the name1 ',john1' we do not   
mean to indicate the presence of any    
,johannine attributes4 ,we simply wish  
to distinguish that being1 in thought   
and language1 from other beings of the  
same kind4 ,roughly speaking1 therefore1
 proper names are devoid of meaning or  
intension4 ,but no name can be entirely 

devoid of meaning4 ,for1 even setting   
aside the fact1 which is not universally
 true1 that proper names indicate the   
sex of the owner1 the mere act of giving
 a name to a thing implies at least that
 the thing exists1 whether in fact or   
thought2 it implies what we may call    
'thinghood'3 so that every term must    
carry with it some small amount of      
intension4   #afa4 ,from another point  
of view1 however1 proper names possess  
more intension than any other terms4    
,for when we know a person1 his name    
calls up to our minds all the individual
 attributes with which we are familiar1 
and these must be far more numerous than
 the attributes which are conveyed by   
any common term which can be applied to 
him4 ,thus the name ',john' means more  
to a person who knows him than          
'attorney1' 'conservative1' 'scamp1' of 
'vestry-man1' or any other term which   
may happen to apply to him4 ,this1      
however1 is the acquired intension of a 
term1 and must be distinguished from the

 original intension4 ,the name ',john'  
was never meant to indicate the         
attributes which its owner has1 as a    
matter of fact1 developed4 ,he would be 
,john all the same1 if he were none of  
these4   #afb4 ,hitherto we have been   
speaking only of christening-names1 but 
it is evident that family names have a  
certain amount of connotation from the  
first4 ,for when we dub ,john with the  
additional appellation of ,smith1 we do 
not give this second name as a mere     
individual mark1 but intend thereby to  
indicate a relationship to other        
persons4  ,the amount of connotation    
that can be conveyed by proper names is 
very noticeable in the ,latin language4 
,let us take for an example the full    
name of a distinguished ,roman--,publius
 ,cornelius ,scipio milianus ,africanus 
minor4 ,here it is only the prnomen1    
,publius1 that can be said to be a mere 
individual mark1 and even this          
distinctly indicates the sex of the     
owner4 ,the nomen proper1 ,cornelius1   

declares the wearer of it to belong to  
the illustrious gens ,cornelia4 ,the    
cognomen1 ,scipio1 further specifies him
 as a member of a distinguished family  
in that gens4 ,the agnomen adoptivum    
indicates his transference by adoption  
from one gens to another4  ,the second  
agnomen recalls the fact of his victory 
over the ,carthaginians1 while the      
addition of the word 'minor'            
distinguishes him from the former wearer
 of the same title4 ,the name1 instead  
of being devoid of meaning1 is a chapter
 of history in itself4 ,homeric         
epithets1 such as ',the                 
,cloud-compeller1' ',the ,earth-shaker' 
are instances of intensive proper names4
 ,many of our own family names are      
obviously connotative in their origin1  
implying either some personal           
peculiarity1 e4g4 ,armstrong1           
,cruikshank1 ,courteney2 or the         
employment1 trade or calling of the     
original bearer of the name1 ,smith1    
,carpenter1 ,baker1 ,clark1 ,leach1     

,archer1 and so on2 or else his abode1  
domain or nationality1 as ,de ,caen1 ,de
 ,montmorency1 ,french1 ,langley2 or    
simply the fact of descent from some    
presumably more noteworthy parent1 as   
,jackson1 ,thomson1 ,fitzgerald1        
,o',connor1 ,macdonald1 ,apjohn1 ,price1
 ,davids1 etc4 ,the question1 however1  
whether a term is connotative or not1   
has to be decided1 not by its origin1   
but by its use4 ,we have seen that there
 are some proper names which1 in a rough
 sense1 may be said to possess no       
intension4   #afc4 ,the other kind of   
singular terms1 namely1 designations 7  
#aac7 are obviously connotative4 ,we    
cannot employ even the simplest of them 
without conveying more or less          
information about the qualities of the  
thing which they are used to denote4    
,when1 for instance1 we say 'this       
table1' 'this book1' we indicate the    
proximity to the speaker of the object  
in question4 ,other designations have a 
higher degree of intension1 as when we  

say 'the present prime minister of      
,england1' 'the honourable member who   
brought forward this motion to-night4'  
,such terms have a good deal of         
significance in themselves1 apart from  
any knowledge we may happen to possess  
of the individuals they denote4   #afd4 
,we have seen that1 speaking quite      
strictly1 there are no terms which are  
non-connotative3 but1 for practical     
purposes1 we may apply the expression to
 proper names1 on the ground that they  
possess no intension1 and to singular   
abstract terms on the ground that their 
extension and intension coincide4 ,in   
the latter case it is indifferent       
whether we call the quantity extension  
or intension4 ,only we cannot call it   
'connotation1' because that implies two 
quantities distinct from one another4 ,a
 term must already denote a subject     
before it can be said to connote its    
attributes4   #afe4 ,the division of    
terms into connotative and              
non-connotative is based on their       

possession of one quantity or two4      
,,chapter ,,iv4  ,of the ,law of        
,inverse ,variation of ,extension and   
,intension4    #aff4 ,in a series of    
terms which fall under one another1 as  
the extension decreases1 the intension  
increases1 and vice vers4 ,take for     
instance the following series--         
,thing        ,substance        ,matter 
,organism        ,animal                
,vertebrate        ,mammal              
,ruminant        ,sheep        ,this    
sheep4  ,here the term at the top       
possesses the widest possible extension1
 since it applies to everything4 ,but at
 the same time it possesses the least   
possible amount of intension1 implying  
nothing more than mere existence1       
whether in fact or thought4 ,on the     
other hand1 the term at the bottom      
possesses the greatest amount of        
intension1 since it implies all the     
attributes of1 an individual superadded 
to those of the class to which it       
belongs3 but its extension is the       

narrowest possible1 being limited to one
 thing4   #afg4 ,at each step in the    
descent from the term at the top1 which 
is called the ',summum genus1' to the   
individual1 we decrease the extension by
 increasing the intension4  ,thus by    
adding on to the bare notion of a thing 
the idea of independent existence1 we   
descend to the term 'substance1' ,this  
process is known as ,determination1 or  
,specialisation4   #afh4 ,again1 by     
withdrawing our attention from the      
individual characteristics of a         
particular sheep1 and fixing it upon    
those which are common to it with other 
animals of the same kind1 we arrive at  
the common term1 'sheep4'  ,here we have
 increased the extension by decreasing  
the intension4 ,this process is known as
 ,generalisation4   #afi4               
,generalisation implies abstraction1 but
 we may have abstraction without        
generalisation4   #agj4 ,the following  
example is useful1 as illustrating to   
the eye how a decrease of extension is  

accompanied by an increase of intension4
 ,at each step of the descent here we   
visibly tack on a fresh attribute4      
,footnote3 ,this example is borrowed    
from ,professor ,jevons4    ,ship       
,steam-ship        ,screw steam-ship    
,iron screw steam-ship        ,british  
iron screw steam-ship4  ,could we see   
the classes denoted by the names the    
pyramid would be exactly inverted4      
#aga4 ,the law of inverse variation of  
extension and intension must of course  
be confined to the inter-relations of a 
series of terms of which each can be    
predicated of the other until we arrive 
at the bottom of the scale4 ,it is not  
meant to apply to the extension and     
intension of the same term4 ,the        
increase of population does not add to  
the meaning of 'baby4'       ,,part     
,,ii4--,,of ,,propositions4             
,,chapter ,i4  ,of the ,proposition as  
distinguished from ,other ,sentences4   
#agb4 ,as in considering the term1 we   
found occasion to distinguish it from   

words generally1 so now1 in considering 
the proposition1 it will be well to     
begin by distinguishing it from other   
sentences4   #agc4 ,every proposition is
 a sentence1 but every sentence is not a
 proposition4   #agd4 ,the field of     
logic is far from being conterminous    
with that of language4 ,language is the 
mirror of man's whole nature1 whereas   
logic deals with language only so far as
 it gives clothing to the products of   
thought in the narrow sense which we    
have assigned to that term4 ,language   
has materials of every sort lying strewn
 about1 among which the logician has to 
seek for his proper implements4   #age4 
,sentences may be employed for a variety
 of purposes--    7#a7 ,to ask a        
question2    7#b7 ,to give an order2    
7#c7 ,to express a feeling2    7#d7 ,to 
make a statement4  ,these various uses  
give rise respectively to    7#a7 ,the  
,interrogative ,sentence2    7#b7 ,the  
,imperative ,sentence2    7#c7 ,the     
,exclamatory ,sentence2    7#d7 ,the    

,enunciative ,sentence2 ,indicative     
,potential4  ,it is with the last of    
these only that logic is concerned4     
#agf4 ,the proposition1 therefore1      
corresponds to the ,indicative and      
,potential1 or ,conditional1 sentences  
of grammar4 ,for it must be borne in    
mind that logic recognises no difference
 between a statement of fact and a      
supposition4 ',it may rain to-morrow' is
 as much a proposition as ',it is       
raining now4'   #agg4 ,leaving the      
grammatical aspect of the proposition1  
we must now consider it from the purely 
logical point of view4   #agh4 ,a       
proposition is a judgement expressed in 
words2 and a judgement is a direct      
comparison between two concepts4   #agi4
 ,the same thing may be expressed more  
briefly by saying that a proposition is 
a direct comparison between two terms4  
#ahj4 ,we say 'direct comparison1'      
because the syllogism also may be       
described as a comparison between two   
terms3 but in the syllogism the two     

terms are compared indirectly1 or by    
means of a third term4   #aha4 ,a       
proposition may be analysed into two    
terms and a ,copula1 which is nothing   
more than the sign of agreement or      
disagreement between them4   #ahb4 ,the 
two terms are called the ,subject and   
the ,predicate 7 #eh74   #ahc4 ,the     
,subject is that of which something is  
stated4   #ahd4 ,the ,predicate is that 
which is stated of the subject4   #ahe4 
,hence the subject is thought of for its
 own sake1 and the predicate for the    
sake of the subject4     ,,chapter ,,ii4
  ,of the ,copula4    #ahf4 ,there are  
two kinds of copula1 one for affirmative
 and one for negative statements4       
#ahg4 ,materially the copula is         
expressed by some part of the verb 'to  
be1' with or without the negative1 or   
else is wrapped up in some inflexional  
form of a verb4   #ahh4 ,the material   
form of the copula is an accident of    
language1 and a matter of indifference  
to logic4 ',the kettle boils' is as     

logical a form of expression as ',the   
kettle is boiling4' ,for it must be     
remembered that the word 'is' here is a 
mere sign of agreement between the two  
terms1 and conveys no notion of actual  
existence4  ,we may use it indeed with  
equal propriety to express              
non-existence1 as when we say ',an idol 
is nothing4'   #ahi4 ,when the verb 'to 
be' expresses existence in fact it is   
known in grammar as 'the substantive    
verb4' ,in this use it is predicate as  
well as copula1 as when we say ',god    
is1' which may be analysed1 if we       
please1 into ',god is existent4'   #aij4
 ,we have laid down above that there are
 two kinds of copula1 affirmative and   
negative3 but some logicians have       
maintained that the copula is always    
affirmative4   #aia4 ,what then1 it may 
be asked1 on this view1 is the meaning  
of negative propositions6 ,to which the 
answer is1 that a negative proposition  
asserts an agreement between the subject
 and a negative term4 ,when1 for        

instance1 we say ',the whale is not a   
fish1' this would be interpreted to mean
 ',the whale is a not-fish4'   #aib4    
,undoubtedly any negative proposition   
may be exhibited in an affirmative form1
 since1 by the law of excluded middle1  
given a pair of contradictory terms1    
wherever the one can be asserted1 the   
other can be denied1 and vice vers4 ,we 
shall find later on that this principle 
gives rise to one of the forms of       
immediate inference4 ,the only question 
then can be1 which is the more natural  
and legitimate form of expression4 ,it  
seems simpler to suppose that we assert 
the agreement of 'whale' with 'not-fish'
 by implication only1 and that what we  
directly do is to predicate a           
disagreement between 'whale' and the    
positive attributes connoted by 'fish4' 
,for since 'not-fish' must apply to     
every conceivable object of thought     
except those which fall under the       
positive term 'fish1' to say that a     
whale is a 'not-fish1' is to say that we

 have still to search for 'whale'       
throughout the whole universe of being1 
minus a limited portion2 which is only a
 more clumsy way of saying that it is   
not to be found in that portion4   #aic4
 ,again1 the term 'not-fish' must be    
understood either in its intension or in
 its extension4 ,if it be understood in 
its intension1 what it connotes is      
simply the absence of the positive      
qualities which constitute a fish1 a    
meaning which is equally conveyed by the
 negative form of proposition4 ,we gain 
nothing in simplicity by thus           
confounding assertion with denial4 ,if1 
on the other hand1 it is to be taken in 
extension1 this involves the awkwardness
 of supposing that the predicative power
 of a term resides in its extensive     
capacity4   #aid4 ,we therefore         
recognise predication as being of two   
kinds--affirmation and                  
negation--corresponding to which there  
are two forms of copula4   #aie4 ,on the
 other hand1 other logicians have       

maintained that there are many kinds of 
copula1 since the copula must vary      
according to the various degrees of     
probability with which we can assert or 
deny a predicate of a subject4 ,this    
view is technically known as the        
doctrine of    ,the ,modality of the    
,copula4    #aif4 ,it may plausibly be  
maintained that the division of         
propositions into affirmative and       
negative is not an exhaustive one1 since
 the result of an act of judgement is   
not always to lead the mind to a clear  
assertion or a clear denial1 but to     
leave it in more or less doubt as to    
whether the predicate applies to the    
subject or not4 ,instead of saying      
simply ,a is ,b1 or ,a is not ,b1 we may
 be led to one of the following forms of
 proposition--    ,a is possibly ,b4    
,a is probably ,b4   ,a is certainly ,b4
  ,the adverbial expression which thus  
appears to qualify the copula is known  
as 'the mode4'   #aig4 ,when we say     
',the accused may be guilty' we have a  

proposition of very different force from
 ',the accused is guilty1' and yet the  
terms appear to be the same4 ,wherein   
then does the difference lie8 ',in the  
copula' would seem to be the obvious    
reply4 ,we seem therefore driven to     
admit that there are as many different  
kinds of copula as there are different  
degrees of assurance with which a       
statement may be made4   #aih4 ,but     
there is another way in which modal     
propositions may be regarded4 ,instead  
of the mode being attached to the       
copula1 it may be considered as itself  
constituting the predicate1 so that the 
above propositions would be analysed    
thus--    ,that ,a is ,b1 is possible4  
,that ,a is ,b1 is probable4   ,that ,a 
is ,b1 is certain4   #aii4 ,the subject 
here is itself a proposition of which we
 predicate various degrees of           
probability4 ,in this way the division  
of propositions into affirmative and    
negative is rendered exhaustive4 ,for   
wherever before we had a doubtful       

assertion1 we have now an assertion of  
doubtfulness4   #bjj4 ,if degrees of    
probability can thus be eliminated from 
the copula1 much more so can expressions
 of time1 which may always be regarded  
as forming part of the predicate4 ',the 
sun will rise to-morrow' may be analysed
 into ',the sun is going to rise        
to-morrow4' ,in either case the tense   
belongs equally to the predicate4 ,it is
 often an awkward task so to analyse    
propositions relative to past or future 
time as to bring out the copula under   
the form 'is' or 'is not'3 but          
fortunately there is no necessity for so
 doing1 since1 as has been said before 7
 #ahh71 the material form of the copula 
is a matter of indifference to logic4   
,indeed in affirmative propositions the 
mere juxtaposition of the subject and   
predicate is often sufficient to        
indicate their agreement1 e4g4 ',most   
haste1 worst speed1' chalepha tha kala4 
,it is because all propositions are not 
affirmative that we require a copula at 

all4 ,moreover the awkwardness of       
expression just alluded to is a mere    
accident of language4 ,in ,latin we may 
say with equal propriety ',sol orietur  
cras' or ',sol est oriturus cras'2 while
 past time may also be expressed in the 
analytic form in the case of deponent   
verbs1 as ',caesar est in ,galliam      
profectus'--',caesar is gone into       
,gaul4'   #bja4 ,the copula then may    
always be regarded as pure1 that is1 as 
indicating mere agreement or            
disagreement between the two terms of   
the proposition4     ,,chapter ,,iii4   
,of the ,divisions of ,propositions4    
#bjb4 ,the most obvious and the most    
important division of propositions is   
into true and false1 but with this we   
are not concerned4 ,formal logic can    
recognise no difference between true and
 false propositions4 ,the one is        
represented by the same symbols as the  
other4   #bjc4 ,we may notice1 however1 
in passing1 that truth and falsehood are
 attributes of propositions and of      

propositions only4 ,for something must  
be predicated1 i4e4  asserted or denied1
 before we can have either truth or     
falsehood4 ,neither concepts or terms1  
on the one hand1 nor reasonings1 on the 
other1 can properly be said to be true  
or false4 ,in the mere notion of a      
,centaur or of a black swan there is    
neither truth nor falsehood2 it is not  
until we make some statement about these
 things1 such as that 'black swans are  
found in ,australia1' or ',i met a      
,centaur in the ,high ,street           
yesterday1' that the question of truth  
or falsehood comes in4 ,in such         
expressions as a 'true friend' or 'a    
false patriot' there is a tacit         
reference to propositions4 ,we mean     
persons of whom the terms 'friend' and  
'patriot' are truly or falsely          
predicated4  ,neither can we with any   
propriety talk of true or false         
reasoning4 ,reasoning is either valid or
 invalid3 it is only the premisses of   
our reasonings1 which are propositions1 

that can be true or false4 ,we may have 
a perfectly valid process of reasoning  
which starts from a false assumption and
 lands us in a false conclusion4   #bjd4
 ,all truth and falsehood then are      
contained in propositions2 and          
propositions are divided according to   
the ,quality of the ,matter into true   
and false4 ,but the consideration of the
 matter is outside the sphere of formal 
or deductive ,logic4 ,it is the problem 
of inductive logic to establish1 if     
possible1 a criterion of evidence       
whereby the truth or falsehood of       
propositions may be judged 7 #b74       
#bje4 ,another usual division of        
propositions is into ,pure and ,modal1  
the latter being those in which the     
copula is modified by some degree of    
probability4 ,this division is excluded 
by the view which has just been taken of
 the copula1 as being always simply     
affirmative or simply negative4   #bjf4 
,we are left then with the following    
divisions of propositions--             

,proposition     according to ,form     
,simple        ,complex                 
,conjunctive  ,disjunctive              
,universal         ,singular  ,general  
according to ,matter       ,verbal      
,real      according to ,quantity       
,universal         ,singular  ,general  
,particular         ,indefinite         
7strictly7 ,particular      according to
 ,quality       ,affirmative            
,negative    ,simple and ,complex       
,propositions4    #bjg4 ,a ,simple      
,proposition is one in which a predicate
 is directly affirmed or denied of a    
subject1 e4g4 ',rain is falling4'       
#bjh4 ,a simple proposition is otherwise
 known as ,categorical4   #bji4 ,a      
,complex ,proposition is one in which a 
statement is made subject to some       
condition1 e4g4 ',if the wind drops1    
rain will fall4'   #baj4 ,hence the     
complex proposition is also known as    
,conditional4   #baa4 ,every complex    
proposition consists of two parts--     
7#a7 ,antecedent2    7#b7 ,consequent4  

#bab4 ,the ,antecedent is the condition 
on which another statement is made to   
depend4 ,it precedes the other in the   
order of thought1 but may either precede
 or follow it in the order of language4 
,thus we may say indifferently--',if the
 wind drops1 we shall have rain' or ',we
 shall have rain1 if the wind drops4'   
#bac4 ,the ,consequent is the statement 
which is made subject to some condition4
   #bad4 ,the complex proposition       
assumes two forms1    7#a7 ,if ,a is ,b1
 ,c is ,d4  ,this is known as the       
,conjunctive or ,hypothetical           
proposition4    7#b7 ,either ,a is ,b or
 ,c is ,d4  ,this is known as the       
,disjunctive proposition4   #bae4 ,the  
disjunctive proposition may also appear 
in the form    ,a is either ,b or ,c1   
which is equivalent to saying    ,either
 ,a is ,b or ,a is ,c2  or again in the 
form    ,either ,a or ,b is ,c1  which  
is equivalent to saying    ,either ,a is
 ,c or ,b is ,c4   #baf4 ,as the double 
nomenclature may cause some confusion1 a

 scheme is appended4                    
,proposition                            
,simple                    ,complex     
7,categorical7                          
7,conditional7                          
,conjunctive            ,disjunctive4   
7,hypothetical7   #bag4 ,the first set  
of names is preferable4 ',categorical'  
properly means 'predicable' and         
'hypothetical' is a mere synonym for    
'conditional4'   #bah4 ,let us examine  
now what is the real nature of the      
statement which is made in the complex  
form of proposition4 ,when1 for         
instance1 we say ',if the sky falls1 we 
shall catch larks1' what is it that we  
really mean to assert8  ,not that the   
sky will fall1 and not that we shall    
catch larks1 but a certain connection   
between the two1 namely1 that the truth 
of the antecedent involves the truth of 
the consequent4 ,this is why this form  
of proposition is called 'conjunctive1' 
because in it the truth of the          
consequent is conjoined to the truth of 

the antecedent4   #bai4 ,again1 when we 
say ',jones is either a knave or a      
fool1' what is really meant to be       
asserted is--',if you do not find ,jones
 to be a knave1 you may be sure that he 
is a fool4' ,here it is the falsity of  
the antecedent which involves the truth 
of the consequent2 and the proposition  
is known as 'disjunctive1' because the  
truth of the consequent is disjoined    
from the truth of the antecedent4       
#bbj4 ,complex propositions then turn   
out to be propositions about            
propositions1 that is1 of which the     
subject and predicate are themselves    
propositions4 ,but the nature of a      
proposition never varies in thought4    
,ultimately every proposition must      
assume the form ',a is1 or is not1 ,b4' 
',if the sky falls1 we shall catch      
larks' may be compressed into           
',sky-falling is lark-catching4'   #bba4
 ,hence this division turns upon the    
form of expression1 and may be said to  
be founded on the simplicity or         

complexity of the terms employed in a   
proposition4   #bbb4 ,in the complex    
proposition there appears to be more    
than one subject or predicate or both1  
but in reality there is only a single   
statement2 and this statement refers1 as
 we have ,seen1 to a certain connection 
between two propositions4   #bbc4 ,if   
there were logically1 and not merely    
grammatically1 more than one subject or 
predicate1 there would be more than one 
proposition4 ,thus when we say ',the    
,jews and ,carthaginians were ,semitic  
peoples and spoke a ,semitic language1' 
we have four propositions compressed    
into a single sentence for the sake of  
brevity4   #bbd4 ,on the other hand when
 we say ',either the ,carthaginians were
 of ,semitic origin or argument from    
language is of no value in ethnology1'  
we have two propositions only in        
appearance4   #bbe4 ,the complex        
proposition then must be distinguished  
from those contrivances of language for 
abbreviating expression in which several

 distinct statements are combined into a
 single sentence4    ,verbal and ,real  
,propositions4    #bbf4 ,a ,verbal      
,proposition is one which states nothing
 more about the subject than is         
contained in its definition1 e4g4 ',man 
is an animal'2 ',men are rational       
beings4'   #bbg4 ,a ,real ,proposition  
states some fact not contained in the   
definition of the subject1 e4g4 ',some  
animals have four feet4'   #bbh4 ,it    
will be seen that the distinction       
between verbal and real propositions    
assumes a knowledge of the precise      
meaning of terms1 that is to say1 a     
knowledge of definitions4   #bbi4 ,to a 
person who does not know the meaning of 
terms a verbal proposition will convey  
as much information as a real one4 ,to  
say ',the sun is in mid-heaven at noon1'
 though a merely verbal proposition1    
will convey information to a person who 
is being taught to attach a meaning to  
the word 'noon4' ,we use so many terms  
without knowing their meaning1 that a   

merely verbal proposition appears a     
revelation to many minds4 ,thus there   
are people who are surprised to hear    
that the lion is a cat1 though in its   
definition 'lion' is referred to the    
class 'cat4' ,the reason of this is that
 we know material objects far better in 
their extension than in their intension1
 that is to say1 we know what things a  
name applies to without knowing the     
attributes which those things possess in
 common4   #bcj4 ,there is nothing in   
the mere look of a proposition to inform
 us whether it is verbal or real2 the   
difference is wholly relative to1 and   
constituted by1 the definition of the   
subject4 ,when we have accepted as the  
definition of a triangle that it is 'a  
figure contained by three sides1' the   
statement of the further fact that it   
has three angles becomes a real         
proposition4 ,again the proposition     
',man is progressive' is a real         
proposition4  ,for though his           
progressiveness is a consequence of his 

rationality1 still there is no actual   
reference to progressiveness contained  
in the usually accepted definition1     
',man is a rational animal4'   #bca4 ,if
 we were to admit1 under the term       
'verbal proposition1' all statements    
which1 though not actually contained in 
the definition of the subject1 are      
implied by it1 the whole body of        
necessary truth would have to be        
pronounced merely verbal1 and the most  
penetrating conclusions of              
mathematicians set down as only another 
way of stating the simplest axioms from 
which they started4  ,for the           
propositions of which necessary truth is
 composed are so linked together that1  
given one1 the rest can always follow4  
,but necessary truth1 which is arrived  
at 'a priori1' that is1 by the mind's   
own working1 is quite as real as        
contingent truth1 which is arrived at 'a
 posteriori1' or by the teachings of    
experience1 in other words1 through our 
own senses or those of others4   #bcb4  

,the process by which real truth1 which 
is other than deductive1 is arrived at  
'a priori' is known as ,intuition4      
,e4g4 ,the mind sees that what has three
 sides cannot but have three angles4    
#bcc4 ,only such propositions then must 
be considered verbal as state facts     
expressly mentioned in the definition4  
#bcd4 ,strictly speaking1 the division  
of propositions into verbal and real is 
extraneous to our subject3 since it is  
not the province of logic to acquaint us
 with the content of definitions4       
#bce1 ,the same distinction as between  
verbal and real proposition1 is conveyed
 by the expressions ',analytical' and   
',synthetical1' or ',explicative' and   
',ampliative' judgements4   #bcf4 ,a    
verbal proposition is called analytical1
 as breaking up the subject into its    
component notions4   #bcg4 ,a real      
proposition is called synthetical1 as   
attaching some new notion to the        
subject4   #bch4 ,among the scholastic  
logicians verbal propositions were known

 as ',essential1' because what was      
stated in the definition was considered 
to be of the essence of the subject1    
while real propositions were known as   
',accidental4'    ,universal ,,and      
,,particular ,propositions4    #bci4 ,a 
,universal proposition is one in which  
it is evident from the form that the    
predicate applies to the subject in its 
whole extent4   #bdj4 ,when the         
predicate does not apply to the subject 
in its whole extent1 or when it is not  
clear that it does so1 the proposition  
is called ,particular4   #bda4 ,to say  
that a predicate applies to a subject in
 its whole extent1 is to say that it is 
asserted or denied of all the things of 
which the subject is a name4   #bdb4    
',all men are mortal' is a universal    
proposition4   #bdc4 ',some men are     
black' is a particular proposition4 ,so 
also is ',men are fallible2' for here it
 is not clear from the form whether     
'all' or only 'some' is meant4   #bdd4  
,the latter kind of proposition is known

 as ,indefinite1 and must be            
distinguished from the particular       
proposition strictly so called1 in which
 the predicate applies to part only of  
the subject4   #bde4 ,the division into 
universal and particular is founded on  
the ,quantity of propositions4   #bdf4  
,the quantity of a proposition is       
determined by the quantity in extension 
of its subject4   #bdg4 ,very often the 
matter of an indefinite proposition is  
such as clearly to indicate to us its   
quantity4  ,when1 for instance1 we say  
',metals are elements1' we are          
understood to be referring to all       
metals2 and the same thing holds true of
 scientific statements in general4      
,formal logic1 however1 cannot take     
account of the matter of propositions2  
and is therefore obliged to set down all
 indefinite propositions as particular1 
since it is not evident from the form   
that they are universal4   #bdh4        
,particular propositions1 therefore1 are
 sub-divided into such as are           

,indefinite and such as are ,particular1
 in the strict sense of the term4       
#bdi4 ,we must now examine the          
sub-division of universal propositions  
into ,singular and ,general4   #bej4 ,a 
,singular proposition is one which has a
 singular term for its subject1 e4g4    
',virtue is beautiful4'   #bea4 ,a      
,general proposition is one which has   
for its subject a common term taken in  
its whole extent4   #beb4 ,now when we  
say ',john is a man' or ',this table is 
oblong1' the proposition is quite as    
universal1 in the sense of the predicate
 applying to the whole of the subject1  
as when we say ',all men are mortal4'   
,for since a singular term applies only 
to one thing1 we cannot avoid using it  
in its whole extent1 if we use it at    
all4   #bec4 ,the most usual signs of   
generality in a proposition are the     
words 'all1' 'every1' 'each1' in        
affirmative1 and the words 'no1' 'none1'
 'not one1' c4 in negative propositions4
   #bed4 ,the terminology of the        

division of propositions according to   
quantity is unsatisfactory4 ,not only   
has the indefinite proposition to be set
 down as particular1 even when the sense
 manifestly declares it to be universal2
 but the proposition which is expressed 
in a particular form has also to be     
construed as indefinite1 so that an     
unnatural meaning is imparted to the    
word 'some1' as used in logic4 ,if in   
common conversation we were to say      
',some cows chew the cud1' the person   
whom we were addressing would doubtless 
imagine us to suppose that there were   
some cows which did not possess this    
attribute4 ,but in logic the word 'some'
 is not held to express more than 'some 
at least1 if not all4' ,hence we find   
not only that an indefinite proposition 
may1 as a matter of fact1 be strictly   
particular1 but that a proposition which
 appears to be strictly particular may  
be indefinite4  ,so a proposition       
expressed in precisely the same form    
',some ,a is ,b' may be either strictly 

particular1 if some be taken to exclude 
all1 or indefinite1 if the word 'some'  
does not exclude the possibility of the 
statement being true of all4 ,it is     
evident that the term 'particular' has  
become distorted from its original      
meaning4 ,it would naturally lead us to 
infer that a statement is limited to    
part of the subject1 whereas1 by its    
being opposed to universal1 in the sense
 in which that term has been defined1 it
 can only mean that we have nothing to  
show us whether part or the whole is    
spoken of4   #bee4 ,this awkwardness of 
expression is due to the indefinite     
proposition having been displaced from  
its proper position4 ,formerly          
propositions were divided under three   
heads--    7#a7 ,universal1    7#b7     
,particular1    7#c7 ,indefinite4  ,but 
logicians anxious for simplification    
asked1 whether a predicate in any given 
case must not either apply to the whole 
of the subject or not8 ,and whether1    
therefore1 the third head of indefinite 

propositions were not as superfluous as 
the so-called 'common gender' of nouns  
in grammar8   #bef4 ,it is quite true   
that1 as a matter of fact1 any given    
predicate must either apply to the whole
 of the subject or not1 so that in the  
nature of things there is no middle     
course between universal and particular4
 ,but the important point is that we may
 not know whether the predicate applies 
to the whole of the subject or not4     
,the primary division then should be    
into propositions whose quantity is     
known and propositions whose quantity is
 unknown4 ,those propositions whose     
quantity is known may be sub-divided    
into 'definitely universal' and         
'definitely particular1' while all those
 whose quantity is unknown are classed  
together under the term 'indefinite4'   
,hence the proper division is as        
follows--                               
,proposition                            
,definite              ,indefinite      
,universal    ,particular4   #beg4      

,another very obvious defeat of         
terminology is that the word 'universal'
 is naturally opposed to 'singular1'    
whereas it is here so used as to include
 it2 while1 on the other hand1 there is 
no obvious difference between universal 
and general1 though in the division the 
latter is distinguished from the former 
as species from genus4    ,affirmative  
and ,negative ,propositions4    #beh4   
,this division rests upon the ,quality  
of propositions4   #bei4 ,it is the     
quality of the form to be affirmative or
 negative3 the quality of the matter1 as
 we saw before 7 #bjd71 is to be true or
 false4 ,but since formal logic takes no
 account of the matter of thought1 when 
we speak of 'quality' we are understood 
to mean the quality of the form4   #bfj4
 ,by combining the division of          
propositions according to quantity with 
the division according to quality1 we   
obtain four kinds of proposition1       
namely--    7#a7 ,universal ,affirmative
 7,a74    7#b7 ,universal ,negative     

7,e74    7#c7 ,particular ,affirmative  
7,i74    7#d7 ,particular ,negative     
7,o74   #bfa4 ,this is an exhaustive    
classification of propositions1 and any 
proposition1 no matter what its form may
 be1 must fall under one or other of    
these four heads4  ,for every           
proposition must be either universal or 
particular1 in the sense that the       
subject must either be known to be used 
in its whole extent or not2 and any     
proposition1 whether universal or       
particular1 must be either affirmative  
or negative1 for by denying modality to 
the copula we have excluded everything  
intermediate between downright assertion
 and denial4 ,this classification       
therefore may be regarded as a          
,procrustes' bed1 into which every      
proposition is bound to fit at its      
proper peril4   #bfb4 ,these four kinds 
of propositions are represented         
respectively by the symbols ,a1 ,e1 ,i1 
,o4   #bfc4 ,the vowels ,a and ,i1 which
 denote the two affirmatives1 occur in  

the ,latin words 'affirmo' and 'aio2' ,e
 and ,o1 which denote the two negatives1
 occur in the ,latin word 'nego4'       
,extensive and ,intensive ,propositions4
    #bfd4 ,it is important to notice the
 difference between ,extensive and      
,intensive propositions2 but this is not
 a division of propositions1 but a      
distinction as to our way of regarding  
them4 ,propositions may be read either  
in extension or intension4 ,thus when we
 say ',all cows are ruminants1' we may  
mean that the class1 cow1 is contained  
in the larger class1 ruminant4 ,this is 
reading the proposition in extension4   
,or we may mean that the attribute of   
chewing the cud is contained in1 or     
accompanies1 the attributes which make  
up our idea of 'cow4' ,this is reading  
the proposition in intension4 ,what1 as 
a matter of fact1 we do mean1 is a      
mixture of the two1 namely1 that the    
class1 cow1 has the attribute of chewing
 the cud4 ,for in the ordinary and      
natural form of proposition the subject 

is used in extension1 and the predicate 
in intension1 that is to say1 when we   
use a subject1 we are thinking of       
certain objects1 whereas when we use a  
predicate1 we indicate the possession of
 certain attributes4 ,the predicate1    
however1 need not always be used in     
intension1 e4g4 in the proposition ',his
 name is ,john' the predicate is not    
intended to convey the idea of any      
attributes at all4 ,what is meant to be 
asserted is that the name of the person 
in question is that particular name1    
,john1 and not ,zacharias or ,abinadab  
or any other name that might be given   
him4   #bfe4 ,let it be noticed that    
when a proposition is read in extension1
 the predicate contains the subject1    
whereas1 when it is read in intension1  
the subject contains the predicate4     
,exclusive ,propositions4    #bff4 ,an  
,exclusive ,proposition is so called    
because in it all but a given subject is
 excluded from participation in a given 
predicate1 e4g4 ',the good alone are    

happy1' ',none but the brave deserve the
 fair1' ',no one except yourself would  
have done this4'   #bfg4 ,by the above  
forms of expression the predicate is    
declared to apply to a given subject and
 to that subject only4 ,hence an        
exclusive proposition is really         
equivalent to two propositions1 one     
affirmative and one negative4  ,the     
first of the above propositions1 for    
instance1 means that some of the good   
are happy1 and that no one else is so4  
,it does not necessarily mean that all  
the good are happy1 but asserts that    
among the good will be found all the    
happy4 ,it is therefore equivalent to   
saying that all the happy are good1 only
 that it puts prominently forward in    
addition what is otherwise a latent     
consequence of that assertion1 namely1  
that some at least of the good are      
happy4   #bfh4 ,logically expressed the 
exclusive proposition when universal    
assumes the form of an ,e proposition1  
with a negative term for its subject    

,no not-,a is ,b4   #bfi4 ,under the    
head of exclusive comes the strictly    
particular proposition1 ',some ,a is    
,b1' which implies at the same time that
 ',some ,a is not ,b4' ,here 'some' is  
understood to mean 'some only1' which is
 the meaning that it usually bears in   
common language4 ,when1 for instance1 we
 say ',some of the gates into the park  
are closed at nightfall1' we are        
understood to mean ',some are left      
open4'    ,exceptive ,propositions4     
#bgj4 ,an ,exceptive ,proposition is so 
called as affirming the predicate of the
 whole of the subject1 with the         
exception of a certain part1 e4g4 ',all 
the jury1 except two1 condemned the     
prisoner4'   #bga4 ,this form of        
proposition again involves two distinct 
statements1 one negative and one        
affirmative1 being equivalent to ',two  
of the jury did not condemn the         
prisoner2 and all the rest did4'   #bgb4
 ,the exceptive proposition is merely an
 affirmative way of stating the         

exclusive--    ,no not-,a is ,b  ,all   
not-,a is not-,b4    ,no one but the    
sage is sane  ,all except the sage are  
mad4    ,tautologous or ,identical      
,propositions    #bgc4 ,a ,tautologous  
or ,identical proposition affirms the   
subject of itself1 e4g4 ',a man's a     
man1' ',what ,i have written1 ,i have   
written1' ',whatever is1 is4' ,the      
second of these instances amounts       
formally to saying ',the thing that ,i  
have written is the thing that ,i have  
written1' though of course the          
implication is that the writing will not
 be altered4     ,,chapter ,,iv4  ,of   
the ,distribution of ,terms4    #bgd4   
,the treatment of this subject falls    
under the second part of logic1 since   
distribution is not an attribute of     
terms in themselves1 but one which they 
acquire in predication4   #bge4 ,a term 
is said to be distributed when it is    
known to be used in its whole extent1   
that is1 with reference to all the      
things of which it is a name4 ,when it  

is not so used1 or is not known to be so
 used1 it is called undistributed4      
#bgf4 ,when we say ',all men are        
mortal1' the subject is distributed1    
since it is apparent from the form of   
the expression that it is used in its   
whole extent4 ,but when we say ',men are
 miserable' or ',some men are black1'   
the subject is undistributed4   #bgg4   
,there is the same ambiguity attaching  
to the term 'undistributed' which we    
found to underlie the use of the term   
'particular4' ',undistributed' is       
applied both to a term whose quantity is
 undefined1 and to one whose quantity is
 definitely limited to a part of its    
possible extent4   #bgh4 ,this          
awkwardness arises from not inquiring   
first whether the quantity of a term is 
determined or undetermined1 and         
afterwards proceeding to inquire1       
whether it is determined as a whole or  
part of its possible extent4  ,as it is1
 to say that a term is distributed1     
involves two distinct statements--      

7#a7 ,that its quantity is known2       
7#b7 ,that its quantity is the greatest 
possible4  ,the term 'undistributed'    
serves sometimes to contradict one of   
these statements and sometimes to       
contradict the other4   #bgi4 ,with     
regard to the quantity of the subject of
 a proposition no difficulty can arise4 
,the use of the words 'all' or 'some1'  
or of a variety of equivalent           
expressions1 mark the subject as being  
distributed or undistributed            
respectively1 while1 if there be nothing
 to mark the quantity1 the subject is   
for that reason reckoned undistributed4 
#bhj4 ,with regard to the predicate more
 difficulty may arise4   #bha4 ,it has  
been laid down already that1 in the     
ordinary form of proposition1 the       
subject is used in extension and the    
predicate in intension4 ,let us         
illustrate the meaning of this by an    
example4 ,if someone were to say ',cows 
are ruminants1' you would have a right  
to ask him whether he meant 'all cows'  

or only 'some4' ,you would not by so    
doing be asking for fresh information1  
but merely for a more distinct          
explanation of the statement already    
made4 ,the subject being used in        
extension naturally assumes the form of 
the whole or part of a class4 ,but1 if  
you were to ask the same person ',do you
 mean that cows are all the ruminants   
that there are1 or only some of them8'  
he would have a right to complain of the
 question1 and might fairly reply1 ',i  
did not mean either one or the other2 ,i
 was not thinking of ruminants as a     
class4 ,i wished merely to assert an    
attribute of cows2 in fact1 ,i meant no 
more than that cows chew the cud4'      
#bhb4 ,since therefore a predicate is   
not used in extension at all1 it cannot 
possibly be known whether it is used in 
its whole extent or not4   #bhc4 ,it    
would appear then that every predicate  
is necessarily undistributed2 and this  
consequence does follow in the case of  
affirmative propositions4   #bhd4 ,in a 

negative proposition1 however1 the      
predicate1 though still used in         
intension1 must be regarded as          
distributed4 ,this arises from the      
nature of a negative proposition4 ,for  
we must remember that in any            
proposition1 although the predicate be  
not meant in extension1 it always admits
 of being so read4 ,now we cannot       
exclude one class from another without  
at the same time wholly excluding that  
other from the former4 ,to take an      
example1 when we say ',no horses are    
ruminants1' the meaning we really wish  
to convey is that no member of the      
class1 horse1 has a particular          
attribute1 namely1 that of chewing the  
cud4 ,but the proposition admits of     
being read in another form1 namely1     
',that no member of the class1 horse1 is
 a member of the class1 ruminant4' ,for 
by excluding a class from the possession
 of a given attribute1 we inevitably    
exclude at the same time any class of   
things which possess that attribute from

 the former class4   #bhe4 ,the         
difference between the use of a         
predicate in an affirmative and in a    
negative proposition may be illustrated 
to the eye as follows4 ,to say ',all ,a 
is ,b' may mean either that ,a is       
included in ,b or that ,a and ,b are    
exactly co-extensive4  ,illustration    
#bhf4 ,as we cannot be sure which of    
these two relations of ,a to ,b is      
meant1 the predicate ,b has to be       
reckoned undistributed1 since a term is 
held to be distributed only when we know
 that it is used in its whole extent4   
#bhg4 ,to say ',no ,a is ,b1' however1  
is to say that ,a falls wholly outside  
of ,b1 which involves the consequence   
that ,b falls wholly outside of ,a4     
,illustration   #bhh4 ,let us now apply 
the same mode of illustration to the    
particular forms of proposition4   #bhi4
 ,if ,i be taken in the strictly        
particular sense1 there are1 from the   
point of view of extension1 two things  
which may be meant when we say ',some ,a

 is ,b'--    7#a7 ,that ,a and ,b are   
two classes which overlap one another1  
that is   to say1 have some members in  
common1 e4g4 ',some cats are black4'    
,illustration    7#b7 ,that ,b is wholly
 contained in ,a1 which is an inverted  
way of   saying that all ,b is ,a1 e4g4 
',some animals are men4'                
,illustration   #bij4 ,since we cannot  
be sure which of these two is meant1 the
 predicate is again reckoned            
undistributed4   #bia4 ,if on the other 
hand #a be taken in an indefinite sense1
 so as to admit the possibility of the  
universal being true1 then the two      
diagrams which have already been used   
for ,a must be extended to #a1 in       
addition to its own1 together with the  
remarks which we made in connection with
 them 7 #bhe-f74   #bib4 ,again1 when we
 say ',some ,a is not ,b1' we mean that 
some1 if not the whole of ,a1 is        
excluded from the possession of the     
attribute ,b4 ,in either case the things
 which possess the attribute ,b are     

wholly excluded either from a particular
 part or from the whole of ,a4  ,the    
predicate therefore is distributed4     
,illustration  ,from the above          
considerations we elicit the following--
   #bic4 ,four ,rules for the           
,distribution of ,terms4   7#a7 ,all    
universal propositions distribute their 
subject4   7#b7 ,no particular          
propositions distribute their subject1  
7#c7 ,all negative propositions         
distribute their predicate4   7#d7 ,no  
affirmative propositions distribute     
their predicate4    #bid4 ,the question 
of the distribution or non-distribution 
of the subject turns upon the quantity  
of the proposition1 whether universal or
 particular2 the question of the        
distribution or non-distribution of the 
predicate turns upon the quality of the 
proposition1 whether affirmative or     
negative4     ,,chapter ,v4  ,of the    
,quantification of the ,predicate4      
#bie4 ,the rules that have been given   
for the distribution of terms1 together 

with the fourfold division of           
propositions into ,a1 ,e1 #a1 #j1 are   
based on the assumption that it is the  
distribution or non-distribution of the 
subject only that needs to be taken into
 account in estimating the quantity of a
 proposition4   #bif4 ,but some         
logicians have maintained that the      
predicate1 though seldom quantified in  
expression1 must always be quantified in
 thought--in other words1 that when we  
say1 for instance1 ',all ,a is ,b1' we  
must mean either that ',all ,a is all   
,b' or only that ',all ,a is some ,b4'  
#big4 ,if this were so1 it is plain that
 the number of possible propositions    
would be exactly doubled1 and that1     
instead of four forms1 we should now    
have to recognise eight1 which may be   
expressed as follows--    #a4 ,all ,a is
 all ,b4 7upsilon74    #b4 ,all ,a is   
some ,b4 7,lambda74    #c4 ,no ,a is any
 ,b4 7,epsilon74    #d4 ,no ,a is some  
,b4 7eta74    #e4 ,some ,a is all ,b4   
7,upsilon74    #f4 ,some ,a is some ,b4 

7,iota74    #g4 ,some ,a is not any ,b4 
7,omega74    #h4 ,some ,a is not some   
,b4 7omega74   #bih4 ,it is evident that
 it is the second of the above          
propositions which represents the       
original ,a1 in accordance with the rule
 that ',no affirmative propositions     
distribute their predicate' 7 #bic74    
#bii4 ,the third represents the original
 ,e1 in accordance with the rule that   
',all negative propositions distribute  
their predicate4'   #cjj4 ,the sixth    
represents the original ,i1 in          
accordance with the rule that ',no      
affirmative propositions distribute     
their predicate4'   #cja4 ,the seventh  
represents the original ,o1 in          
accordance with the rule that ',all     
negative propositions distribute their  
predicate4'   #cjb4 ,four new symbols   
are required1 if the quantity of the    
predicate as well as that of the subject
 be taken into account in the           
classification of propositions4 ,these  
have been supplied1 somewhat fancifully1

 as follows--   #cjc4 ,the first1 ',all 
,a is all ,b1' which distributes both   
subject and predicate1 has been called  
upsilon1 to mark its extreme            
universality4   #cjd4 ,the fourth1 ',no 
,a is some ,b1' is contained in ,e1 and 
has therefore been denoted by the symbol
 eta1 to show its connection with ,e4   
#cje4 ,the fifth1 ',some ,a is all ,b1' 
is the exact converse of the second1    
',all ,a is some ,b1' and has therefore 
been denoted by the symbol ,upsilon1    
which resembles an inverted ,a4   #cjf4 
,the eighth is contained in ,o1 as part 
in whole1 and has therefore had assigned
 to it the symbol omega1   #cjg4 ,the   
attempt to take the predicate in        
extension1 instead of1 as it should     
naturally be taken1 in intension1 leads 
to some curious results4 ,let us take1  
for instance1 the u proposition4 ,either
 the sign of quantity 'all' must be     
understood as forming part of the       
predicate or not4  ,if it is not1 then  
the u proposition ',all ,a is all ,b'   

seems to contain within itself1 not one 
proposition1 but two1 namely1 ',all ,a  
is ,b' and ',all ,b is ,a4' ,but if on  
the other hand 'all' is understood to   
form part of the predicate1 then u is   
not really a general but a singular     
proposition4 ,when we say1 ',all men are
 rational animals1' we have a true      
general proposition1 because the        
predicate applies to the subject        
distributively1 and not collectively4   
,what we mean is that 'rational animal' 
may be affirmed of every individual in  
the class1 man4 ,but when we say ',all  
men are all rational animals1' the      
predicate no longer applies to the      
subject distributively1 but only        
collectively4  ,for it is obvious that  
'all rational animals' cannot be        
affirmed of every individual in the     
class1 man4 ,what the proposition means 
is that the class1 man1 is co-extensive 
with the class1 rational animal4 ,the   
same meaning may be expressed           
intensively by saying that the one class

 has the attribute of co-extension with 
the other4   #cjh4 ,under the head o u  
come all propositions in which both     
subject and predicate are singular      
terms1 e4g4 ',homer was the author of   
the ,iliad1' ',virtue is the way to     
happiness4'   #cji4 ,the proposition eta
 conveys very little information to the 
mind4 ',no ,a is some ,b' is compatible 
with the ,a proposition in the same     
matter4 ',no men are some animals' may  
be true1 while at the same time it is   
true that ',all men are animals4' ,no   
men1 for instance1 are the particular   
animals known as kangaroos4   #caj4 ,the
 omega proposition conveys still less   
information than the eta4 ,for omega is 
compatible1 not only with ,a1 but with  
upsilon4 ,even though ',all men are all 
rational animals1' it is still true that
 ',some men are not some rational       
animals'3 for no given human being is   
the same rational animal as any other4  
#caa4 ,nay1 even when the upsilon is an 
identical proposition1 omega will still 

hold in the same matter4 ',all rational 
animals are all rational animals'3 but1 
for all that1 ',some rational animals   
are not some others4' ,this last form of
 proposition therefore is almost wholly 
devoid of meaning4   #cab4 ,the chief   
advantage claimed for the quantification
 of the predicate is that it reduces    
every affirmative proposition to an     
exact equation between its subject and  
predicate4 ,as a consequence every      
proposition would admit of simple       
conversion1 that is to say1 of having   
the subject and predicate transposed    
without any further change in the       
proposition4 ,the forms also of         
,reduction 7a term which will be        
explained later on7 would be simplified2
 and generally the introduction of the  
quantified predicate into logic might be
 attended with certain mechanical       
advantages4 ,the object of the logician1
 however1 is not to invent an ingenious 
system1 but to arrive at a true analysis
 of thought4 ,now1 if it be admitted    

that in the ordinary form of proposition
 the subject is used in extension and   
the predicate in intension1 the ground  
for the doctrine is at once cut away4   
,for1 if the predicate be not used in   
its extensive capacity at all1 we       
plainly cannot be called upon to        
determine whether it is used in its     
whole extent or not4     ,,chapter ,,vi4
  ,of the ,heads of ,predicables4       
#cac4 ,a predicate is something which is
 stated of a subject4   #cad4 ,a        
predicable is something which can be    
stated of a subject4   #cae4 ,the ,heads
 of ,predicables are a classification of
 the various things which can be stated 
of a subject1 viewed in their relation  
to it4   #caf4 ,the treatment of this   
topic1 therefore1 as it involves the    
relation of a predicate to a subject1   
manifestly falls under the second part  
of logic1 which deals with the          
proposition4 ,it is sometimes treated   
under the first part of logic1 as though
 the heads of predicables were a        

classification of universal notions1    
i4e4 common terms1 in relation to one   
another1 without reference to their     
place in the proposition4   #cag4 ,the  
heads of predicables are commonly       
reckoned as five1 namely1    7#a7       
,genus4    7#b7 ,species4    7#c7       
,difference4    7#d7 ,property4    7#e7 
,accident4   #cah4 ,we will first define
 these terms in the sense in which they 
are now used1 and afterwards examine the
 principle on which the classification  
is founded and the sense in which they  
were originally intended4    7#a7 ,a    
,genus is a larger class containing     
under it smaller   classes4 ,animal is a
 genus in relation to man and brute4    
7#b7 ,a ,species is a smaller class     
contained under a larger one4 ,man   is 
a species in relation to animal4    7#c7
 ,difference is the attribute1 or       
attributes1 which distinguish   one     
species from others contained under the 
same genus4 ,rationality   is the       
attribute which distinguishes the       

species1 man1 from the   species1 brute4
    ,n4,b4 ,the genus and the difference
 together make up the ,definition of   a
 class-name1 or common term4    7#d7 ,a 
,property is an attribute which is not  
contained in the   definition of a term1
 but which flows from it4    ,a ,generic
 ,property is one which flows from the  
genus4    ,a ,specific ,property is one 
which flows from the difference4    ,it 
is a generic property of man that he is 
mortal1 which is a   consequence of his 
animality4  ,it is a specific property  
of man that   he is progressive1 which  
is a consequence of his rationality4    
7#e7 ,an ,accident is an attribute1     
which is neither contained in the       
definition1 nor flows from it4   #cai4  
,accidents are either ,separable or     
,inseparable4  ,a ,separable ,accident  
is one which belongs only to some       
members of a class4  ,an ,inseparable   
,accident is one which belongs to all   
the members of a class4  ,blackness is a
 separable accident of man1 an          

inseparable accident of coals4   #cbj4  
,the attributes which belong to anything
 may be distinguished broadly under the 
two heads of essential and              
non-essential1 or accidental4 ,by the   
essential attributes of anything are    
meant those which are contained in1 or  
which flow from1 the definition4 ,now it
 may be questioned whether there can1 in
 the nature of things1 be such a thing  
as an inseparable accident4 ,for if an  
attribute were found to belong          
invariably to all the members of a      
class1 we should suspect that there was 
some causal connection between it and   
the attributes which constitute the     
definition1 that is1 we should suspect  
the attribute in question to be         
essential and not accidental4           
,nevertheless the term 'inseparable     
accident' may be retained as a cloak for
 our ignorance1 whenever it is found    
that an attribute does1 as a matter of  
fact1 belong to all the members of a    
class1 without there being any apparent 

reason why it should do so4 ,it has been
 observed that animals which have horns 
chew the cud4 ,as no one can adduce any 
reason why animals that have horns      
should chew the cud any more than       
animals which have not1 we may call the 
fact of chewing the cud an inseparable  
accident of horned animals4   #cba4 ,the
 distinction between separable and      
inseparable accidents is sometimes      
extended from classes to individuals4   
,an inseparable accident of an          
individual is one which belongs to him  
at all times4 ,a separable accident of  
an individual is one which belongs to   
him at one time and not at another4     
#cbb4 ,it is an inseparable accident of 
an individual that he was born at a     
certain place and on a certain date4    
,it is a separable accident of an       
individual that he resides at a certain 
place and is of a certain age4   #cbc4  
,there are some remarks which it may be 
well to make about the above five terms 
before we pass on to investigate the    

principle upon which the division is    
based4   #cbd4 ,in the first place1 it  
must of course be borne in mind that    
genus and species are relative terms4   
,no class in itself can be either a     
genus or a species2 it only becomes so  
in reference to some other class1 as    
standing to it in the relation of       
containing or contained4   #cbe4 ,again1
 the distinction between genus and      
difference on the one hand and property 
on the other is wholly relative to an   
assumed definition4 ,when we say ',man  
is an animal1' ',man is rational1' ',man
 is progressive1' there is nothing in   
the nature of these statements          
themselves to tell us that the predicate
 is genus1 difference1 or property      
respectively4 ,it is only by a tacit    
reference to the accepted definition of 
man that this becomes evident to us1    
,similarly1 we cannot know beforehand   
that the fact of a triangle having three
 sides is its difference1 and the fact  
of its having three angles a property4  

,it is only when we assume the          
definition of a triangle as a           
three-sided figure that the fact of its 
having three angles sinks into a        
property4 ,had we chosen to define it1  
in accordance with its etymological     
meaning1 as a figure with three angles1 
its three-sidedness would then have been
 a mere property1 instead of being the  
difference2 for these two attributes are
 so connected together that1 whichever  
is postulated1 the other will           
necessarily follow4   #cbf4 ,lastly1 it 
must be noticed that we have not really 
defined the term 'accident1' not having 
stated what it is1 but only what it is  
not4 ,it has in fact been reserved as a 
residual head to cover any attribute    
which is neither a difference nor a     
property4   #cbg4 ,if the five heads of 
predicables above given were offered to 
us as an exhaustive classification of   
the possible relations in which the     
predicate can stand to the subject in a 
proposition1 the first thing that would 

strike us is that they do not cover the 
case in which the predicate is a        
singular term4 ,in such a proposition as
 ',this man is ,john1' we have neither a
 predication of genus or species nor of 
attribute3 but merely the identification
 of one term with another1 as applying  
to the same object4 ,such criticism as  
this1 however1 would be entirely        
erroneous1 since no singular term was   
regarded as a predicate4 ,a predicable  
was another name for a universal1 the   
common term being called a predicable in
 one relation and a universal in        
another-a predicable1 extensively1 in so
 far as it was applicable to several    
different things1 a universal1          
intensively1 in so far as the attributes
 indicated were implied in several other
 notions1 as the attributes indicated by
 'animal' are implied in 'horse1'       
'sheep1' 'goat1' c4   #cbh4 ,it would be
 less irrelevant to point out how the   
classification breaks down in relation  
to the singular term as subject4 ,when1 

for instance1 we say ',socrates is an   
animal1' ',socrates is a man1' there is 
nothing in the proposition to show us   
whether the predicate is a genus or a   
species3 for we have not here the       
relation of class to class1 which gives 
us genus or species according to their  
relative extension1 but the relation of 
a class to an individual4   #cbi4       
,again1 when we say    7#a7 ,some       
animals are men1    7#b7 ,some men are  
black1  what is there to tell us that   
the predicate is to be regarded in the  
one case as a species and in the other  
as an accident of the subject8 ,nothing 
plainly but the assumption of a         
definition already known4   #ccj4 ,but  
if this assumption be granted1 the      
classification seems to admit of a more 
or less complete defense by logic4      
,for1 given any subject1 we can         
predicate of it either a class or an    
attribute4  ,when the predicate is a    
class1 the term predicated is called a  
,genus1 if the subject itself be a      

class1 or a ,species1 if it be an       
individual4  ,when1 on the other hand1  
the predicate is an attribute1 the      
attribute predicated may be either the  
very attribute which distinguishes the  
subject from other members of the same  
class1 in which case it is called the   
,difference1 or it may be some attribute
 connected with the definition1 i4e4    
,property1 or not connected with it1    
i4e4 ,accident4   #cca4 ,these results  
may be exhibited in the following       
scheme--                                
,predicate                              
,class                                  
,attribute                              
7,subject a     7,subject a       7,the 
7,not the   common          singular    
distinguishing     distinguishing       
term7            term7                  
,attribute7         attribute7   ,genus 
,species      ,difference               
7,connected        7,not connected      
with the             with the           
definition7         definition7         

,property            ,accident   #ccb4  
,the distinction which underlies this   
division between predicating a class and
 predicating an attribute 7in quid or in
 quale7 is a perfectly intelligible one1
 corresponding as it does to the        
grammatical distinction between the     
predicate being a noun substantive or a 
noun adjective4 ,nevertheless it is a   
somewhat arbitrary one1 since1 even when
 the predicate is a class-name1 what we 
are concerned to convey to the mind1 is 
the fact that the subject possesses the 
attributes which are connoted by that   
class-name4 ,we have not here the       
difference between extensive and        
intensive predication1 since1 as we have
 already seen 7 #bfd71 that is not a    
difference between one proposition and  
another1 but a distinction in our mode  
of interpreting any and every           
proposition4 ,whatever proposition we   
like to take may be read either in      
extension or in intension1 according as 
we fix our minds on the fact of         

inclusion in a class or the fact of the 
possession of attributes4   #ccc4 ,it   
will be seen that the term 'species1' as
 it appears in the scheme1 has a wholly 
different meaning from the current      
acceptation in which it was defined     
above4 ,species1 in its now accepted    
meaning1 signifies the relation of a    
smaller class to a larger one3 as it was
 originally intended in the heads of    
predicables it signifies a class in     
reference to individuals4   #ccd4       
,another point which requires to be     
noticed with regard to this five-fold   
list of heads of predicables1 if its    
object be to classify the relations of a
 predicate to a subject1 is that it     
takes no account of those forms of      
predication in which class and attribute
 are combined4  ,under which of the five
 heads would the predicates in the      
following propositions fall8    7#a7    
,man is a rational animal4    7#b7 ,man 
is a featherless biped4  ,in the one    
case we have a combination of genus and 

difference2 in the other we have a genus
 combined with an accident4   #cce4 ,the
 list of heads of predicables which we  
have been discussing is not derived from
 ,aristotle1 but from the               
',introduction' of ,porphyry1 a ,greek  
commentator who lived more than six     
centuries later4    ,aristotle's ,heads 
of ,predicables4    #ccf4 ,aristotle    
himself1 by adopting a different basis  
of division1 has allowed room in his    
classification for the mixed forms of   
predication above alluded to4 ,his list 
contains only four heads1 namely1       
,genus 7,greek3 gnos7    ,definition    
7,greek3 risms7    ,proprium 7,greek3   
dion7    ,accident 7,greek3 sumbebeks7  
#ccg4 ,genus here is not distinguished  
from difference4  ,whether we say ',man 
is an animal' or ',man is rational1' we 
are equally understood to be predicating
 a genus4   #cch4 ,there is no account  
taken of species1 which1 when           
predicated1 resolves itself either into 
genus or accident4 ,when predicated of  

an individual1 it is regarded as a      
genus1 e4g4 ',socrates is a man'2 when  
predicated of a class1 it is regarded as
 an accident1 e4g4  ',some animals are  
men4'   #cci4 ,aristotle's              
classification may easily be seen to be 
exhaustive4 ,for every predicate must   
either be coextensive with its subject  
or not1 i4e4 predicable of the same     
things4 ,and if the two terms coincide  
in extension1 the predicate must either 
coincide also in intension with the     
subject or not4  ,a predicate which     
coincides both in extension and         
intension with its subject is exactly   
what is meant by a definition4 ,one     
which coincides in extension without    
coinciding in intension1 that is1 which 
applies to the same things without      
expressing the whole meaning1 of the    
subject1 is what is known as a ,proprium
 or ,peculiar ,property4  ,if1 on the   
other hand1 the two terms are not       
co-extensive1 the predicate must either 
partially coincide in intension with the

 subject or not4 ,footnote3 ,the case   
could not arise of a predicate which was
 entirely coincided in intension with a 
subject with which it was not           
co-extensive4 ,for1 if the extension of 
the predicate were greater than that of 
the subject1 its intension would be     
less1 and if less1 greater1 in          
accordance with the law of inverse      
variation of the two quantities 7 #aff74
 ,this is equivalent to saying that it  
must either state part of the definition
 of the subject or not4 ,now the        
definition is made up of genus and      
difference1 either of which may form the
 predicate3 but as the two are          
indistinguishable in relation to a      
single subject1 they are lumped together
 for the present purpose under the one  
head1 genus4 ,when the predicate1 not   
being co-extensive1 is not even         
partially co-intensive with its subject1
 it is called an ,accident4   #cdj4     
,proprium1 it will be seen1 differs from
 property4  ,a proprium is an attribute 

which is possessed by all the members of
 a class1 and by them alone1 e4g4 ',men 
are the only religious animals4'   #cda4
 ,under the head of definition must be  
included all propositions in which the  
predicate is a mere synonym of the      
subject1 e4g4 ',naso is ,ovid1' ',a     
,hebrew is a ,jew1' ',the skipper is the
 captain4' ,in such propositions the    
predicate coincides in extension with   
the subject1 and may be considered to   
coincide in intension where the         
intension of both subject and predicate 
is at zero1 as in the case of two proper
 names4   #cdb4 ,designations and       
descriptions will fall under the head of
 'proprium' or peculiar property1 e4g4  
',lord ,salisbury is the present prime  
minister of ,england1' ',man is a mammal
 with hands and without hair4' ,for     
here1 while the terms are coincident in 
extension1 they are far from being so in
 intension4   #cdc4 ,the term 'genus'   
must be understood to include not only  
genus in the accepted sense1 but        

difference and generic property as well4
   #cdd4 ,these results may be exhibited
 in the following scheme--              
,predicate                              
,coextensive with                       
not               the subject           
coextensive                             
,co-intensive          not              
partially    not at all   with the      
subject   cointensive        cointensive
  ,greek3 sumbubeks   ,greek3 risms     
,greek3 dion   ,greek3 gnos             
,accident                               
,defini-  ,synonym ,designa- ,descrip-  
,peculiar  ,genus ,differ- ,generic     
tion              tion     tion         
,property         ence  ,property       
#cde4 ,thus ,aristotle's four heads of  
predicables may be split up1 if we      
please1 into nine--    #a4 ,definition  
,greek3 risms4   #b4 ,synonym    _/     
#c4 ,designation                        
#d4 ,description         ,greek3 dion4  
#e4 ,peculiar ,property_/    #f4 ,genus 
#g4 ,difference         ,greek3 gnos4   

#h4 ,generic ,property_/    #i4         
,accident--,greek3 sumbebeks4   #cdf4   
,we now pass on to the two subjects of  
,definition and ,division1 the          
discussion of which will complete our   
treatment of the second part of logic4  
,definition and division correspond     
respectively to the two kinds of        
quantity possessed by terms4            
,definition is unfolding the quantity of
 a term in intension4  ,division is     
unfolding the quantity of a term in     
extension4     ,,chapter ,,vii4  ,of    
,definition4    #cdg4 ,to define a term 
is to unfold its intension1 i4e4 to     
explain its meaning4   #cdh4 ,from this 
it follows that any term which possesses
 no intension cannot be defined4   #cdi4
 ,hence proper names do not admit of    
definition1 except just in so far as    
they do possess some slight degree of   
intension3 ,thus we can define the term 
',john' only so far as to say that      
',john' is the name of a male person4   
,this is said with regard to the        

original intension of proper names2     
their acquired intension will be        
considered later4   #cej4 ,again1 since 
definition is unfolding the intension of
 a term1 it follows that those terms    
will not admit of being defined whose   
intension is already so simple that it  
cannot be unfolded further4 ,of this    
nature are names of simple attributes1  
such as greenness1 sweetness1 pleasure1 
existence4 ,we know what these things   
are1 but we cannot define them4 ,to a   
man who has never enjoyed sight1 no     
language can convey an idea of the      
greenness of the grass or the blueness  
of the sky2 and if a person were unaware
 of the meaning of the term 'sweetness1'
 no form of words could convey to him an
 idea of it4 ,we might put a lump of    
sugar into his mouth1 but that would not
 be a logical definition4   #cea4 ,thus 
we see that1 for a thing to admit of    
definition1 the idea of it must be      
complex4 ,simple ideas baffle           
definition1 but at the same time do not 

require it4  ,in defining we lay out the
 simpler ideas which are combined in our
 notion of something1 and so explain    
that complex notion4 ,we have defined   
'triangle1' when we analyse it into     
'figure' and 'contained by three lines4'
  ,similarly we have defined 'substance'
 when we analyse it into 'thing' and    
'which can be conceived to exist by     
itself4'   #ceb4 ,but when we get to    
'thing' we have reached a limit4 ,the   
,summum ,genus1 or highest class under  
which all things fall1 cannot be defined
 any more than a simple attribute2 and  
for the very good reason that it        
connotes nothing but pure being1 which  
is the simplest of all attributes4 ,to  
say that a thing is an 'object of       
thought' is not really to define it1 but
 to explain its etymology1 and to       
reclaim a philosophical term from its   
abuse by popular language1 in which it  
is limited to the concrete and the      
lifeless4 ,again1 to define it          
negatively and to say that a thing is   

'that which is not nothing' does not    
carry us any further than we were       
before4 ,the law of contradiction       
warrants us in saying as much as that4  
#cec4 ,definition is confined to        
subject-terms1 and does not properly    
extend to attributives4 ,for definition 
is of things through names1 and an      
attributive out of predication is not   
the name of anything4 ,the attributive  
is defined1 so far as it can be1 through
 the corresponding abstract term4       
#ced4 ,common terms1 other than         
attributives1 ought always to admit of  
definition4 ,for things are distributed 
by the mind into classes owing to their 
possessing certain attributes in common1
 and the definition of the class-name   
can be effected by detailing these      
attributes1 or at least a sufficient    
number of them4   #cee4 ,it is different
 with singular terms4 ,singular terms1  
when abstract1 admit of definition1 in  
so far as they are not names of         
attributes so simple as to evade        

analysis4  ,when singular terms are     
concrete1 we have to distinguish between
 the two cases of proper names and      
designations4  ,designations are        
connotative singular terms4 ,they are   
formed by limiting a common term to the 
'case in hand4'  ,whatever definition   
therefore fits the common term will fit 
also the designation which is formed    
from it1 if we add the attributes       
implied by the limitations4 ,thus       
whatever definition fits the common term
 'prime minister' will fit also the     
singular term 'the present prime        
minister of ,england' by the addition to
 it of the attributes of place and time 
which are indicated by the expression4  
,such terms as this have a definite     
amount of intension1 which can therefore
 be seized upon and expounded by a      
definition4   #cef4 ,but proper names1  
having no original intension of their   
own1 cannot be defined at all2 whereas1 
if we look upon them from the point of  
view of their acquired intension1 they  

defy definition by reason of the very   
complexity of their meaning4 ,we cannot 
say exactly what ',john' and ',mary'    
mean1 because those names1 to us who    
know the particular persons denoted by  
them1 suggest all the most trifling     
accidents of the individual as well as  
the essential attributes of the genus4  
#ceg4 ,definition serves the practical  
purpose of enabling us mentally to      
distinguish1 or1 as the name implies1   
'mark off' the thing defined from all   
other things whatsoever4  ,this may seem
 at first an endless task1 but there is 
a short cut by which the goal may be    
reached4 ,for1 if we distinguish the    
thing in hand from the things which it  
is most like1 we shall1 'a fortiori1'   
have distinguished it from things to    
which it bears a less resemblance4      
#ceh4 ,hence the first thing to do in   
seeking for a definition is to fix upon 
the class into which the thing to be    
defined most naturally falls1 and then  
to distinguish the thing in question    

from the other members of that class4   
,if we were asked to define a triangle1 
we would not begin by distinguishing it 
from a hawser1 but from a square and    
other figures with which it is more     
possible to confound it4 ,the class into
 which a thing falls is called its      
,genus1 and the attribute or attributes 
which distinguish it from other members 
of that class are called its            
,difference4   #cei4 ,if definition thus
 consists in referring a thing to a     
class1 we see a further reason why the  
summum genus of all things cannot be    
defined4   #cfj4 ,we have said that     
definition is useful in enabling us to  
distinguish things from one another in  
our minds3 but this must not be regarded
 as the direct object of the process4   
,for this object may be accomplished    
without giving a definition at all1 by  
means of what is called a ,description4 
,by a description is meant an           
enumeration of accidents with or without
 the mention of some class-name4 ,it is 

as applicable to proper names as to     
common terms4 ,when we say ',john ,smith
 lives next door on the right-hand side 
and passes by to his office every       
morning at nine o'clock1' we have1 in   
all probability1 effectually            
distinguished ,john ,smith from other   
people3 but living next1 c41 cannot be  
part of the intension of ,john ,smith1  
since ,john ,smith may change his       
residence or abandon his occupation     
without ceasing to be called by his     
name4  ,indirectly then definition      
serves the purpose of distinguishing    
things in the mind1 but its direct      
object is to unfold the intension of    
terms1 and so impart precision to our   
thoughts by setting plainly before us   
the meaning of the words we are using4  
#cfa4 ,but when we say that definition  
is unfolding the intension of terms1 it 
must not be imagined that we are bound  
in defining to unfold completely the    
intension of terms4 ,this would be a    
tedious1 and often an endless1 task4 ,a 

term may mean1 or convey to the mind1 a 
good many more attributes than those    
which are stated in its definition4     
,there is no limit indeed to the meaning
 which a term may legitimately convey1  
except the common attributes of the     
things denoted by it4 ,who shall say1   
for instance1 that a triangle means a   
figure with three sides1 and does not   
mean a figure with three angles1 or the 
surface of the perpendicular bisection  
of a cone8 ,or again1 that man means a  
rational1 and does not mean a speaking1 
a religious1 or an aesthetic animal1 or 
a biped with two eyes1 a nose1 and a    
mouth8 ,the only attributes of which it 
can safely be asserted that they can    
form no part of the intension of a term 
are those which are not common to all   
the things to which the name applies4   
,thus a particular complexion1 colour1  
height1 creed1 nationality cannot form  
any part of the intension of the term   
'man4'  ,but among the attributes common
 to a class we cannot distinguish       

between essential and unessential1      
except by the aid of definition itself4 
,formal logic cannot recognise any order
 of priority between the attributes     
common to all the members of a class1   
such as to necessitate our recognising  
some as genera and differentiae and     
relegating others to the place of       
properties or inseparable accidents4    
#cfb4 ,the art of giving a good         
definition is to seize upon the salient 
characteristics of the thing defined and
 those wherefrom the largest number of  
other attributes can be deduced as      
consequences4 ,to do this well requires 
a special knowledge of the thing in     
question1 and is not the province of the
 formal logician4   #cfc4 ,we have seen 
already1 in treating of the ,heads of   
,predicables 7 #cbe71 that the          
difference between genus and difference 
on the one hand and property on the     
other is wholly relative to some assumed
 definition4 ,now definitions are always
 to a certain extent arbitrary1 and will

 vary with the point of view from which 
we consider the thing required to be    
defined4 ,thus 'man' is usually         
contrasted with 'brute1' and from this  
point of view it is held a sufficient   
definition of him to say that he is 'a  
rational animal1' ,but a theologian     
might be more anxious to contrast man   
with supposed incorporeal intelligences1
 and from this point of view man would  
be defined as an 'embodied spirit4'     
#cfd4 ,in the two definitions just given
 it will be noticed that we have really 
employed exactly the same attributes1   
only their place as genus and difference
 has been reversed4 ,it is man's        
rational1 or spiritual1 nature which    
distinguishes him from the brutes3 but  
this is just what he is supposed to have
 in common with incorporeal             
intelligences1 from whom he is          
differentiated by his animal nature4    
,illustration  ,this illustration is    
sufficient to show us that1 while there 
is no absolute definition of anything1  

in the sense of a fixed genus and       
difference1 there may at the same time  
be certain attributes which permanently 
distinguish the members of a given class
 from those of all other classes4       
#cfe4 ,the above remarks will have made 
it clear that the intension of a term is
 often much too wide to be conveyed by  
any definition2 and that what a         
definition generally does is to select  
certain attributes from the whole       
intension1 which are regarded as being  
more typical of the thing than the      
remainder4 ,no definition can be        
expected to exhaust the whole intension 
of a term1 and there will always be room
 for varying definitions of the same    
thing1 according to the different points
 of view from which it is approached4   
#cff4 ,names of attributes lend         
themselves to definition far more easily
 than names of substances4 ,the reason  
of this is that names of attributes are 
primarily intensive in force1 whereas   
substances are known to us in extension 

before they become known to us in       
intension4 ,there is no difficulty in   
defining a term like 'triangle' or      
'monarchy1' because these terms were    
expressly invented to cover certain     
attributes2 but the case is different   
with such terms as 'dog1' 'tree1'       
'plant1' 'metal1' and other names of    
concrete things4 ,we none of us have any
 difficulty in recognising a dog or     
tree1 when we see them1 or in           
distinguishing them from other animals  
or plants respectively4 ,we are         
therefore led to imagine that we know   
the meaning of these terms4 ,it is not  
until we are called upon for a          
definition that we discover how         
superficial our knowledge really is of  
the common attributes possessed by the  
things which these names denote4   #cfg4
 ,it might be imagined that a common    
name would never be given to things     
except in virtue of our knowledge of    
their common attributes4 ,but as a      
matter of fact1 the common name was     

first given from a confused notion of   
resemblance1 and we had afterwards to   
detect the common attributes1 when      
sometimes the name had been so extended 
from one thing to another like it1 that 
there were hardly any definite          
attributes possessed in common by the   
earlier and later members of the class4 
#cfh4 ,this is especially the case where
 the meaning of terms has been extended 
by analogy1 e4g4 head1 foot1 arm1 post1 
pole1 pipe1 c4   #cfi4 ,but in the      
progress of thought we come to form     
terms in which the intensive capacity is
 everything4 ,of this kind notably are  
mathematical conceptions4 ,terms of this
 kind1 as we said before1 lend          
themselves readily to definition4       
#cgj4 ,we may lay down then roughly that
 words are easy or difficult of         
definition according as their intensive 
or extensive capacity predominates4     
#cga4 ,there is a marked distinction to 
be observed between the classes made by 
the mind of man and the classes made by 

nature1 which are known as 'real kinds4'
  ,in the former there is generally     
little or nothing in common except the  
particular attribute which is selected  
as the ground of classification1 as in  
the case of red and white things1 which 
are alike only in their redness or      
whiteness2 or else their attributes are 
all necessarily connected1 as in the    
case of circle1 square and triangle4    
,but the members of nature's classes    
agree in innumerable attributes which   
have no discoverable connection with one
 another1 and which must therefore1     
provisionally at least1 be regarded as  
standing in the relation of inseparable 
accidents to any particular attributes  
which we may select for the purposes of 
definition4 ,there is no assignable     
reason why a rational animal should have
 hair on its head or a nose on its face1
 and yet man1 as a matter of fact1 has  
both2 and generally the particular      
bodily configuration of man can only be 
regarded as an inseparable accident of  

his nature as a rational animal4   #cgb4
 ',real kinds' belong to the class of   
words mentioned above in which the      
extension predominates over the         
intension4 ,we know well enough the     
things denoted by them1 while most of us
 have only a dim idea of the points of  
resemblance between these things4       
,nature's classes moreover shade off    
into one another by such imperceptible  
degrees that it is often impossible to  
fix the boundary line between one class 
and another4 ,a still greater source of 
perplexity in dealing with real kinds is
 that it is sometimes almost impossible 
to fix upon any attribute which is      
common to every individual member of the
 class without exception4 ,all that we  
can do in such cases is to lay down a   
type of the class in its perfect form1  
and judge of individual instances by the
 degree of their approximation to it4   
,again1 real kinds being known to us    
primarily in extension1 the intension   
which we attach to the names is hable to

 be affected by the advance of          
knowledge4  ,in dealing therefore with  
such terms we must be content with      
provisional definitions1 which          
adequately express our knowledge of the 
things denoted by them1 at the time1    
though a further study of their         
attributes may induce us subsequently to
 alter the definition4 ,thus the old    
definition of animal as a sentient      
organism has been rendered inadequate by
 the discovery that so many of the      
phenomena of sensation can be exhibited 
by plants1   #cgc4 ,but terms in which  
intension is the predominant idea are   
more capable of being defined once for  
all4  ,aristotle's definitions of       
'wealth' and 'monarchy' are as          
applicable now as in his own day1 and no
 subsequent discoveries of the          
properties of figures will render       
,euclid's definitions unavailable4      
#cgd4 ,we may distinguish therefore     
between two kinds of definition1 namely1
    7#a7 ,final4    7#b7 ,provisional4  

#cge4 ,a distinction is also observed   
between ,real and ,nominal ,definitions4
 ,both of these explain the meaning of a
 term3 but a real definition further    
assumes the actual existence of the     
thing defined4 ,thus the explanation of 
the term ',centaur' would be a nominal1 
that of 'horse' a real definition4  ,it 
is useless to assert1 as is often done1 
that a nominal definition explains the  
meaning of a term and a real definition 
the nature of a thing2 for1 as we have  
seen already1 the meaning of a term is  
whatever we know of the nature of a     
thing4   #cgf4 ,it now remains to lay   
down certain rules for correct          
definition4   #cgg4 ,the first rule that
 is commonly given is that a definition 
should state the essential attributes of
 the thing defined4 ,but this amounts   
merely to saying that a definition      
should be a definition2 since it is only
 by the aid of definition that we can   
distinguish between essential and       
non-essential among the common          

attributes exhibited by a class of      
things4 ,the rule however may be        
retained as a material test of the      
soundness of a definition1 in the sense 
that he who seeks to define anything    
should fix upon its most important      
attributes4 ,to define man as a         
mammiferous animal having two hands1 or 
as a featherless biped1 we feel to be   
absurd and incongruous1 since there is  
no reference to the most salient        
characteristic of man1 namely1 his      
rationality4 ,nevertheless we cannot    
quarrel with these definitions on       
formal1 but only on material grounds4   
,again1 if anyone chose to define logic 
as the art of thinking1 all we could say
 is that we differ from him in opinion1 
as we think logic is more properly to be
 regarded as the science of the laws of 
thought4 ,but here also it is on        
material grounds that we dissent from   
the definition4   #cgh4 ,confining      
ourselves therefore to the sphere with  
which we are properly concerned1 we lay 

down the following    ,rules for        
,definition4     7#a7 ,a definition must
 be co-extensive with the term defined4 
7#b7 ,a definition must not state       
attributes which imply one another4     
7#c7 ,a definition must not contain the 
name defined1 either directly   or by   
implication4    7#d7 ,a definition must 
be clearer than the term defined4       
7#e7 ,a definition must not be negative1
 if it can be affirmative4  ,briefly1 a 
definition must be adequate 7#a71 terse 
7#b71 clear 7#d72 and must not be       
tautologous 7#c71 or1 if it can be      
avoided1 negative 7#e74   #cgi4 ,it is  
worth while to notice a slight ambiguity
 in the term 'definition' itself4       
,sometimes it is applied to the whole   
proposition which expounds the meaning  
of the term2 at other times it is       
confined to the predicate of this       
proposition4 ,thus in stating the first 
four rules we have used the term in the 
latter sense1 and in stating the fifth  
in the former4   #chj4 ,we will now     

illustrate the force of the above rules 
by giving examples of their violation4  
,rule #a4 ,violations4 ,a triangle is a 
figure with three equal sides4    ,a    
square is a four-sided figure having all
 its sides equal4  ,in the first        
instance the definition is less         
extensive than the term defined1 since  
it applies only to equilateral          
triangles4 ,this fault may be amended by
 decreasing the intension1 which we do  
by eliminating the reference to the     
equality of the sides4  ,in the second  
instance the definition is more         
extensive than the term defined4 ,we    
must accordingly increase the intension 
by adding a new attribute 'and all its  
angles right angles4'    ,rule #b4      
,violation4 ,a triangle is a figure with
 three sides and three   angles4  ,one  
of the chief merits of a definition is  
to be terse1 and this definition is     
redundant1 since what has three sides   
cannot but have three angles4    ,rule  
#c4 ,violations4 ,a citizen is a person 

both of whose parents were   citizens4  
,man is a human being4    ,rule #d4     
,violations4 ,a net is a reticulated    
fabric1 decussated at   regular         
intervals4    ,life is the definite     
combination of heterogeneous changes1   
both   simultaneous and successive1 in  
correspondence with external            
co-existences and sequences4    ,rule   
#e4 ,violations4 ,a mineral is that     
which is neither animal nor   vegetable4
    ,virtue is the absence of vice4     
#cha4 ,the object of definition being to
 explain what a thing is1 this object is
 evidently defeated1 if we confine      
ourselves to saying what it is not4 ,but
 sometimes this is impossible to be     
avoided4 ,for there are many terms      
which1 though positive in form1 are     
privative in force4 ,these terms serve  
as a kind of residual heads under which 
to throw everything within a given      
sphere1 which does not exhibit certain  
positive attributes4 ,of this           
unavoidably negative nature was the     

definition which we give of 'accident1' 
which amounted merely to saying that it 
was any attribute which was neither a   
difference nor a property4   #chb4 ,the 
violation of ,rule #c1 which guards     
against defining a thing by itself1 is  
technically known as 'circulus in       
definiendo1' or defining in a circle4   
,this rule is often apparently violated1
 without being really so4 ,thus ,euclid 
defines an acute-angled triangle as one 
which has three acute angles4 ,this     
seems a glaring violation of the rule1  
but is perfectly correct in its context2
 for it has already been explained what 
is meant by the terms 'triangle' and    
'acute angle1' and all that is now      
required is to distinguish the          
acute-angled triangle from its cognate  
species4  ,he might have said that an   
acute-angled triangle is one which has  
neither a right angle nor an obtuse     
angle3 but rightly preferred to throw   
the same statement into a positive form4
   #chc4 ,the violation of ,rule #d is  

known as 'ignotum per ignotius' or 'per 
aeque ignotum4' ,this rule also may     
seemingly be violated when it is not    
really so4 ,for a definition may be     
correct enough from a special point of  
view1 which1 apart from that particular 
context1 would appear ridiculous4 ,from 
the point of view of conic sections1 it 
is correct enough to define a triangle  
as that section of a cone which is      
formed by a plane passing through the   
vertex perpendicularly to the base1 but 
this could not be expected to make      
things clearer to a person who was      
inquiring for the first time into the   
meaning of the word triangle4 ,but a    
real violation of the fourth rule may   
arise1 not only from obscurity1 but from
 the employment of ambiguous language or
 metaphor4 ,to say that 'temperance is a
 harmony of the soul' or that 'bread is 
the staff of life1' throws no real light
 upon the nature of the definiend4      
#chd4 ,the material correctness of a    
definition is1 as we have already seen1 

a matter extraneous to formal logic4 ,an
 acquaintance with the attributes which 
terms imply involves material knowledge 
quite as much as an acquaintance with   
the things they apply to2 knowledge of  
the intension and of the extension of   
terms is alike acquired by experience4  
,no names are such that their meaning is
 rendered evident by the very           
constitution of our mental faculties2   
yet nothing short of this would suffice 
to bring the material content of        
definition within the province of formal
 logic4     ,,chapter ,,viii4  ,of      
,division4    #che4 ,to divide a term is
 to unfold its extension1 that is1 to   
set forth the things of which it is a   
name4   #chf4 ,but as in definition we  
need not completely unfold the intension
 of a term1 so in division we must not  
completely unfold its extension4   #chg4
 ,completely to unfold the extension of 
a term would involve stating all the    
individual objects to which the name    
applies1 a thing which would be         

impossible in the case of most common   
terms4 ,when it is done1 it is called   
,enumeration4 ,to reckon up all the     
months of the year from ,january to     
,december would be an enumeration1 and  
not a division1 of the term 'month4'    
#chh4 ,logical division always stops    
short at classes4  ,it may be defined as
 the statement of the various classes of
 things that can be called by a common  
name4 ,technically we may say that it   
consists in breaking up a genus into its
 component species4   #chi4 ,since      
division thus starts with a class and   
ends with classes1 it is clear that it  
is only common terms which admit of     
division1 and also that the members of  
the division must themselves be common  
terms4   #cij4 ,an 'individual' is so   
called as not admitting of logical      
division4 ,we may divide the term 'cow' 
into classes1 as ,jersey1 ,devonshire1  
c41 to which the name 'cow' will still  
be applicable1 but the parts of an      
individual cow are no longer called by  

the name of the whole1 but are known as 
beefsteaks1 briskets1 c4   #cia4 ,in    
dividing a term the first requisite is  
to fix upon some point wherein certain  
members of the class differ from others4
 ,the point thus selected is called the 
,fundamentum ,divisionis or ,basis of   
the ,division4   #cib4 ,the basis of the
 division will of course differ         
according to the purpose in hand1 and   
the same term will admit of being       
divided on a number of different        
principles4  ,thus we may divide the    
term 'man1' on the basis of colour1 into
 white1 black1 brown1 red1 and yellow2  
or1 on the basis of locality1 into      
,europeans1 ,asiatics1 ,africans1       
,americans1 ,australians1 ,new          
,zealanders1 and ,polynesians2 or again1
 on a very different principle1 into men
 of nervous1 sanguine1 bilious1         
lymphatic and mixed temperaments4       
#cic4 ,the term required to be divided  
is known as the ,totum ,divisum or      
,divided ,whole4 ,it might also be      

called the ,dividend4   #cid4 ,the      
classes into which the dividend is split
 up are called the ,membra ,dividentia1 
or ,dividing ,members4   #cie4 ,only two
 rules need be given for division--     
7#a7 ,the division must be conducted on 
a single basis4    7#b7 ,the dividing   
members must be coextensive with the    
divided whole4   #cif4 ,more briefly1 we
 may put the same thing thus--,there    
must be no cross-division 7#a7 and the  
division must be exhaustive 7#b74       
#cig4 ,the rule1 which is commonly      
given1 that each dividing member must be
 a common term1 is already provided for 
under our definition of the process4    
#cih4 ,the rule that the dividend must  
be predicable of each of the dividing   
members is contained in our second rule2
 since1 if there were any term of which 
the dividend were not predicable1 it    
would be impossible for the dividing    
members to be exactly coextensive with  
it4 ,it would not do1 for instance1 to  
introduce mules and donkeys into a      

division of the term horse4   #cii4     
,another rule1 which is sometimes given1
 namely1 that the constituent species   
must exclude one another1 is a          
consequence of our first2 for1 if the   
division be conducted on a single       
principle1 the constituent species must 
exclude one another4 ,the converse1     
however1 does not hold true4 ,we may    
have a division consisting of mutually  
exclusive members1 which yet involves a 
mixture of different bases1 e4g4 if we  
were to divide triangle into scalene1   
isosceles and equiangular4 ,this happens
 because two distinct attributes may be 
found in invariable conjunction4   #djj4
 ,there is no better test1 however1 of  
the soundness of a division than to try 
whether the species overlap1 that is to 
say1 whether there are any individuals  
that would fall into two or more of the 
classes4 ,when this is found to be the  
case1 we may be sure that we have mixed 
two or more different fundamenta        
divisionis4 ,if man1 for instance1 were 

to be divided into ,european1 ,american1
 ,aryan1 and ,semitic1 the species would
 overlap2 for both ,europe and ,america 
contain inhabitants of ,aryan and       
,semitic origin4 ,we have here members  
of a division based on locality mixed up
 with members of another division1 which
 is based on race as indicated by       
language4   #dja4 ,the classes which are
 arrived at by an act of division may   
themselves be divided into smaller      
classes4  ,this further process is      
called ,subdivision4   #djb4 ,let it be 
noticed that ,rule #a applies only to a 
single act of division4 ,the moment that
 we begin to subdivide we not only may1 
but must1 adopt a new basis of division2
 since the old one has1 'ex hypothesi1' 
been exhausted4 ,thus1 having divided   
men according to the colour of their    
skins1 if we wish to subdivide any of   
the classes1 we must look out for some  
fresh attribute wherein some men of the 
same complexion differ from others1 e4g4
 we might divide black men into         

woolly-haired blacks1 such as the       
,negroes1 and straight-haired blacks1   
like the natives of ,australia4   #djc4 
,we will now take an instance of        
division and subdivision1 with a view to
 illustrating some of the technical     
terms which are used in connection with 
the process4 ,keeping closely to our    
proper subject1 we will select as an    
instance a division of the products of  
thought1 which it is the province of    
logic to investigate4                   
,product of thought                     
,term               ,proposition        
,inference                              
,singular  ,common    ,universal        
,particular  ,immediate     ,mediate    
,a       ,e    ,i       ,o  ,here we    
have first a threefold division of the  
products of thought based on their      
comparative complexity4 ,the first two  
of these1 namely1 the term and the      
proposition1 are then subdivided on the 
basis of their respective quantities4   
,in the case of inference the basis of  

the division is again the degree of     
complexity4 ,the subdivision of the     
proposition is carried a step further   
than that of the others4 ,having        
exhausted our old basis of quantity1 we 
take a new attribute1 namely1 quality1  
on which to found the next step of      
subdivision4   #djd4 ,now in such a     
scheme of division and subdivision as   
the foregoing1 the highest class taken  
is known as the ,summum ,genus4 ,thus   
the summum genus is the same thing as   
the divided whole1 viewed in a different
 relation4 ,the term which is called the
 divided whole with reference to a      
single act of division1 is called the   
summum genus whenever subdivision has   
taken place4   #dje4 ,the classes at    
which the division stops1 that is1 any  
which are not subdivided1 are known as  
the ,infimae ,species4   #djf4 ,all     
classes intermediate between the summum 
genus and the infimae species are called
 ,subaltern ,genera or ,subaltern       
,species1 according to the way they are 

looked at1 being genera in relation to  
the classes below them and species in   
relation to the classes above them4     
#djg4 ,any classes which fall           
immediately under the same genus are    
called ,cognate ,species1 e4g4 singular 
and common terms are cognate species of 
term4   #djh4 ,the classes under which  
any lower class successively falls are  
called ,cognate ,genera4 ,the relation  
of cognate species to one another is    
like that of children of the same       
parents1 whereas cognate genera resemble
 a line of ancestry4   #dji4 ,the       
,specific ,difference of anything is the
 attribute or attributes which          
distinguish it from its cognate species4
 ,thus the specific difference of a     
universal proposition is that the       
predicate is known to apply to the whole
 of the subject4 ,a specific difference 
is said to constitute the species4      
#daj4 ,the specific difference of a     
higher class becomes a ,generic         
,difference with respect to the class   

below it4  ,a generic difference then   
may be said to be the distinguishing    
attribute of the whole class to which a 
given species belongs4 ,the generic     
difference is common to species that are
 cognate to one another1 whereas the    
specific difference is peculiar to each4
 ,it is the generic difference of an ,a 
proposition that it is universal1 the   
specific difference that it is          
affirmative4   #daa4 ,the same          
distinction is observed between the     
specific and generic properties of a    
thing4 ,a ,specific ,property is an     
attribute which flows from the          
difference of a thing itself2 a ,generic
 ,property is an attribute which flows  
from the difference of the genus to     
which the thing belongs4 ,it is a       
specific property of an ,e proposition  
that its predicate is distributed1 a    
generic property that its contrary      
cannot be true along with it 7 #dfe72   
for this last characteristic flows from 
the nature of the universal proposition 

generally4   #dab4 ,it now remains to   
say a few words as to the place in logic
 of the process of division4 ,since the 
attributes in which members of the same 
class differ from one another cannot    
possibly be indicated by their common   
name1 they must be sought for by the aid
 of experience2 or1 to put the same     
thing in other words1 since all the     
infimae species are alike contained     
under the summum genus1 their           
distinctive attributes can be no more   
than separable accidents when viewed in 
relation to the summum genus4 ,hence    
division1 being always founded on the   
possession or non-possession of         
accidental attributes1 seems to lie     
wholly outside the sphere of formal     
logic4  ,this however is not quite the  
case1 for1 in virtue of the ,law of     
,excluded ,middle1 there is always open 
to us1 independently of experience1 a   
hypothetical division by dichotomy4 ,by 
dichotomy is meant a division into two  
classes by a pair of contradictory      

terms1 e4g4 a division of the class1    
man1 into white and not-white4 ,now we  
cannot know1 independently of           
experience1 that any members of the     
class1 man1 possess whiteness2 but we   
may be quite sure1 independently of all 
experience1 that men are either white or
 not4 ,hence division by dichotomy comes
 strictly within the province of formal 
logic4 ,only it must be noticed that    
both sides of the division must be      
hypothetical4 ,for experience alone can 
tell us1 on the one hand1 that there are
 any men that are white1 and on the     
other1 that there are any but white men4
   #dac4 ,what we call a division on a  
single basis is in reality the          
compressed result of a scheme of        
division and subdivision by dichotomy1  
in which a fresh principle has been     
introduced at every step4 ,thus when we 
divide men1 on the basis of colour1 into
 white1 black1 brown1 red and yellow1 we
 may be held to have first divided men  
into white and not-white1 and then to   

have subdivided the men that are        
not-white into black and not-black1 and 
so on4 ,from the strictly formal point  
of view this division can only be       
represented as follows--                
,men                                    
,white 7if any7          ,not-white 7if 
any7                                    
,black 7if any7           ,not-black 7if
 any7                                   
,brown 7if any7           ,not-brown 7if
 any7                                   
,red 7if any7              ,not-red 7if 
any74   #dad4 ,formal correctness       
requires that the last term in such a   
series should be negative4 ,we have here
 to keep the term 'not-red' open1 to    
cover any blue or green men that might  
turn up4 ,it is only experience that    
enables us to substitute the positive   
term 'yellow' for 'not-red1' since we   
know as a matter of fact that there are 
no men but those of the five colours    
given in the original division4   #dae4 
,any correct logical division always    

admits of being arrived at by the longer
 process of division and subdivision by 
dichotomy4 ,for instance1 the term      
quadrilateral1 or four-sided rectilinear
 figure1 is correctly divided into      
square1 oblong1 rhombus1 rhomboid and   
trapezium4  ,the steps of which this    
division consists are as follows--      
,quadrilateral                          
,parallelogram          ,trapezium      
,rectangle                              
,non-rectangle                          
,square   ,oblong           ,rhombus    
,rhomboid4   #daf4 ,in reckoning up the 
infimae species in such a scheme1 we    
must of course be careful not to include
 any class which has been already       
subdivided2 but no harm is done by      
mixing an undivided class1 like         
trapezium1 with the subdivisions of its 
cognate species4   #dag4 ,the two       
processes of definition and division are
 intimately connected with one another4 
,every definition suggests a division by
 dichotomy1 and every division supplies 

us at once with a complete definition of
 all its members4   #dah4 ,definition   
itself1 so far as concerns its content1 
is1 as we have already seen1 extraneous 
to formal logic3 but when once we have  
elicited a genus and difference out of  
the material elements of thought1 we are
 enabled1 without any further appeal to 
experience1 to base thereon a division  
by dichotomy4 ,thus when man has been   
defined as a rational animal1 we have at
 once suggested to us a division of     
animal into rational and irrational4    
#dai4 ,again1 the addition of the       
attributes1 rational and irrational     
respectively1 to the common genus1      
animal1 ipso facto supplies us with     
definitions of the species1 man and     
brute4 ,similarly1 when we subdivided   
rectangle into square and oblong on the 
basis of the equality or inequality of  
the adjacent sides1 we were by so doing 
supplied with a definition both of      
square and oblong--',a square is a      
rectangle having all its sides equal1'  

and ',an oblong is a rectangle which has
 only its opposite sides equal4'   #dbj4
 ,the definition of a square just given 
amounts to the same thing as ,euclid's  
definition1 but it complies with a rule 
which has value as a matter of method1  
namely1 that the definition should state
 the ,proximate ,genus of the thing     
defined4   #dba4 ,since definition and  
division are concerned with the         
intension and extension of terms1 they  
are commonly treated of under the first 
part of logic3 but as the treatment of  
the subject implies a familiarity with  
the ,heads of ,predicables1 which in    
their turn imply the proposition1 it    
seems more desirable to deal with them  
under the second4   #dbb4 ,we have      
already had occasion to distinguish     
division from ,enumeration4 ,the latter 
is the statement of the individual      
things to which a name applies4 ,in     
enumeration1 as in division1 the wider  
term is predicable of each of the       
narrower ones4   #dbc4 ,partition is the

 mapping out of a physical whole into   
its component parts1 as when we say that
 a tree consists of roots1 stem1 and    
branches4 ,in a partition the name of   
the whole is not predicable of each of  
the parts4   #dbd4 ,distinction is the  
separation from one another of the      
various meanings of an equivocal term4  
,the term distinguished is predicable   
indeed of each of the members1 but of   
each in a different sense4 ,an equivocal
 term is in fact not one but several    
terms1 as would quickly appear1 if we   
were to use definitions in place of     
names4   #dbe4 ,we have seen that a     
logical whole is a genus viewed in      
relation to its underlying species4     
,from this must be distinguished a      
metaphysical whole1 which is a substance
 viewed in relation to its attributes1  
or a class regarded in the same way4    
,logically1 man is a part of the class1 
animal2 metaphysically1 animal is       
contained in man4 ,thus a logical whole 
is a whole in extension1 while a        

metaphysical whole is a whole in        
intension4 ,from the former point of    
view species is contained in genus2 from
 the latter genus is contained in       
species4      ,,part ,,iii4--,,of       
,,inferences4     ,,chapter ,i4  ,of    
,inferences in ,general4    #dbf4 ,to   
infer is to arrive at some truth1 not by
 direct experience1 but as a consequence
 of some truth or truths already known4 
,if we see a charred circle on the      
grass1 we infer that somebody has been  
lighting a fire there1 though we have   
not seen anyone do it4 ,this conclusion 
is arrived at in consequence of our     
previous experience of the effects of   
fire4   #dbg4 ,the term ,inference is   
used both for a process and for a       
product of thought4  ,as a process      
inference may be defined as the passage 
of the mind from one or more            
propositions to another4  ,as a product 
of thought inference may be loosely     
declared to be the result of comparing  
propositions4   #dbh4 ,every inference  

consists of two parts--    7#a7 the     
truth or truths already known2    7#b7  
the truth which we arrive at therefrom4 
,the former is called the ,antecedent1  
the latter the ,consequent4 ,but this   
use of the terms 'antecedent' and       
'consequent' must be carefully          
distinguished from the use to which they
 were put previously1 to denote the two 
parts of a complex proposition4   #dbi4 
,strictly speaking1 the term inference1 
as applied to a product of thought1     
includes both the antecedent and        
consequent3 but it is often used for the
 consequent to the exclusion of the     
antecedent4 ,thus1 when we have stated  
our premisses1 we say quite naturally1  
',and the inference ,i draw is so and   
so4'   #dcj4 ,inferences are either     
,inductive or ,deductive4  ,in induction
 we proceed from the less to the more   
general2 in deduction from the more to  
the less general1 or1 at all events1 to 
a truth of not greater generality than  
the one from which we started4 ,in the  

former we work up to general principles2
 in the latter we work down from them1  
and elicit the particulars which they   
contain4   #dca4 ,hence induction is a  
real process from the known to the      
unknown1 whereas deduction is no more   
than the application of previously      
existing knowledge2 or1 to put the same 
thing more technically1 in an inductive 
inference the consequent is not         
contained in the antecedent1 in a       
deductive inference it is4   #dcb4      
,when1 after observing that gold1       
silver1 lead1 and other metals1 are     
capable of being reduced to a liquid    
state by the application of heat1 the   
mind leaps to the conclusion that the   
same will hold true of some other metal1
 as platinum1 or of all metals1 we have 
then an inductive inference1 in which   
the conclusion1 or consequent1 is a new 
proposition1 which was not contained in 
those that went before4 ,we are led to  
this conclusion1 not by reason1 but by  
an instinct which teaches us to expect  

like results1 under like circumstances4 
,experience can tell us only of the     
past3 but we allow it to affect our     
notions of the future through a blind   
belief that 'the thing that hath been1  
it is that which shall be2 and that     
which is done is that which shall be    
done2 and there is no new thing under   
the sun4' ,take away this conviction1   
and the bridge is cut which connects the
 known with the unknown1 the past with  
the future4 ,the commonest acts of daily
 life would fail to be performed1 were  
it not for this assumption1 which is    
itself no product of the reason4 ,thus  
man's intellect1 like his faculties     
generally1 rests upon a basis of        
instinct4 ,he walks by faith1 not by    
sight4   #dcc4 ,it is a mistake to talk 
of inductive reasoning1 as though it    
were a distinct species from deductive4 
,the fact is that inductive inferences  
are either wholly instinctive1 and so   
unsusceptible of logical vindication1 or
 else they may be exhibited under the   

form of deductive inferences4 ,we cannot
 be justified in inferring that platinum
 will be melted by heat1 except where we
 have equal reason for asserting the    
same thing of copper or any other metal4
  ,in fact we are justified in drawing  
an individual inference only when we can
 lay down the universal proposition1    
',every metal can be melted by heat4'   
,but the moment this universal          
proposition is stated1 the truth of the 
proposition in the individual instance  
flows from it by way of deductive       
inference4 ,take away the universal1 and
 we have no logical warrant for arguing 
from one individual case to another4 ,we
 do so1 as was said before1 only in     
virtue of that vague instinct which     
leads us to anticipate like results from
 like appearances4   #dcd4 ,inductive   
inferences are wholly extraneous to the 
science of formal logic1 which deals    
only with formal1 or necessary1         
inferences1 that is to say with         
deductive inferences1 whether immediate 

or mediate4 ,these are called formal1   
because the truth of the consequent is  
apparent from the mere form of the      
antecedent1 whatever be the nature of   
the matter1 that is1 whatever be the    
terms employed in the proposition or    
pair of propositions which constitutes  
the antecedent4 ,in deductive inference 
we never do more than vary the form of  
the truth from which we started4 ,when  
from the proposition ',brutus was the   
founder of the ,roman ,republic1' we    
elicit the consequence ',the founder of 
the ,roman ,republic was ,brutus1' we   
certainly have nothing more in the      
consequent than was already contained in
 the antecedent2 yet all deductive      
inferences may be reduced to identities 
as palpable as this1 the only difference
 being that in more complicated cases   
the consequent is contained in the      
antecedent along with a number of other 
things1 whereas in this case the        
consequent is absolutely all that the   
antecedent contains4   #dce4 ,on the    

other hand1 it is of the very essence of
 induction that there should be a       
process from the known to the unknown4  
,widely different as these two          
operations of the mind are1 they are yet
 both included under the definition     
which we have given of inference1 as the
 passage of the mind from one or more   
propositions to another4 ,it is         
necessary to point this out1 because    
some logicians maintain that all        
inference must be from the known to the 
unknown1 whereas others confine it to   
'the carrying out into the last         
proposition of what was virtually       
contained in the antecedent judgements4'
   #dcf4 ,another point of difference   
that has to be noticed between induction
 and deduction is that no inductive     
inference can ever attain more than a   
high degree of probability1 whereas a   
deductive inference is certain1 but its 
certainty is purely hypothetical4       
#dcg4 ,without touching now on the      
metaphysical difficulty as to how we    

pass at all from the known to the       
unknown1 let us grant that there is no  
fact better attested by experience than 
this--',that where the circumstances are
 precisely alike1 like results follow4' 
,but then we never can be absolutely    
sure that the circumstances in any two  
cases are precisely alike4 ,all the     
experience of all past ages in favour of
 the daily rising of the sun is not     
enough to render us theoretically       
certain that the sun will rise tomorrow 
,we shall act indeed with a perfect     
reliance upon the assumption of the     
coming day-break2 but1 for all that1 the
 time may arrive when the conditions of 
the universe shall have changed1 and the
 sun will rise no more4   #dch4 ,on the 
other hand a deductive inference has all
 the certainty that can be imparted to  
it by the laws of thought1 or1 in other 
words1 by the structure of our mental   
faculties2 but this certainty is purely 
hypothetical4 ,we may feel assured that 
if the premisses are true1 the          

conclusion is true also4 ,but for the   
truth of our premisses we have to fall  
back upon induction or upon intuition4  
,it is not the province of deductive    
logic to discuss the material truth or  
falsity of the propositions upon which  
our reasonings are based4 ,this task is 
left to inductive logic1 the aim of     
which is to establish1 if possible1 a   
test of material truth and falsity4     
#dci4 ,thus while deduction is concerned
 only with the relative truth or falsity
 of propositions1 induction is concerned
 with their actual truth or falsity4    
,for this reason deductive logic has    
been termed the logic of consistency1   
not of truth4   #ddj4 ,it is not quite  
accurate to say that in deduction we    
proceed from the more to the less       
general1 still less to say1 as is often 
said1 that we proceed from the universal
 to the particular4 ,for it may happen  
that the consequent is of precisely the 
same amount of generality as the        
antecedent4 ,this is so1 not only in    

most forms of immediate inference1 but  
also in a syllogism which consists of   
singular propositions only1 e4g4    ,the
 tallest man in ,oxford is under eight  
feet4   ,so and so is the tallest man in
 ,oxford4   4'4 ,so and so is under     
eight feet4  ,this form of inference has
 been named ,traduction2 but there is no
 essential difference between its laws  
and those of deduction4   #dda4         
,subjoined is a classification of       
inferences1 which will serve as a map of
 the country we are now about to        
explore4                                
,inference                              
,inductive                              
,deductive                              
,immediate                              
,mediate                                
,simple               ,compound         
,simple       ,complex                  
,opposition ,conversion ,permutation    
,conjunctive  ,disjunctive ,dilemma     
,conversion         ,conversion         
by                 by                   

,negation           position            
,,chapter ,,ii4  ,of ,deductive         
,inferences4    #ddb4 ,deductive        
inferences are of two kinds--,immediate 
and ,mediate4   #ddc4 ,an immediate     
inference is so called because it is    
effected without the intervention of a  
middle term1 which is required in       
mediate inference4   #ddd4 ,but the     
distinction between the two might be    
conveyed with at least equal aptness in 
this way--  ,an immediate inference is  
the comparison of two propositions      
directly4  ,a mediate inference is the  
comparison of two propositions by means 
of a third4   #dde4 ,in that sense of   
the term inference in which it is       
confined to the consequent1 it may be   
said that--  ,an immediate inference is 
one derived from a single proposition4  
,a mediate inference is one derived from
 two propositions conjointly4   #ddf4   
,there are never more than two          
propositions in the antecedent of a     
deductive inference4 ,wherever we have a

 conclusion following from more than two
 propositions1 there will be found to be
 more than one inference4   #ddg4 ,there
 are three simple forms of immediate    
inference1 namely ,opposition1          
,conversion and ,permutation4   #ddh4   
,besides these there are certain        
compound forms1 in which permutation is 
combined with conversion4     ,,chapter 
,,iii4  ,of ,opposition4    #ddi4       
,opposition is an immediate inference   
grounded on the relation between        
propositions which have the same terms1 
but differ in quantity or in quality or 
in both4   #dej4 ,in order that there   
should be any formal opposition between 
two propositions1 it is necessary that  
their terms should be the same4 ,there  
can be no opposition between two such   
propositions as these--    7#a7 ,all    
angels have wings4    7#b7 ,no cows are 
carnivorous4   #dea4 ,if we are given a 
pair of terms1 say ,a for subject and ,b
 for predicate1 and allowed to affix    
such quantity and quality as we please1 

we can of course make up the four kinds 
of proposition recognised by logic1     
namely1    ,a4 ,all ,a is ,b4    ,e4 ,no
 ,a is ,b4    ,i4 ,some ,a is ,b4    ,o4
 ,some ,a is not ,b4   #deb4 ,now the   
problem of opposition is this3 ,given   
the truth or falsity of any one of the  
four propositions ,a1 ,e1 ,i1 ,o1 what  
can be ascertained with regard to the   
truth or falsity of the rest1 the matter
 of them being supposed to be the same8 
#dec4 ,the relations to one another of  
these four propositions are usually     
exhibited in the following scheme--     
,a 4 4 4 4 ,contrary 4 4 4 4 ,e       4 
4                      4 4       4   4  
4   4       4     4              4     4
       4       4          4       4     
4         4      4         4       4    
4  4           4   ,subaltern           
,contradictory    ,subaltern       4    
4  4           4       4         4      
4         4       4       4          4  
4       4     4              4     4    
4   4                  4   4       4 4  

4 4       ,i 4 4 4 ,sub-contrary 4 4 4  
,o   #ded4 ,contrary ,opposition is     
between two universals which differ in  
quality4   #dee4 ,sub-contrary          
,opposition is between two particulars  
which differ in quality4   #def4        
,subaltern ,opposition is between two   
propositions which differ only in       
quantity4   #deg4 ,contradictory        
,opposition is between two propositions 
which differ both in quantity and in    
quality4   #deh4 ,subaltern ,opposition 
is also known as ,subalternation1 and of
 the two propositions involved the      
universal is called the ,subalternant   
and the particular the ,subalternate4   
,both together are called ,subalterns1  
and similarly in the other forms of     
opposition the two propositions involved
 are known respectively as ,contraries1 
,sub-contraries and ,contradictories4   
#dei4 ,for the sake of convenience some 
relations are classed under the head of 
opposition in which there is1 strictly  
speaking1 no opposition at all between  

the two propositions involved4   #dfj4  
,between sub-contraries there is an     
apparent1 but not a real opposition1    
since what is affirmed of one part of a 
term may often with truth be denied of  
another4 ,thus there is no              
incompatibility between the two         
statements4    7#a7 ,some islands are   
inhabited4    7#b7 ,some islands are not
 inhabited4   #dfa4 ,in the case of     
subaltern opposition the truth of the   
universal not only may1 but must1 be    
compatible with that of the particular4 
#dfb4 ,immediate ,inference by ,relation
 would be a more appropriate name than  
,opposition2 and ,relation might then be
 subdivided into ,compatible and        
,incompatible ,relation4 ,by            
'compatible' is here meant that there is
 no conflict between the truth of the   
two propositions4 ,subaltern and        
sub-contrary opposition would thus fall 
under the head of compatible relation2  
contrary and contradictory relation     
under that of incompatible relation4    

,relation                               
,compatible                             
,incompatible                           
,subaltern  ,sub-contrary               
,contrary  ,contradictory4   #dfc4 ,it  
should be noticed that the inference in 
the case of opposition is from the truth
 or falsity of one of the opposed       
propositions to the truth or falsity of 
the other4   #dfd4 ,we will now lay down
 the accepted laws of inference with    
regard to the various kinds of          
opposition4   #dfe4 ,contrary           
propositions may both be false1 but     
cannot both be true4 ,hence if one be   
true1 the other is false1 but not vice  
vers4   #dff4 ,sub-contrary propositions
 may both be true1 but cannot both be   
false4 ,hence if one be false1 the other
 is true1 but not vice vers4   #dfg4 ,in
 the case of subaltern propositions1 if 
the universal be true1 the particular is
 true2 and if the particular be false1  
the universal is false2 but from the    
truth of the particular or the falsity  

of the universal no conclusion can be   
drawn4   #dfh4 ,contradictory           
propositions cannot be either true or   
false together4 ,hence if one be true1  
the other is false1 and vice vers4      
#dfi4 ,by applying these laws of        
inference we obtain the following       
results--    ,if ,a be true1 ,e is      
false1 ,o false1 ,i true4    ,if ,a be  
false1 ,e is unknown1 ,o true1 ,i       
unknown4    ,if ,e be true1 ,o is true1 
,i false1 ,a false4    ,if ,e be false1 
,o is unknown1 ,i true1 ,a unknown4     
,if ,o be true1 ,i is unknown1 ,a false1
 ,e unknown4    ,if ,o be false1 ,i is  
true1 ,a true1 ,e false4    ,if ,i be   
true1 ,a is unknown1 ,e false1 ,o       
unknown4    ,if ,i be false1 ,a is      
false1 ,e true1 ,o true4   #dgj4 ,it    
will be seen from the above that we     
derive more information from deriving a 
particular than from denying a          
universal4 ,should this seem surprising1
 the paradox will immediately disappear1
 if we reflect that to deny a universal 

is merely to assert the contradictory   
particular1 whereas to deny a particular
 is to assert the contradictory         
universal4 ,it is no wonder that we     
should obtain more information from     
asserting a universal than from         
asserting a particular4   #dga4 ,we have
 laid down above the received doctrine  
with regard to opposition3 but it is    
necessary to point out a flaw in it4    
,when we say that of two sub-contrary   
propositions1 if one be false1 the other
 is true1 we are not taking the         
propositions ,i and ,o in their now     
accepted logical meaning as indefinite 7
 #bed71 but rather in their popular     
sense as 'strict particular'            
propositions4 ,for if ,i and ,o were    
taken as indefinite propositions1       
meaning 'some1 if not all1' the truth of
 ,i would not exclude the possibility of
 the truth of ,a1 and1 similarly1 the   
truth of ,o would not exclude the       
possibility of the truth of ,e4 ,now ,a 
and ,e may both be false4 ,therefore ,i 

and ,o1 being possibly equivalent to    
them1 may both be false also4 ,in that  
case the doctrine of contradiction      
breaks down as well4 ,for ,i and ,o may1
 on this showing1 be false1 without     
their contradictories ,e and ,a being   
thereby rendered true4  ,this           
illustrates the awkwardness1 which we   
have previously had occasion to allude  
to1 which ensures from dividing         
propositions primarily into universal   
and particular1 instead of first        
dividing them into definite and         
indefinite1 and particular 7 #bef74     
#dgb4 ,to be suddenly thrown back upon  
the strictly particular view of ,i and  
,o in the special case of opposition1   
after having been accustomed to regard  
them as indefinite propositions1 is a   
manifest inconvenience4 ,but the        
received doctrine of opposition does not
 even adhere consistently to this view4 
,for if ,i and ,o be taken as strictly  
particular propositions1 which exclude  
the possibility of the universal of the 

same quality being true along with them1
 we ought not merely to say that ,i and 
,o may both be true1 but that if one be 
true the other must also be true4 ,for  
,i being true1 ,a is false1 and         
therefore ,o is true2 and we may argue  
similarly from the truth of ,o to the   
truth of ,i1 through the falsity of ,e4 
,or--to put the ,same thing in a less   
abstract form--since the strictly       
particular proposition means 'some1 but 
not all1' it follows that the truth of  
one sub-contrary necessarily carries    
with it the truth of the other1 ,if we  
lay down that some islands only are     
inhabited1 it evidently follows1 or     
rather is stated simultaneously1 that   
there are some islands also which are   
not inhabited4 ,for the strictly        
particular form of proposition ',some ,a
 only is ,b' is of the nature of an     
exclusive proposition1 and is really    
equivalent to two propositions1 one     
affirmative and one negative4   #dgc4   
,it is evident from the above           

considerations that the doctrine of     
opposition requires to be amended in one
 or other of two ways4 ,either we must  
face the consequences which follow from 
regarding ,i and ,o as indefinite1 and  
lay down that sub-contraries may both be
 false1 accepting the awkward corollary 
of the collapse of the doctrine of      
contradiction2 or we must be consistent 
with ourselves in regarding ,i and ,o1  
for the particular purposes of          
opposition1 as being strictly           
particular1 and lay down that it is     
always possible to argue from the truth 
of one sub-contrary to the truth of the 
other4 ,the latter is undoubtedly the   
better course1 as the admission of ,i   
and ,o as indefinite in this connection 
confuses the theory of opposition       
altogether4   #dgd4 ,of the several     
forms of opposition contradictory       
opposition is logically the strongest4  
,for this three reasons may be given--  
7#a7 ,contradictory opposites differ    
both in quantity and in quality1        

whereas others differ only in one or the
 other4    7#b7 ,contradictory opposites
 are incompatible both as to truth and  
falsity1 whereas in other cases it is   
only the truth or   falsity of the two  
that is incompatible4    7#c7           
,contradictory opposition is the safest 
form to adopt in   argument4 ,for the   
contradictory opposite refutes the      
adversary's   proposition as effectually
 as the contrary1 and is not so hable to
 a   counter-refutation4   #dge4 ,at    
first sight indeed contrary opposition  
appears stronger1 because it gives a    
more sweeping denial to the adversary's 
assertion4 ,if1 for instance1 some      
person with whom we were arguing were to
 lay down that ',all poets are bad      
logicians1' we might be tempted in the  
heat of controversy to maintain against 
him the contrary proposition ',no poets 
are bad logicians4' ,this would         
certainly be a more emphatic            
contradiction1 but1 logically           
considered1 it would not be as sound a  

one as the less obtrusive contradictory1
 ',some poets are not bad logicians1'   
which it would be very difficult to     
refute4   #dgf4 ,the phrase             
'diametrically opposed to one another'  
seems to be one of the many expressions 
which have crept into common language   
from the technical usage of logic4 ,the 
propositions ,a and ,o and ,e and ,i    
respectively are diametrically opposed  
to one another in the sense that the    
straight lines connecting them          
constitute the diagonals of the         
parallelogram in the scheme of          
opposition4   #dgg4 ,it must be noticed 
that in the case of a singular          
proposition there is only one mode of   
contradiction possible4 ,since the      
quantity of such a proposition is at the
 minimum1 the contrary and contradictory
 are necessarily merged into one4 ,there
 is no way of denying the proposition   
',this house is haunted1' save by       
maintaining the proposition which       
differs from it only in quality1 namely1

 ',this house is not haunted4'  #dgh4 ,a
 kind of generality might indeed he     
imparted even to a singular proposition 
by expressing it in the form ',a is     
always ,b4' ,thus we may say1 ',this man
 is always idle'--a proposition which   
admits of being contradicted under the  
form ',this man is sometimes not idle4' 
,,chapter ,,iv4  ,of ,conversion4       
#dgi4 ,conversion is an immediate       
inference grounded ,on the transposition
 of the subject and predicate of a      
proposition4   #dhj4 ,in this form of   
inference the antecedent is technically 
known as the ,convertend1 i4e4 the      
proposition to be converted1 and the    
consequent as the ,converse1 i4e4 the   
proposition which has been converted4   
#dha4 ,in a loose sense of the term we  
may be said to have converted a         
proposition when we have merely         
transposed the subject and predicate1   
when1 for instance1 we turn the         
proposition ',all ,a is ,b' into ',all  
,b is ,a' or ',some ,a is not ,b' into  

',some ,b is not ,a4' ,but these        
propositions plainly do not follow from 
the former ones1 and it is only with    
conversion as a form of inference--with 
,illative ,conversion as it is          
called--that ,logic is concerned4       
#dhb4 ,for conversion as a form of      
inference two rules have been laid      
down--    7#a7 ,no term must be         
distributed in the converse which was   
not   distributed in the convertend4    
7#b7 ,the quality of the converse must  
be the same as that of the   convertend4
   #dhc4 ,the first of these rules is   
founded on the nature of things4 ,a     
violation of it involves the fallacy of 
arguing from part of a term to the      
whole4   #dhd4 ,the second rule is      
merely a conventional one4  ,we may make
 a valid inference in defiance of it3   
but such an inference will be seen      
presently to involve something more than
 mere conversion4   #dhe4 ,there are two
 kinds of conversion--    7#a7 ,simple4 
7#b7 ,per ,accidens or by ,limitation4  

#dhf4 ,we are said to have simply       
converted a proposition when the        
quantity remains the same as before4    
#dhg4 ,we are said to have converted a  
proposition per accidens1 or by         
limitation1 when the rules for the      
distribution of terms necessitate a     
reduction in the original quantity of   
the proposition4   #dhh4    ,a can only 
be converted per accidens4    ,e and ,i 
can be converted simply4    ,o cannot be
 converted at all4   #dhi4 ,the reason  
why ,a can only be converted per        
accidens is that1 being affirmative1 its
 predicate is undistributed 7 #bic74    
,since ',all ,a is ,b' does not mean    
more than ',all ,a is some ,b1' its     
proper converse is ',some ,b is ,a4'    
,for1 if we endeavoured to elicit the   
inference1 ',all ,b is ,a1' we should be
 distributing the term ,b in the        
converse1 which was not distributed in  
the convertend4  ,hence we should be    
involved in the fallacy of arguing from 
the part to the whole4 ,because ',all   

doctors are men' it by no means follows 
that ',all men are doctors4'   #dii4 ,e 
and ,i admit of simple conversion1      
because the quantity of the subject and 
predicate is alike in each1 both subject
 and predicate being distributed in ,e  
and undistributed in ,i4        _/ ,no  
,a is ,b4   ,e        4'4 ,no ,b is ,a4 
_/ ,some ,a is ,b4   ,i        4'4 ,some
 ,b is ,a4   #dia4 ,the reason why ,o   
cannot be converted at all is that its  
subject is undistributed and that the   
proposition is negative4 ,now1 when the 
proposition is converted1 what was the  
subject becomes the predicate1 and1 as  
the proposition must still be negative1 
the former subject would now be         
distributed1 since every negative       
proposition distributes its predicate4  
,hence we should necessarily have a term
 distributed in the converse which was  
not distributed in the convertend4 ,from
 ',some men are not doctors1' it plainly
 does not follow that ',some doctors are
 not men'2 and1 generally from ',some ,a

 is not ,b' it cannot be inferred that  
',some ,b is not ,a1' since the         
proposition ',some ,a is not ,b' admits 
of the interpretation that ,b is wholly 
contained in ,a4  ,illustration   #dib4 
,it may often happen as a matter of fact
 that in some given matter a proposition
 of the form ',all ,b is ,a' is true    
simultaneously with ',all ,a is ,b4'    
,thus it is as true to say that ',all   
equiangular triangles are equilateral'  
as that ',all equilateral triangles are 
equiangular4' ,nevertheless we are not  
logically warranted in inferring the one
 from the other4 ,each has to be        
established on its separate evidence4   
#dic4 ,on the theory of the quantified  
predicate the difference between simple 
conversion and conversion by limitation 
disappears4 ,for the quantity of a      
proposition is then no longer determined
 solely by reference to the quantity of 
its subject4 ',all ,a is some ,b' is of 
no greater quantity than ',some ,b is   
all ,a1' if both subject and predicate  

have an equal claim to be considered4   
#did4 ,some propositions occur in       
ordinary language in which the quantity 
of the predicate is determined4 ,this is
 especially the case when the subject is
 a singular term4  ,such propositions   
admit of conversion by a mere           
transposition of their subject and      
predicate1 even though they fall under  
the form of the ,a proposition1 e4g4    
,virtue is the condition of happiness4  
4'4 ,the condition of happiness is      
virtue4  ,and again1    ,virtue is a    
condition of happiness4   4'4 ,a        
condition of happiness is virtue4  ,in  
the one case the quantity of the        
predicate is determined by the form of  
the expression as distributed1 in the   
other as undistributed4   #die4         
,conversion offers a good illustration  
of the principle on which we have before
 insisted1 namely1 that in the ordinary 
form of proposition the subject is used 
in extension and the predicate in       
intension4 ,for when by conversion we   

change the predicate into the subject1  
we are often obliged to attach a noun   
substantive to the predicate1 in order  
that it may be taken in extension1      
instead of1 as before1 in intension1    
e4g4    ,some mothers are unkind4   4'4 
,some unkind persons are mothers4       
,again1    ,virtue is conducive to      
happiness4   4'4 ,one of the things     
which are conducive to happiness is     
virtue4     ,,chapter ,v4  ,of          
,permutation4    #dif4 ,permutation     
,footnote3 ,called by some writers      
,obversion4 is an immediate inference   
grounded on a change of quality in a    
proposition and a change of the         
predicate into its contradictory-term4  
#dig4 ,in less technical language we may
 say that permutation is expressing     
negatively what was expressed           
affirmatively and vice vers4   #dih4    
,permutation is equally applicable to   
all the four forms of proposition4      
7,a7 ,all ,a is ,b4       4'4 ,no ,a is 
not-,b 7,e74    7,e7 ,no ,a is ,b4      

4'4 ,all ,a is not-,b 7,a74    7,i7     
,some ,a is ,b4       4'4 ,some ,a is   
not not-,b 7,o74    7,o7 ,some ,a is not
 ,b4       4'4 ,some ,a is not-,b 7,i74 
#dii1 ,or1 to take concrete examples--  
7,a7 ,all men are fallible4       4'4   
,no men are not-fallible 7,e74    7,e7  
,no men are perfect4       4'4 ,all men 
are not-perfect 7,a74    7,i7 ,some     
poets are logical4       4'4 ,some poets
 are not not-logical 7,o74    7,o7 ,some
 islands are not inhabited4       4'4   
,some islands are not-inhabited 7,i74   
#ejj4 ,the validity of permutation rests
 on the principle of excluded middle1   
namely--,that one or other of a pair of 
contradictory terms must be applicable  
to a given subject1 so that1 when one   
may be predicated affirmatively1 the    
other may be predicated negatively1 and 
vice vers 7 #ca74   #eja4 ,merely to    
alter the quality of a proposition would
 of course affect its meaning2 but when 
the predicate is at the same time       
changed into its contradictory term1 the

 original meaning of the proposition is 
retained1 whilst the form alone is      
altered4 ,hence we may lay down the     
following practical rule for            
permutation--  ,change the quality of   
the proposition and change the predicate
 into its contradictory term4   #ejb4   
,the law of excluded middle holds only  
with regard to contradictories4 ,it is  
not true of a pair of positive and      
privative terms1 that one or other of   
them must be applicable to any given    
subject4 ,for the subject may happen to 
fall wholly outside the sphere to which 
such a pair of terms is limited4 ,but   
since the fact of a term being applied  
is a sufficient indication of its       
applicability1 and since within a given 
sphere positive and privative terms are 
as mutually destructive as              
contradictories1 we may in all cases    
substitute the privative for the        
negative term in immediate inference by 
permutation1 which will bring the       
inferred proposition more into          

conformity with the ordinary usage of   
language4 ,thus the concrete instances  
given above will appear as follows--    
7,a7 ,all men are fallible4       4'4   
,no men are infallible 7,e74    7,e7 ,no
 men are perfect4       4'4 ,all men are
 imperfect 7,a74    7,i7 ,some poets are
 logical4       4'4 ,some poets are not 
illogical 7,o74    7,o7 ,some islands   
are not inhabited4       4'4 ,some      
islands are uninhabited 7,i74           
,,chapter ,,vi4  ,of ,compound ,forms of
 ,immediate ,inference4    #ejc4 ,having
 now treated of the three simple forms  
of immediate inference1 we go on to     
speak of the compound forms1 and first  
of    ,conversion by ,negation4    #ejd4
 ,when ,a and ,o have been permuted1    
they become respectively ,e and ,i1 and1
 in this form1 admit of simple          
conversion4 ,we have here two steps of  
inference3 but the process may be       
performed at a single stroke1 and is    
then known as ,conversion by ,negation4 
,thus from ',all ,a is ,b' we may infer 

',no not-,b is ,a1' and again from      
',some ,a is not ,b' we may infer ',some
 not-,b is ,a4' ,the nature of these    
inferences will be seen better in       
concrete examples4   #eje4    7,a7 ,all 
poets are imaginative4       4'4 ,no    
unimaginative persons are poets 7,e74   
7,o7 ,some parsons are not clerical4    
4'4 ,some unclerical persons are parsons
 7,i74   #ejf4 ,the above inferences1   
when analysed1 will be found to resolve 
themselves into two steps1 namely1      
7#a7 ,permutation4    7#b7 ,simple      
,conversion4    7,a7 ,all ,a is ,b4     
4'4 ,no ,a is not-,b 7by permutation74  
4'4 ,no not-,b is ,a 7by simple         
conversion74    7,o7 ,some ,a is not ,b4
       4'4 ,some ,a is not-,b 7by       
permutation74       4'4 ,some not-,b is 
,a 7by simple conversion74   #ejg4 ,the 
term conversion by negation has been    
arbitrarily limited to the exact        
inferential procedure of permutation    
followed by simple conversion4 ,hence it
 necessarily applies only to ,a and #j  

propositions1 since these when permuted 
become ,e and #a1 which admit of simple 
conversion2 whereas ,e and #a themselves
 are permuted into ,a and #j1 which do  
not4 ,there seems to be no good reason1 
however1 why the term 'conversion by    
negation' should be thus restricted in  
its meaning2 instead of being extended  
to the combination of permutation with  
conversion1 no matter in what order the 
two processes may be performed4 ,if this
 is not done1 inferences quite as       
legitimate as those which pass under the
 title of conversion by negation are    
left without a name4   #ejh4 ,from ,e   
and #a inferences may be elicited as    
follows--    7,e7 ,no ,a is ,b4         
4'4 ,all ,b is not-,a 7,a74    7,i7     
,some ,a is ,b4       4'4 ,some ,b is   
not not-,a 7,o74    7,e7 ,no good       
actions are unbecoming4       4'4  ,all 
unbecoming actions are not-good 7,a74   
7,i7 ,some poetical persons are         
logicians4       4'4 ,some logicians are
 not unpoetical 7,o74  ,or1 taking a    

privative term for our subject1    ,some
 unpractical persons are statesmen4     
4'4 ,some statesmen are not practical4  
#eji4 ,when the inferences just given   
are analysed1 it will be found that the 
process of simple conversion precedes   
that of permutation4   #eaj4 ,in the    
case of the ,e proposition a compound   
inference can be drawn even in the      
original order of the processes1    ,no 
,a is ,b4   4'4 ,some not-,b is ,a4     
,no one who employs bribery is honest4  
4'4 ,some dishonest men employ bribery4 
,the inference here1 it must be         
remembered1 does not refer to matter of 
fact1 but means that one of the possible
 forms of dishonesty among men is that  
of employing bribery4   #eaa4 ,if we    
analyse the preceding1 we find that the 
second step is conversion by limitation4
    ,no ,a is ,b4   4'4 ,all ,a is      
not-,b 7by permutation74   4'4 ,some    
not-,b is ,a 7by conversion per         
accidens74   #eab4 ,from ,a again an    
inference can be drawn in the reverse   

order of conversion per accidens        
followed by permutation--    ,all ,a is 
,b4   4'4 ,some ,b is not not-,a4       
,all ingenuous persons are agreeable4   
4'4 ,some agreeable persons are not     
disingenuous4   #eac4 ,the intermediate 
link between the above two propositions 
is the converse per accidens of the     
first--',some ,b is ,a4' ,this          
inference1 however1 coincides with that 
from #a 7 #ejh71 as the similar         
inference from ,e 7 #eaj7 coincides with
 that from #j 7 #ejf74   #ead4 ,all     
these inferences agree in the essential 
feature of combining permutation with   
conversion1 and should therefore be     
classed under a common name4   #eae4    
,adopting then this slight extension of 
the term1 we define conversion by       
negation as--,a form of conversion in   
which the converse differs in quality   
from the convertend1 and has the        
contradictory of one of the original    
terms4   #eaf4 ,a still more complex    
form of immediate inference is known as 

,conversion by ,contraposition4   ,this 
mode of inference assumes the following 
form--    ,all ,a is ,b4   4'4 ,all     
not-,b is not-,a4    ,all human beings  
are fallible4   4'4 ,all infallible     
beings are not-human4   #eag4 ,this will
 be found to resolve itself on analysis 
into three steps of inference in the    
following order--    7#a7 ,permutation4 
7#b7 ,simple ,conversion4    7#c7       
,permutation4   #eah4 ,let us verify    
this statement by performing the three  
steps4    ,all ,a is ,b4   4'4 ,no ,a is
 not-,b 7by permutation74   4'4 ,no     
not-,b is ,a 7by simple conversion74    
4'4 ,all not-,b is not-,a 7by           
permutation74    ,all ,englishmen are   
,aryans4   4'4 ,no ,englishmen are      
non-,aryans4   4'4 ,no non-,aryans are  
,englishmen4   4'4 ,all non-,aryans are 
non-,englishmen4   #eai4 ,conversion by 
contraposition may be complicated in    
appearance by the occurrence of a       
negative term in the subject or         
predicate or both1 e4g4    ,all not-,a  

is ,b4   4'4 ,all not-,b is ,a4  ,again1
    ,all ,a is not-,b4   4'4 ,all ,b is 
not-,a4  ,lastly1    ,all not-,a is     
not-,b4   4'4 ,all ,b is ,a4   #ebj4    
,the following practical rule will be   
found of use for the right performing of
 the process--    ,transpose the subject
 and predicate1 and substitute for each 
its   contradictory term4   #eba4 ,as   
concrete illustrations of the above     
forms of inference we may take the      
following--    ,all the men on this     
board that are not white are red4   4'4 
,all the men ,on this board that are not
 red are white4  ,again1    ,all        
compulsory labour is inefficient4   4'4 
,all efficient labour is free           
7non-compulsory74  ,lastly1    ,all     
inexpedient acts are unjust4   4'4 ,all 
just acts are expedient4   #ebb4        
,conversion by contraposition may be    
said to rest on the following           
principle--    ,if one class be wholly  
contained in another1 whatever is       
external to   the containing class is   

external also to the class contained4   
,illustration   #ebc4 ,the same         
principle may be expressed intensively  
as follows3--    ,if an attribute       
belongs to the whole of a subject1      
whatever fails to   exhibit that        
attribute does not come under the       
subject4   #ebd4 ,this statement        
contemplates conversion by              
contraposition only in reference to the 
,a proposition1 to which the process has
 hitherto been confined4 ,logicians seem
 to have overlooked the fact that       
conversion by contraposition is as      
applicable to the ,o as to the ,a       
proposition1 though1 when expressed in  
symbols1 it presents a more clumsy      
appearance4    ,some ,a is not ,b4   4'4
 ,some not-,b is not not-,a4    ,some   
wholesome things are not pleasant4   4'4
 ,some unpleasant things are not        
unwholesome4   #ebe4 ,the above admits  
of analysis in exactly the same way as  
the same process when applied to the ,a 
proposition4    ,some ,a is not ,b4     

4'4 ,some ,a is not-,b 7by permutation74
   4'4 ,some not-,b is ,a 7by simple    
conversion74   4'4 ,some not-,b is not  
not-,a 7by permutation74  ,the result1  
as in the case of the ,a proposition1 is
 the converse by negation of the        
original proposition permuted4   #ebf4  
,contraposition may also be applied to  
the ,e proposition by the use of        
conversion per accidens in the place of 
simple conversion4 ,but1 owing to the   
limitation of quantity thus effected1   
the result arrived at is the same as in 
the case of the ,o proposition4 ,thus   
from ',no wholesome things are pleasant'
 we could draw the same inference as    
before4 ,here is the process in symbols1
 when expanded4    ,no ,a is ,b4   4'4  
,all ,a is not-,b 7by permutation74     
4'4 ,some not-,b is ,a 7by conversion   
per accidens74   4'4 ,some not-,b is not
 not-,a 7by permutation74    #ebg4 ,in  
its unanalysed form conversion by       
contraposition may be defined generally 
as--,a form of conversion in which both 

subject and predicate are replaced by   
their contradictories4   #ebh4          
,conversion by contraposition differs in
 several respects from conversion by    
negation4    7#a7 ,in conversion by     
negation the converse differs in quality
 from   the convertend3 whereas in      
conversion by contraposition the quality
   of the two is the same4    7#b7 ,in  
conversion by negation we employ the    
contradictory either of   the subject or
 predicate1 but in conversion by        
contraposition we   employ the          
contradictory of both4    7#c7          
,conversion by negation involves only   
two steps of immediate   inference3     
conversion by contraposition three4     
#ebi4 ,conversion by contraposition     
cannot be applied to the ordinary ,e    
proposition except by limitation 7      
#ebf74  ,from ',no ,a is ,b' we cannot  
infer ',no not-,b is not-,a4' ,for1 if  
we could1 the contradictory of the      
latter1 namely1 ',some not-,b is not-,a'
 would be false4 ,but it is manifest    

that this is not necessarily false4 ,for
 when one term is excluded from another1
 there must be numerous individuals     
which fall under neither of them1 unless
 it should so happen that one of the    
terms is the direct contradictory of the
 other1 which is clearly not conveyed by
 the form of the expression ',no ,a is  
,b4 ',no ,a is not-,a' stands alone     
among ,e propositions in admitting of   
full conversion by contraposition1 and  
the form of that is the same after it as
 before4   #ecj4 ,nor can conversion by 
contraposition be applied at all to ,i4 
,illustration  ,from ',some ,a is ,b' we
 cannot infer that ',some not-,b is     
not-,a4' ,for though the proposition    
holds true as a matter of fact1 when ,a 
and ,b are in part mutually exclusive1  
yet this is not conveyed by the form of 
the expression4  ,it may so happen that 
,b is wholly contained under ,a1 while  
,a itself contains everything4 ,in this 
case it will be true that ',no not-,b is
 not-,a1' which contradicts the         

attempted inference4 ,thus from the     
proposition ',some things are           
substances' it cannot be inferred that  
',some not-substances are not-things1'  
for in this case the contradictory is   
true that ',no not-substances are       
not-things'2 and unless an inference is 
valid in every case1 it is not formally 
valid at all4   #eca4 ,it should be     
noticed that in the case of the nu      
proposition immediate inferences are    
possible by mere contraposition without 
conversion4    ,all ,a is all ,b4   4'4 
,all not-,a is not-,b4  ,for example1 if
 all the equilateral triangles are all  
the equiangular1 we know at once that   
all non-equilateral triangles are also  
non-equiangular4   #ecb4 ,the principle 
upon which this last kind of inference  
rests is that when two terms are        
co-extensive1 whatever is excluded from 
the one is excluded also from the other4
     ,,chapter ,,vii4  ,of other ,forms 
of ,immediate ,inference4    #ecc4      
,having treated of the main forms of    

immediate inference1 whether simple or  
compound1 we will now close this subject
 with a brief allusion to some other    
forms which have been recognised by     
logicians4   #ecd4 ,every statement of a
 relation may furnish us with ail       
immediate inference in which the same   
fact is presented from the opposite     
side4 ,thus from ',john hit ,james' we  
infer ',james was hit by ,john'2 from   
',dick is the grandson of ,tom' we infer
 ',tom is the grandfather of ,dick'2    
from ',bicester is north-east of        
,oxford' we infer ',oxford is south-west
 of ,bicester'2 from ',so and so visited
 the ,academy the day after he arrived  
in ,london' we infer ',so and so arrived
 in ,london the day before he visited   
the ,academy'2 from ',a is greater than 
,b' we infer ',b is less than ,a'2 and  
so on without limit4 ,such inferences as
 these are material1 not formal4 ,no law
 can be laid down for them except the   
universal postulate1 that    ',whatever 
is true in one form of words is true in 

every other form   of words which       
conveys the same meaning4'   #ece4      
,there is a sort of inference which goes
 under the title of ,immediate          
,inference by ,added ,determinants1 in  
which from some proposition already made
 another is inferred1 in which the same 
attribute is attached both to the       
subject and the predicate1 e4g41    ,a  
horse is a quadruped4   4'4 ,a white    
horse is a white quadruped4   #ecf4     
,such inferences are very deceptive4    
,the attributes added must be definite  
qualities1 like whiteness1 and must in  
no way involve a comparison4 ,from ',a  
horse is a quadruped' it may seem at    
first sight to follow that ',a swift    
horse is a swift quadruped4' ,but we    
need not go far to discover how little  
formal validity there is about such an  
inference4 ,from ',a horse is a         
quadruped' it by no means follows that  
',a slow horse is a slow quadruped'2 for
 even a slow horse is swift compared    
with most quadrupeds4  ,all that really 

follows here is that ',a slow horse is a
 quadruped which is slow for a horse4'  
,similarly1 from ',a ,bushman is a man' 
it does not follow that ',a tall        
,bushman is a tall man1' but only that  
',a tall ,bushman is a man who is tall  
for a ,bushman'2 and so on generally4   
#ecg4 ,very similar to the preceding is 
the process known as ,immediate         
,inference by ,complex ,conception1 e4g4
    ,a horse is a quadruped4   4'4 ,the 
head of a horse is the head of a        
quadruped4   #ech4 ,this inference1 like
 that by added determinants1 from which 
it differs in name rather than in       
nature1 may be explained on the         
principle of ,substitution4 ,starting   
from the identical proposition1 ',the   
head of a quadruped is the head of a    
quadruped1' and being given that ',a    
horse is a quadruped1' so that whatever 
is true of 'quadruped' generally we know
 to be true of 'horse1' we are entitled 
to substitute the narrower for the wider
 term1 and in this manner we arrive at  

the proposition1    ,the head of a horse
 is the head of a quadruped4   #eci4    
,such an inference is valid enough1 if  
the same caution be observed as in the  
case of added determinants1 that is1 if 
no difference be allowed to intervene in
 the relation of the fresh conception to
 the generic and the specific terms4    
,,chapter ,,viii4  ,of ,mediate         
,inferences or ,syllogisms4    #edj4 ,a 
,mediate ,inference1 or ,syllogism1     
consists of two propositions1 which are 
called the ,premisses1 and a third      
proposition known as the ,conclusion1   
which flows from the two conjointly4    
#eda4 ,in every syllogism two terms are 
compared with one another by means of a 
third1 which is called the ,middle      
,term4 ,in the premisses each of the two
 terms is compared separately with the  
middle term2 and in the conclusion they 
are compared with one another4   #edb4  
,hence every syllogism consists of three
 terms1 one of which occurs twice in the
 premisses and does not appear at all in

 the conclusion4 ,this term is called   
the ,middle ,term4 ,the predicate of the
 conclusion is called the ,major ,term  
and its subject the ,minor ,term4       
#edc4 ,the major and minor terms are    
called the ,extremes1 as opposed to the 
,mean or ,middle ,term4   #edd4 ,the    
premiss in which the major term is      
compared with the middle is called the  
,major ,premiss4   #ede4 ,the other     
premiss1 in which the minor term is     
compared with the middle1 is called the 
,minor ,premiss4   #edf4 ,the order in  
which the premisses occur in a syllogism
 is indifferent1 but it is usual1 for   
convenience1 to place the major premiss 
first4   #edg4 ,the following will serve
 as a typical instance of a syllogism-- 
,middle term     ,major term      ,major
 ,premiss4 ,all mammals are warm-blooded
    ,antecedent                         
or                  ,minor term         
,middle term       ,premisses   ,minor  
,premiss4 ,all whales are mammals       
_/                   ,minor term        

,major term     ,consequent or          
4'4 ,all whales are warm-blooded        
,conclusion4   #edh4 ,the reason why the
 names 'major1 'middle' and 'minor'     
terms were originally employed is that  
in an affirmative syllogism such as the 
above1 which was regarded as the perfect
 type of syllogism1 these names express 
the relative quantity in extension of   
the three terms4  ,illustration   #edi4 
,it must be noticed however that1 though
 the middle term cannot be of larger    
extent than the major nor of smaller    
extent than the minor1 if the latter be 
distributed1 there is nothing to prevent
 all three1 or any two of them1 from    
being coextensive4   #eej4 ,further1    
when the minor term is undistributed1 we
 either have a case of the intersection 
of two classes1 from which it cannot be 
told which of them is the larger1 or the
 minor term is actually larger than the 
middle1 when it stands to it in the     
relation of genus to species1 as in the 
following syllogism--    ,all ,negroes  

have woolly hair4   ,some ,africans are 
,negroes4   4'4 ,some ,africans have    
woolly hair4    ,illustration   #eea4   
,hence the names are not applied with   
strict accuracy even in the case of the 
affirmative syllogism2 and when the     
syllogism is negative1 they are not     
applicable at all3 since in negative    
propositions we have no means of        
comparing the relative extension of the 
terms employed4 ,had we said in the     
major premiss of our typical syllogism1 
',no mammals are cold-blooded1' and     
drawn the conclusion ',no whales are    
cold-blooded1' we could not have        
compared the relative extent of the     
terms 'mammal' and 'cold-blooded1' since
 one has been simply excluded from the  
other4    ,illustration   #eeb4 ,so far 
we have rather described than defined   
the syllogism4 ,all the products of     
thought1 it will be remembered1 are the 
results of comparison4 ,the syllogism1  
which is one of them1 may be so regarded
 in two ways--    7#a7 ,as the          

comparison of two propositions by means 
of a third4    7#b7 ,as the comparison  
of two terms by means of a third or     
middle   term4   #eec4 ,the two         
propositions which are compared with one
 another are the major premiss and the  
conclusion1 which are brought into      
connection by means of the minor        
premiss4 ,thus in the syllogism above   
given we compare the conclusion ',all   
whales are warm-blooded' with the major 
premiss ',all mammals are warm-blooded1'
 and find that the former is contained  
under the latter1 as soon as we become  
acquainted with the intermediate        
proposition ',all whales are mammals4'  
#eed4 ,the two terms which are compared 
with one another are of course the major
 and minor4   #eee4 ,the syllogism is   
merely a form into which our deductive  
inferences may be thrown for the sake of
 exhibiting their conclusiveness4 ,it is
 not the form which they naturally      
assume in speech or writing4            
,practically the conclusion is generally

 stated first and the premisses         
introduced by some causative particle as
 'because1' 'since1' 'for1' c4 ,we start
 with our conclusion1 and then give the 
reason for it by supplying the          
premisses4   #eef4 ,the conclusion1 as  
thus stated first1 was called by        
logicians the ,problema or ,quaestio1   
being regarded as a problem or question1
 to which a solution or answer was to be
 found by supplying the premisses4      
#eeg4 ,in common discourse and writing  
the syllogism is usually stated         
defectively1 one of the premisses or1 in
 some cases1 the conclusion itself being
 omitted4 ,thus instead of arguing at   
full length    ,all men are fallible1   
,the ,pope is a man1   4'4 ,the ,pope is
 fallible1  we content ourselves with   
saying ',the ,pope is fallible1 for he  
is a man1' or ',the ,pope is fallible1  
because all men are so'2 or perhaps we  
should merely say ',all men are         
fallible1 and the ,pope is a man1'      
leaving it to the sagacity of our       

hearers to supply the desired           
conclusion4 ,a syllogism1 as thus       
elliptically stated1 is commonly1 though
 incorrectly1 called an ,enthymeme4     
,when the major premiss is omitted1 it  
is called an ,enthymeme of the ,first   
,order2 when the minor is omitted1 an   
,enthymeme of the ,second ,order2 and   
when the conclusion is omitted an       
,enthymeme of the ,third ,order4        
,,chapter ,,ix4  ,of ,mood and ,figure4 
#eeh4 ,syllogisms may differ in two     
ways--    7#a7 in ,mood2    7#b7 in     
,figure4   #eei4 ,mood depends upon the 
kind of propositions employed4 ,thus a  
syllogism consisting of three universal 
affirmatives1 ,,aaa1 would be said to   
differ in mood from one consisting of   
such propositions as ,,eio or any other 
combination that might be made4 ,the    
syllogism previously given to prove the 
fallibility of the ,pope belongs to the 
mood ,,aaa4 ,had we drawn only a        
particular conclusion1 ',some ,popes are
 fallible1' it would have fallen into   

the mood ,,aai4   #efj4 ,figure depends 
upon the arrangement of the terms in the
 propositions4 ,thus a difference of    
figure is internal to a difference of   
mood1 that is to say1 the same mood can 
be in any figure4   #efa4 ,we will now  
show how many possible varieties there  
are of mood and figure1 irrespective of 
their logical validity4   #efb4 ,and    
first as to mood4  ,since every         
syllogism consists of three             
propositions1 and each of these         
propositions may be either ,a1 ,e1 ,i1  
or ,o1 it is clear that there will be as
 many possible moods as there can be    
combinations of four things1 taken three
 together1 with no restrictions as to   
repetition4 ,it will be seen that there 
are just sixty-four of such             
combinations4  ,for ,a may be followed  
either by itself or by ,e1 ,i1 or ,o4   
,let us suppose it to be followed by    
itself4 ,then this pair of premisses1   
,,aa1 may have for its conclusion either
 ,a1 ,e1 ,i1 or ,o1 thus giving four    

combinations which commence with ,,aa4  
,in like manner there will be four      
commencing with ,,ae1 four with ,,ai1   
and four with ,,ao1 giving a total of   
sixteen combinations which commence with
 ,a4 ,similarly there will be sixteen   
commencing with ,e1 sixteen with ,i1    
sixteen with ,o--in all sixty-four4 ,it 
is very few1 however1 of these possible 
combinations that will be found         
legitimate1 when tested by the rules of 
syllogism4   #efc4 ,next as to figure4  
,there are four possible varieties of   
figure in a syllogism1 as may be seen by
 considering the positions that can be  
occupied by the middle term in the      
premisses4 ,for as there are only two   
terms in each premiss1 the position     
occupied by the middle term necessarily 
determines that of the others4 ,it is   
clear that the middle term must either  
occupy the same position in both        
premisses or not1 that is1 it must      
either be subject in both or predicate  
in both1 or else subject in one and     

predicate in the other4 ,now1 if we are 
not acquainted with the conclusion of   
our syllogism1 we do not know which is  
the major and which the minor term1 and 
have therefore no means of              
distinguishing between one premiss and  
another2 consequently we must ,stop     
here1 and say that there are only three 
different arrangements possible4 ,but1  
if the ,conclusion also be assumed as   
known1 then we are able to distinguish  
one premiss as the major and the other  
as the minor2 and so we can go further1 
and lay down that1 if the middle term   
does not hold the same position in both 
premisses1 it must either be subject in 
the major and predicate in the minor1 or
 else predicate in the major and subject
 in the minor4   #efd4 ,hence there     
result    ,the ,four ,figures4  ,when   
the middle term is subject in the major 
and predicate in the minor1 we are said 
to have the ,first ,figure4  ,when the  
middle term is predicate in both        
premisses1 we are said to have the      

,second ,figure4  ,when the middle term 
is subject in both premisses1 we are    
said to have the ,third ,figure4  ,when 
the middle term is predicate in the     
major premiss and subject in the minor1 
we are said to have the ,fourth ,figure4
   #efe4 ,let ,a be the major term2 ,b  
the middle4 ,c the minor4    ,figure ,i4
 ,figure ,,ii4 ,figure ,,iii4 ,figure   
,,iv4   ,b--,a       ,a--,b             
,b--,a        ,a--,b   ,c--,b           
,c--,b        ,b--,c        ,b--,c      
,c--,a       ,c--,a        ,c--,a       
,c--,a  ,all these figures are          
legitimate1 though the fourth is        
comparatively valueless4   #eff4 ,it    
will be well to explain by an instance  
the meaning of the assertion previously 
made1 that a difference of figure is    
internal to a difference of mood4 ,we   
will take the mood ,,eio1 and by varying
 the position of the terms1 construct a 
syllogism in it in each of the four     
figures4    ,i4     ,e ,no wicked man is
 happy4     ,i ,some prosperous men are 

wicked4     ,o 4'4 ,some prosperous men 
are not happy4    ,,ii4     ,e ,no happy
 man is wicked4     ,i ,some prosperous 
men are wicked4     ,o 4'4 ,some        
prosperous men are not happy4    ,,iii4 
,e ,no wicked man is happy4     ,i ,some
 wicked men are prosperous4     ,o 4'4  
,some prosperous men are not happy4     
,,iv4     ,e ,no happy man is wicked4   
,i ,some wicked men are prosperous4     
,o 4'4 ,some prosperous men are not     
happy4   #efg4 ,in the mood we have     
selected1 owing to the peculiar nature  
of the premisses1 both of which admit of
 simple conversion1 it happens that the 
resulting syllogisms are all valid4 ,but
 in the great majority of moods no      
syllogism would be valid at all1 and in 
many moods a syllogism would be valid in
 one figure and invalid in another4 ,as 
yet however we are only concerned with  
the conceivable combinations1 apart from
 the question of their legitimacy4      
#efh4 ,now since there are four         
different figures and sixty-four        

different moods1 we obtain in all #bef  
possible ways of arranging three terms  
in three propositions1 that is1 #bef    
possible forms of syllogism4            
,,chapter ,x4  ,of the ,canon of        
,reasoning4    #efi4 ,the first figure  
was regarded by logicians as the only   
perfect type of syllogism1 because the  
validity of moods in this figure may be 
tested directly by their complying1 or  
failing to comply1 with a certain axiom1
 the truth of which is self-evident4    
,this axiom is known as the ,dictum de  
,omni et ,nullo4 ,it may be expressed as
 follows--    ,whatever may be affirmed 
or denied of a whole class may be       
affirmed   or denied of everything      
contained in that class4   #egj4 ,this  
mode of stating the axiom contemplates  
predication as being made in extension1 
whereas it is more naturally to be      
regarded as being made in intension4    
#ega4 ,the same principle may be        
expressed intensively as follows--      
,whatever has certain attributes has    

also the attributes which   invariably  
accompany them 4,footnote3 ,nota notae  
est nota rei   ipsius4 ',whatever has   
any mark has that which it is a mark    
of4'   ,mill1 vol4 i1 p4 #bja1   #egb4  
,by ,aristotle himself the principle was
 expressed in a neutral form thus--     
',whatever is stated of the predicate   
will be stated also of the   subject    
,footnote3 ,greek3 osa kat to           
kategoroumnou lgetai pnta ka   kat to   
hypokeimnou rhaetsetai4 ,cat4 #c1  ,i4' 
,this way of putting it1 however1 is too
 loose4   #egc4 ,the principle precisely
 stated is as follows--    ,whatever may
 be affirmed or denied universally of   
the predicate of   an affirmative       
proposition1 may be affirmed or denied  
also of the   subject4   #egd4 ,thus1   
given an affirmative proposition        
',whales are mammals1' if we can affirm 
anything universally of the predicate   
'mammals1' as1 for instance1 that ',all 
mammals are warm-blooded1' we shall be  
able to affirm the same of the subject  

'whales'2 and1 if we can deny anything  
universally of the predicate1 as that   
',no mammals are oviparous1' we shall be
 able to deny the same of the subject4  
#ege4 ,in whatever way the supposed     
canon of reasoning may be stated1 it has
 the defect of applying only to a single
 figure1 namely1 the first4 ,the        
characteristic of the reasoning in that 
figure is that some general rule is     
maintained to hold good in a particular 
case4 ,the major premiss lays down some 
general principle1 whether affirmative  
or negative2 the minor premiss asserts  
that a particular case falls under this 
principle2 and the conclusion applies   
the general principle to the particular 
case4 ,but though all syllogistic       
reasoning may be tortured into          
conformity with this type1 some of it   
finds expression more naturally in other
 ways4   #egf4 ,modern logicians        
therefore prefer to abandon the ,dictum 
de ,omni et ,nullo in any shape1 and to 
substitute for it the following three   

axioms1 which apply to all figures      
alike4    ,three ,axioms of ,mediale    
,inference4     7#a7 ,if two terms agree
 with the same third term1 they agree   
with one   another4    7#b7 ,if one term
 agrees1 and another disagrees1 with the
 same third   term1 they disagree with  
one another4    7#c7 ,if two terms      
disagree with the same third term1 they 
may or may   not agree with one another4
   #egg4 ,the first of these axioms is  
the principle of all affirmative1 the   
second of all negative1 syllogisms2 the 
third points out the conditions under   
which no conclusion can be drawn4  ,if  
there is any agreement at all between   
the two terms and the third1 as in the  
cases contemplated in the first and     
second axioms1 then we have a conclusion
 of some kind3 if it is otherwise1 we   
have none4   #egh4 ,it must be          
understood with regard to these axioms  
that1 when we speak of terms agreeing or
 disagreeing with the same third term1  
we mean that they agree or disagree with

 the same part of it4   #egi4 ,hence in 
applying these axioms it is necessary to
 bear in mind the rules for the         
distinction of terms4  ,thus from       
,all ,b is ,a1   ,no ,c is ,b1  the only
 inference which can be drawn is that   
,some ,a is not ,c 7which alters the    
figure from the first to the fourth74   
,for it was only part of ,a which was   
known to agree with ,b4  ,on the theory 
of the quantified predicate we could    
draw the inference ,no ,c is some ,a4   
#ehj4 ,it is of course possible for     
terms to agree with different parts of  
the same third term1 and yet to have no 
connection with one another4 ,thus      
,all birds fly4   ,all bats fly4  ,but  
we do not infer therefrom that bats are 
birds or vice vers4   #eha4 ,on the     
other hand1 had we said1--    ,all birds
 lay eggs1   ,no bats lay eggs1  we     
might confidently have drawn the        
conclusion    ,no bats are birds  ,for  
the term 'bats1' being excluded from the
 whole of the term 'lay eggs1' is       

thereby necessarily excluded from that  
part of it which coincides with 'birds4'
  ,illustration     ,,chapter ,,xi4  ,of
 the ,generad ,rules of ,syllogism4     
#ehb4 ,we now proceed to lay down       
certain general rules to which all valid
 syllogisms must conform4  ,these are   
divided into primary and derivative4    
,i4 ,primary4    7#a7 ,a syllogism must 
consist of three propositions only4     
7#b7 ,a syllogism must consist of three 
terms only4    7#c7 ,the middle term    
must be distributed at least once in the
   premisses4    7#d7 ,no term must be  
distributed in the conclusion which was 
not   distributed in the premisses4     
7#e7 ,two negative premisses prove      
nothing4    7#f7 ,if one premiss be     
negative1 the conclusion must be        
negative4    7#g7 ,if the conclusion be 
negative1 one of the premisses must be  
negative3 but if the conclusion be      
affirmative1 both premisses must   be   
affirmative4  ,,ii4 ,derivative4    7#h7
 ,two particular premisses prove        

nothing4    7#i7 ,if one premiss be     
particular1 the conclusion must be      
particular4   #ehc4 ,the first two of   
these rules are involved in the         
definition of the syllogism with which  
we started4  ,we said it might be       
regarded either as the comparison of two
 propositions by means of a third or as 
the comparison of two terms by means of 
a third4  ,to violate either of these   
rules therefore would be inconsistent   
with the fundamental conception of the  
syllogism4  ,the first of our two       
definitions indeed 7 #eeb7 applies      
directly only to the syllogisms in the  
first figure2 but since all syllogisms  
may be expressed1 as we shall presently 
see1 in the first figure1 it applies    
indirectly to all4  ,when any process of
 mediate inference appears to have more 
than two premisses1 it will always be   
found that there is more than one       
syllogism4  ,if there are less than     
three propositions1 as in the fallacy of
 'begging the question1' in which the   

conclusion simply reiterates one of the 
premisses1 there is no syllogism at all4
  ,with regard to the second rule1 it is
 plain that any attempted syllogism     
which has more than three terms cannot  
conform to the conditions of any of the 
axioms of mediate inference4   #ehd4    
,the next two rules guard against the   
two fallacies which are fatal to most   
syllogisms whose constitution is        
unsound4   #ehe4  ,the violation of     
,rule #c is known as the ,fallacy of    
,undistributed ,middle4  ,the reason for
 this rule is not far to seek4 ,for if  
the middle term is not used in either   
premiss in its whole extent1 we may be  
referring to one part of it in one      
premiss and to quite another part of it 
in another1 so that there will be really
 no middle term at all4  ,from such     
premisses as these--    ,all pigs are   
omnivorous1   ,all men are omnivorous1  
it is plain that nothing follows4 ,or   
again1 take these premisses--    ,some  
men are fallible1   ,all ,popes are men4

  ,here it is possible that ',all       
,popes' may agree with precisely that   
part of the term 'man1' of which it is  
not known whether it agrees with        
'fallible' or not4   #ehf4 ,the         
violation of ,rule #d is known as the   
,fallacy of ,illicit ,process4 ,if the  
major term is distributed in the        
conclusion1 not having been distributed 
in the premiss1 we have what is called  
,illicit ,process of the ,major2 if the 
same is the case with the minor term1 we
 have ,illicit ,process of the ,minor4  
#ehg4 ,the reason for this rule is that 
if a term be used in its whole extent in
 the conclusion1 which was not so used  
in the premiss in which it occurred1 we 
would be arguing from the part to the   
whole4 ,it is the same sort of fallacy  
which we found to underlie the simple   
conversion of an ,a proposition4   #ehh4
 ,take for instance the following--     
,all learned men go mad4   ,john is not 
a learned man4   4'4 ,john will not go  
mad4  ,in the conclusion ',john' is     

excluded from the whole class of persons
 who go mad1 whereas in the premisses1  
granting that all learned men go mad1 it
 has not been said that they are all the
 men who do so4 ,we have here an illicit
 process of the major term4   #ehi4 ,or 
again take the following--    ,all      
,radicals are covetous4   ,all ,radicals
 are poor4   4'4 ,all poor men are      
covetous4  ,the conclusion here is      
certainly not warranted by our          
premisses4 ,for in them we spoke only of
 some poor men1 since the predicate of  
an affirmative proposition is           
undistributed4   #eij4 ,rule #e is      
simply another way of stating the third 
axiom of mediate inference4 ,to know    
that two terms disagree with the same   
third term gives us no ground for any   
inference as to whether they agree or   
disagree with one another1 e4g4         
,ruminants are not oviparous4   ,sheep  
are not oviparous4  ,for ought that can 
be inferred from the premisses1 sheep   
may or may not be ruminants4   #eia4    

,this rule may sometimes be violated in 
appearance1 though not in reality4 ,for 
instance1 the following is perfectly    
legitimate reasoning4    ,no remedy for 
corruption is effectual that does not   
render it   useless4   ,nothing but the 
ballot renders corruption useless4      
4'4 ,nothing but the ballot is an       
effectual remedy for corruption4  ,but  
on looking into this we find that there 
are four terms--    ,no not-,a is ,b4   
,no not-,c is ,a4   4'4 ,no not-,c is   
,b4  ,the violation of ,rule #e is here 
rendered possible by the additional     
violation of ,rule #b4 ,in order to have
 the middle term the same in both       
premisses we are obliged to make the    
minor affirmative1 thus    ,no not-,a is
 ,b4   ,all not-,c is not-,a4   4'4 ,no 
not-,c is ,b4    ,no remedy that fails  
to render corruption useless is         
effectual4   ,all but the ballot fails  
to render corruption useless4   4'4     
,nothing but the ballot is effectual4   
#eib4 ,rule #f declares that1 if one    

premiss be negative1 the conclusion must
 be negative4 ,now in compliance with   
,rule #e1 if one premiss be negative1   
the other must be affirmative4 ,we have 
therefore the case contemplated in the  
second axiom1 namely1 of one term       
agreeing and the other disagreeing with 
the same third term2 and we know that   
this can only give ground for a         
judgement of disagreement between the   
two terms themselves--in other words1 to
 a negative conclusion4   #eic4 ,rule #g
 declares that1 if the conclusion be    
negative1 one of the premisses must be  
negative2 but1 if the conclusion be     
affirmative1 both premisses must be     
affirmative4 ,it is plain from the      
axioms that a judgement of disagreement 
can only be elicited from a judgement of
 agreement combined with a judgement of 
disagreement1 and that a judgement of   
agreement can result only from two prior
 judgements of agreement4   #eid4 ,the  
seven rules already treated of are      
evident by their own light1 being of the

 nature of definitions and axioms3 but  
the two remaining rules1 which deal with
 particular premisses1 admit of being   
proved from their predecessors4   #eie4 
,proof of ,rule #h4--,that two          
particular premisses prove nothing4  ,we
 know by ,rule #e that both premisses   
cannot be negative4 ,hence they must be 
either both affirmative1 ,,ii1 or one   
affirmative and one negative1 ,,io or   
,,oi4  ,now ,,ii premisses do not       
distribute any term at all1 and         
therefore the middle term cannot be     
distributed1 which would violate ,rule  
#c4  ,again in ,,io or ,,oi premisses   
there is only one term distributed1     
namely1 the predicate of the ,o         
proposition4  ,but ,rule #c requires    
that this one term should be the middle 
term4 ,therefore the major term must be 
undistributed in the major premiss4 ,but
 since one of the premisses is negative1
 the conclusion must be negative1 by    
,rule #f4 ,and every negative           
proposition distributes its predicate4  

,therefore the major term must be       
distributed where it occurs as predicate
 of the conclusion4 ,but it was not     
distributed in the major premiss4       
,therefore in drawing any conclusion we 
violate ,rule #d by an illicit process  
of the major term4   #eif4 ,proof of    
,rule #i4--,that1 if one premiss be     
particular1 the conclusion must be      
particular4  ,two negative premisses    
being excluded by ,rule #e1 and two     
particular by ,rule #h1 the only pairs  
of premisses we can have are--    ,,ai1 
,,ao1 ,,ei4  ,of course the particular  
premiss may precede the universal1 but  
the order of the premisses will not     
affect the reasoning4  ,,ai premisses   
between them distribute one term only4  
,this must be the middle term by ,rule  
#c4 ,therefore the conclusion must be   
particular1 as its subject cannot be    
distributed1  ,,ao and ,,ei premisses   
each distribute two terms1 one of which 
must be the middle term by ,rule #c3 so 
that there is only one term left which  

may be distributed in the conclusion4   
,but the conclusion must be negative by 
,rule #d4 ,therefore its predicate must 
be distributed4 ,hence its subject      
cannot be so4 ,therefore the conclusion 
must be particular4   #eig4 ,rules #f   
and #i are often lumped together in a   
single expression--',the conclusion must
 follow the weaker part1' negative being
 considered weaker than affirmative1 and
 particular than universal4   #eih4 ,the
 most important rules of syllogism are  
summed up in the following mnemonic     
lines1 which appear to have been        
perfected1 though not invented1 by a    
medival logician known as ,petrus       
,hispanus1 who was afterwards raised to 
the ,papal ,chair under the title of    
,pope ,john ,,xxi1 and who died in      
#abgg--    ,distribuas medium1 nec      
quartus terminus adsit2   ,utraque nec  
praemissa negans1 nec particularis2     
,sectetur partem conclusio deteriorem1  
,et non distribuat1 nisi cum praemissa1 
negetve4     ,,chapter ,,xii4  ,of the  

,determination of the ,legitimate ,moods
 of ,syllogism4    #eii4 ,it will be    
remembered that there were found to be  
#fd possible moods1 each of which might 
occur in any of the four figures1 giving
 us altogether #bef possible varieties  
of syllogism4 ,the task now before us is
 to determine how many of these         
combinations of mood and figure are     
legitimate4   #fjj4 ,by the application 
of the preceding rules we are enabled to
 reduce the #fd possible moods to #aa   
valid ones4  ,this may be done by a     
longer or a shorter method4 ,the longer 
method1 which is perhaps easier of      
comprehension1 is to write down the #fd 
possible moods1 and then strike out such
 as violate any of the rules of         
syllogism4     ,,aaa   -,,aea-  -,,aia- 
-,,aoa-   -,,aae-   ,,aee   -,,aie-     
-,,aoe-    ,,aai   -,,aei-   ,,aii      
-,,aoi-   -,,aao-   ,,aeo   -,,aio-     
,,aoo    -,,eaa-  -,,eea-  -,,eia-      
-,,eoa-    ,,eae   -,,eee-  -,,eie-     
-,,eoe-   -,,eai-  -,,eei-  -,,eii-     

-,,eoi-    ,,eao   -,,eeo-   ,,eio      
-,,eoo-  ,illustration   #fja4 ,the     
batches which are crossed are those in  
which the premisses can yield no        
conclusion at all1 owing to their       
violating ,rule #f or #i2 in the rest   
the premises are legitimate1 but a wrong
 conclusion is drawn from each of them  
as are translineated4   #fjb4 ,,ieo     
stands alone1 as violating ,rule #d4    
,this may require a little explanation4 
,since the conclusion is negative1 the  
major term1 which is its predicate1 must
 be distributed4 ,but the major premiss1
 being #a1 does not distribute either   
subject or predicate4 ,hence ,,ieo must 
always involve an illicit process of the
 major4   #fjc4 ,the ,,ii moods which   
have been left valid1 after being tested
 by the syllogistic rules1 are as       
follows--    ,,aaa4  ,,aai4  ,,aee4     
,,aeo4  ,,aii4  ,,aoo4   ,,eae4  ,,eao4 
,,eio4   ,,iai4   ,,oao4   #fjd4 ,we    
will now arrive at the same result by a 
shorter and more scientific method4     

,this method consists in first          
determining what pairs of premisses are 
valid in accordance with ,rules #f and  
g1 and then examining what conclusions  
may be legitimately inferred from them  
in accordance with the other rules of   
syllogism4   #fje4 ,the major premiss   
may be either ,a1 ,e1 ,i or ,o4  ,if it 
is ,a1 the minor also may be either ,a1 
,e1 ,i or ,o4 ,if it is ,e1 the minor   
can only be ,a or ,i4 ,if it is ,i1 the 
minor can only be ,a or ,e4 ,if it is   
,o1 the minor can only be ,a4  ,hence   
there result #i valid pairs of          
premisses4    ,,aa4  ,,ae4  ,,ai4  ,,ao4
   ,,ea4  ,,ei4   ,,ia4  ,,ie4   ,,oa4  
,three of these pairs1 namely ,,aa1     
,,ae1 ,,ea1 yield two conclusions       
apiece1 one universal and one           
particular1 which do not violate any of 
the rules of syllogism2 one of them1    
,,ie1 yields no conclusion at all2 the  
remaining five have their conclusion    
limited to a single proposition1 on the 
principle that the conclusion must      

follow the weaker part4 ,hence we arrive
 at the same result as before1 of ,,ii  
legitimate moods--    ,,aaa4   ,,aai4   
,,aee4   ,,aeo4   ,,eae4   ,,eao4       
,,aii4   ,,aoo4   ,,eio4   ,,iai4       
,,oao4      ,,chapter ,,xiii4  ,of the  
,special ,rules of the ,four ,figures4  
#fjf4 ,our next task must be to         
determine how far the #aa moods which we
 arrived at in the last chapter are     
valid in the four figures4 ,but before  
this can be done1 we must lay down the  
,special ,rules of the ,four ,figures4  
,,figure #a4    ,rule #a1 ,the minor    
premiss must be affirmative4    ,rule   
#b4 ,the major premiss must be          
universal4     ,,figure ,,ii4    ,rule  
#a4 ,one or other premiss must be       
negative4    ,rule #b4 ,the conclusion  
must be negative4    ,rule #c4 ,the     
major premiss must be universal4        
,,figure ,,iii4    ,rule #a4 ,the minor 
premiss must be affirmative4    ,rule   
#b4 ,the conclusion must be particular4 
,,figure ,,iv4    ,rule #a4 ,when the   

major premiss is affirmative1 the minor 
must be   universal4    ,rule #b4 ,when 
the minor premiss is particular1 the    
major must be   negative4    ,rule #c1  
,when the minor premiss is affirmative1 
the conclusion must   be particular4    
,rule #d4 ,when the conclusion is       
negative1 the major premiss must be     
universal4    ,rule #e4 ,the conclusion 
cannot be a universal affirmative4      
,rule #f4 ,neither of the premisses can 
be a particular negative4    #fjg4 ,the 
special rules of the first figure are   
merely a reassertion in another form of 
the ,dictum de ,omni et ,nullo4 ,for if 
the major premiss were particular1 we   
should not have anything affirmed or    
denied of a whole class2 and if the     
minor premiss were negative1 we should  
not have anything declared to be        
contained in that class4 ,nevertheless  
these rules1 like the rest1 admit of    
being proved from the position of the   
terms in the figure1 combined with the  
rules for the distribution of terms 7   

#bic74    ,proof of the ,special ,rules 
of the ,four ,figures4   ,,figure #a4   
#fjh4 ,proof of ,rule #a4--,the minor   
premiss must be affirmative4    ,b--,a  
,c--,b   ,c--,a  ,if possible1 let the  
minor premiss be negative4 ,then the    
major must be affirmative 7by ,rule #e71
 ,footnote3 ,this refers to the ,general
 ,rules of ,syllogism4 and the          
conclusion must be negative 7by ,rule   
#f74 ,but the major being affirmative1  
its predicate is undistributed2 and the 
conclusion being negative1 its predicate
 is distributed4 ,now the major term is 
in this figure predicate both in the    
major premiss and in the conclusion4    
,hence there results illicit process of 
the major term4 ,therefore the minor    
premiss must be affirmative4   #fji4    
,proof of ,rule #b4--,the major premiss 
must be universal4  ,since the minor    
premiss is affirmative1 the middle term1
 which is its predicate1 is             
undistributed there4 ,therefore it must 
be distributed in the major premiss1    

where it is subject4 ,therefore the     
major premiss must be universal4        
,,figure ,,ii4   #faj4 ,proof of ,rule  
#a1--,one or other premiss must be      
negative4    ,a--,b   ,c--,b   ,c--,a   
,the middle term being predicate in both
 premisses1 one or other must be        
negative2 else there would be           
undistributed middle4   #faa4 ,proof of 
,rule #b4--,the conclusion must be      
negative4  ,since one of the premisses  
is negative1 it follows that the        
conclusion also must be so 7by ,rule    
#f74   #fab4 ,proof of ,rule #c4--,the  
major premiss must be universal4  ,the  
conclusion being negative1 the major    
term will there be distributed4 ,but the
 major term is subject in the major     
premiss4 ,therefore the major premiss   
must be universal 7by ,rule #d74        
,,figure ,,iii4   #fac4 ,proof of ,rule 
#a4--,the minor premiss must be         
affirmative4    ,b--,a   ,b--,c   ,c--,a
  ,the proof of this rule is the same as
 in the first figure1 the two figures   

being alike so far as the major term is 
concerned4   #fad4 ,proof of ,rule      
#b4--,the conclusion must be particular4
  ,the minor premiss being affirmative1 
the minor term1 which is its predicate1 
will be undistributed there4 ,hence it  
must be undistributed in the conclusion 
7by ,rule #d74  ,therefore the          
conclusion must be particular4          
,,figure ,,iv4   #fae4 ,proof of ,rule  
,i4--,when the major premiss is         
affirmative1 the minor must be          
universal4  ,if the minor were          
particular1 there would be undistributed
 middle4 ,footnote3 ,shorter proofs are 
employed in this figure1 as the student 
is by this time familiar with the method
 of procedure4   #faf4 ,proof of ,rule  
#b4--,when the minor premiss is         
particular1 the major must be negative4 
,a--,b   ,b--,c   ,c--,a  ,this rule is 
the converse of the preceding1 and      
depends upon the same principle4   #fag4
 ,proof of ,rule #c4--,when the minor   
premiss is affirmative1 the conclusion  

must be particular4  ,if the conclusion 
were universal1 there would be illicit  
process of the minor4   #fah4 ,proof of 
,rule #d4--,when the conclusion is      
negative1 the major premiss must be     
universal4  ,if the major premiss were  
particular1 there would be illicit      
process of the major4   #fai4 ,proof of 
,rule #e4--,the conclusion ,,cannot be  
,a ,,universal affirmative4  ,the       
conclusion being affirmative1 the       
premisses must be so too 7by ,rule #g74 
,therefore the minor term is            
undistributed in the minor premiss1     
where it is predicate4 ,hence it cannot 
be distributed in the conclusion 7by    
,rule #d74  ,therefore the affirmative  
conclusion must be particular4   #fbj4  
,proof of ,rule #f4--,neither of the    
premisses can lie a1 ,,particular       
,,negative4  ,if the major premiss were 
a particular negative1 the conclusion   
would be negative4 ,therefore the major 
term would be distributed in the        
conclusion4 ,but the major premiss being

 particular1 the major term could not be
 distributed there4 ,therefore we should
 have an illicit process of the major   
term4  ,if the minor premiss were a     
particular negative1 then1 since the    
major must be affirmative 7by ,rule #e71
 we should have undistributed middle4   
,,chapter ,,xiv  ,of the ,determination 
of the ,moods that are valid in the     
,four ,figures4    #fba4 ,by applying   
the special rules just given we shall be
 able to determine how many of the      
eleven legitimate moods are valid in the
 four figures4  #fbb4 ,these eleven     
legitimate moods were found to be       
,,aaa4  ,,aai4  ,,aee4  ,,aeo4  ,,aii4  
,,aoo4  ,,eae4   ,,eao4  ,,eio4  ,,iai4 
,,oao4   ,,figure #a4   #fbc4 ,the rule 
that the major premiss must be universal
 excludes the last two moods1 ,,iai1    
,,oao4 ,the rule that the minor premiss 
must be affirmative excludes three more1
 namely1 ,,aee1 ,,aeo1 ,,aoo4  ,thus we 
are left with six moods which are valid 
in the first figure1 namely1    ,,aaa4  

,,eae4  ,,aii4  ,,eio4  ,,aai4  ,,eao4  
,,figure ,,ii4   #fbd4 ,the rule that   
one premiss must be negative excludes   
four moods1 namely1 ,,aaa1 ,,aai1 ,,aii1
 ,,iai4 ,the rule that the major must be
 universal excludes ,,oao4 ,thus we are 
left with six moods which are valid in  
the second figure1 namely1    ,,eae4    
,,aee4  ,,eio4  ,,aoo4  ,,eao4  ,,aeo4  
,,figure ,,iii4   #fbe4 ,the rule that  
the conclusion must be particular       
confines us to eight moods1 two of      
which1 namely ,,aee and ,,aoo1 are      
excluded by the rule that the minor     
premiss must be affirmative4  ,thus we  
are left with six moods which are valid 
in the third figure1 namely1    ,,aai4  
,,iai4  ,,aii4  ,,eao4  ,,oao4  ,,eio4  
,,figure ,,iv4   #fbf4 ,the first of the
 eleven moods1 ,,aaa1 is excluded by the
 rule that the conclusion cannot be a   
universal affirmative4  ,two more moods1
 namely ,,aoo and ,,oao1 are excluded by
 the rule that neither of the premisses 
can be a particular negative4  ,,aii    

violates the rule that when the major   
premiss is affirmative1 the minor must  
be universal4  ,,eae violates the rule  
that1 when the minor premiss is         
affirmative1 the conclusion must be     
particular4  ,thus we are left with six 
moods which are valid in the fourth     
figure1 namely1    ,,aai4  ,,aee4       
,,iai4  ,,eao4  ,,eio4  ,,aeo4   #fbg4  
,thus the #bef possible forms of        
syllogism have been reduced to two dozen
 legitimate combinations of mood and    
figure1 six moods being valid in each of
 the four figures4    ,,figure ,i4      
,,aaa4  ,,eae4  ,,aii4  ,,eio4  7,,aai4 
,,eao47    ,,figure ,,ii4  ,,eae4       
,,aee4  ,,eio4  ,,ago4  7,,eao4  ,,aeo47
    ,,figure ,,iii4 ,,aai4  ,,iai4      
,,aii4  ,,eao4   ,,oao4  ,,eio4         
,,figure ,,iv4  ,,aai4  ,,aee4  ,,iai4  
,,eao4   ,,eio4 7,,aeo47   #fbh4 ,the   
five moods enclosed in brackets1 though 
valid1 are useless4 ,for the conclusion 
drawn is less than is warranted by the  
premisses4 ,these are called ,subaltern 

,moods1 because their conclusions might 
be inferred by subalternation from the  
universal conclusions which can justly  
be drawn from the same premisses4 ,thus 
,,aai is subaltern to ,,aaa1 ,,eao to   
,,eae1 and so on with the rest4   #fbi4 
,the remaining #ai combinations of mood 
and figure1 which are loosely called    
'moods1' though in strictness they      
should be called 'figured moods1' are   
generally spoken of under the names     
supplied by the following mnemonics--   
,barbara1 ,celarent1 ,darii1 ,ferioque  
prioris2   ,cesare1 ,camestres1         
,festino1 ,baroko secund2   ,tertia     
,darapti1 ,disamis1 ,datisi1 ,felapton1 
,bokardo1 ,ferison habet2 ,quarta       
insuper addit   ,bramantip1 ,camenes1   
,dimaris1 ,fesapo1 ,fresison3   ,quinque
 ,subalterni1 totidem ,generalibus orti1
   ,nomen habent nullum1 nee1 si bene   
colligis1 usum4   #fcj4 ,the vowels in  
these lines indicate the letters of the 
mood4 ,all the special rules of the four
 figures can be gathered from an        

inspection of them4 ,the following      
points should be specially noted4  ,the 
first figure proves any kind of         
conclusion1 and is the only one which   
can prove ,a4  ,the second figure proves
 only negatives4  ,the third figure     
proves only particulars4  ,the fourth   
figure proves any conclusion except ,a4 
#fca4 ,the first figure is called the   
,perfect1 and the rest the ,imperfect   
figures4 ,the claim of the first to be  
regarded as the perfect figure may be   
rested on these grounds--    #a4 ,it    
alone conforms directly to the ,dictum  
de ,omni et ,nullo4    #b4 ,it suffices 
to prove every kind of conclusion1 and  
is the only   figure in which a         
universal affirmative proposition can be
   established4    #c4 ,it is only in a 
mood of this figure that the major1     
middle and   minor terms are to be found
 standing in their relative order of    
extension4   #fcb4 ,the reason why a    
universal affirmative1 which is of      
course infinitely the most important    

form of proposition1 can only be proved 
in the first figure may be seen as      
follows4  ,proof that ,a can only be    
established in figure ,i4  ,an ,a       
conclusion necessitates both premisses  
being ,a propositions 7by ,rule #g74    
,but the minor term is distributed in   
the conclusion1 as being the subject of 
an ,a proposition1 and must therefore be
 distributed in the minor premiss1 in   
order to which it must be the subject4  
,therefore the middle term must be the  
predicate and is consequently           
undistributed4 ,in order therefore that 
the middle term may be distributed1 it  
must be subject in the major premiss1   
since that also is an ,a proposition4   
,but when the middle term is subject in 
the major and predicate in the minor    
premiss1 we have what is called the     
first figure4     ,,chapter ,,xv4  ,of  
the ,special ,canons of the ,four       
,figures4    #fcc4 ,so far we have given
 only a negative test of legitimacy1    
having shown what moods are not         

invalidated by running counter to any of
 the special rules of the four figures4 
,we will now lay down special canons for
 the four figures1 conformity to which  
will serve as a positive test of the    
validity of a given mood in a given     
figure4 ,the special canon of the first 
figure--will of course be practically   
equivalent to the ,dictum de ,omni et   
,nullo4 ,all of them will be expressed  
in terms of extension1 for the sake of  
perspicuity4    ,special ,canons of the 
,four ,figures4   ,,figure #a4   #fcd4  
,,canon4 ,if one term wholly includes or
 excludes another1 which wholly or      
partly includes a third1 the first term 
wholly or partly includes or excludes   
the third4  ,here four cases arise--    
,illustration    7#a7 ,total inclusion  
7,barbara74    ,all ,b is ,a4   ,all ,c 
is ,b4   4'4 ,all ,c is ,a4             
,illustration    7#b7 ,partial inclusion
 7,darii74    ,all ,b is ,a4   ,some ,c 
is ,b4   4'4 ,some ,c is ,a4            
,illustration    7#c7 ,total exclusion  

7,celarent74    ,no ,b is ,a4   ,all ,c 
is ,b4   4'4 ,no ,c is ,a4              
,illustration    7#d7 ,partial exclusion
 7,ferio74    ,no ,b is ,a4   ,some ,c  
is ,b4   4'4 ,some ,c is not ,a4        
,,figure ,,ii4   #fce4 ,,canon4 ,if one 
term is excluded from another1 which    
wholly or partly includes a third1 or is
 included in another from which a third 
is wholly or partly excluded1 the first 
is excluded from the whole or part of   
the third4  ,here we have four cases1   
all of exclusion--    7#a7 ,total       
exclusion on the ground of inclusion in 
an excluded term   7,cesare74           
,illustration      ,no ,a is ,b4        
,all ,c is ,b4     4'4 ,no ,c is ,a4    
7#b7 ,partial exclusion on the ground of
 a similar partial inclusion            
7,festino74      ,illustration      ,no 
,a is ,b4     ,some ,c is ,b4     4'4   
,some ,c is not ,a4    7#c7 ,total      
exclusion on the ground of exclusion    
from an including   term 7,camestres74  
,illustration      ,all ,a is ,b4       

,no ,c is ,b4     4'4 ,no ,c is ,a4     
7#d7 ,partial exclusion on the ground of
 a similar partial exclusion            
7,baroko74      ,illustration      ,all 
,a is ,b4     ,some ,c is not ,b4       
4'4 ,some ,c is not ,a4    ,,figure     
,,iii4   #fcf4 ,,canon4 ,if two terms   
include another term in common1 or if   
the first includes the whole and the    
second a part of the same term1 or vice 
vers1 the first of these two terms      
partly includes the second2 and if the  
first is excluded from the whole of a   
term which is wholly or in part included
 in the second1 or is excluded from part
 of a term which is wholly included in  
the second1 the first is excluded from  
part of the second4  ,here it is evident
 from the statement that six cases      
arise--    7#a7 ,total inclusion of the 
same term in two others   7,darapti74   
,illustration      ,all ,b is ,a4       
,all ,b is ,c4     4'4 some ,c is ,a4   
7#b7 ,total inclusion in the first and  
partial inclusion   in the second       

7,datisi74      ,illustration      ,all 
,b is ,a4     ,some ,b is ,c4     4'4   
some ,c is ,a4    7#c7 ,partial         
inclusion in the first and total        
inclusion in   the second 7,disamis74   
,illustration      ,some ,b is ,a4      
,all ,b is ,c4     4'4 some ,c is ,a4   
7#d7 ,total exclusion of the first from 
a term which is   wholly included in the
 second 7,felapton74      ,illustration 
,no ,b is ,a4     ,all ,b is ,c4     4'4
 some ,c is not ,a4    7#e7 ,total      
exclusion of the first from a term which
 is   partly included in the second     
7,ferison74      ,illustration      ,no 
,b is ,a4     ,some ,b is ,c4     4'4   
some ,c is not ,a4    7#f7 ,exclusion of
 the first from part of a term which    
is wholly included in the second        
7,bokardo74      ,illustration          
,some ,b is not ,a4     ,all ,b is ,c4  
4'4 ,some ,c is not ,a4    ,,figure     
,,iv4   #fcg4 ,,canon4 ,if one term is  
wholly or partly included in another    
which is wholly included in or excluded 

from a third1 the third term wholly or  
partly includes the first1 or1 in the   
case of total inclusion1 is wholly      
excluded from it2 and if a term is      
excluded from another which is wholly or
 partly included in a third1 the third  
is partly excluded from the first4      
,here we have five cases--    7#a7 ,of  
the inclusion of a whole term           
7,bramsntip74      ,illustration        
,all ,a is ,b4     ,all ,b is ,c4       
4'4 ,some ,c is 7all7 ,a4    7#b7 ,of   
the inclusion of part of a term         
7,,dimaris74      ,illustration         
,some ,a is ,b4     ,all ,b is ,c4      
4'4 ,some ,c is 7some7 ,a1    7#c7 ,of  
the exclusion of a whole term           
7,camenes74      ,illustration      ,all
 ,a is ,b4     ,no ,b is ,c4     4'4 ,no
 ,c is ,a4    7#d7 ,partial exclusion on
 the ground of including   the whole of 
an excluded term 7,fesapo74             
,illustration      ,no ,a is ,b4        
,all ,b is ,c4     4'4 ,some ,c is not  
,a4    7#e7 ,partial exclusion on the   

ground of including   part of an        
excluded term 7,fresison74              
,illustration      ,no ,a is ,b4        
,some ,b is ,c4     4'4 ,some ,c is not 
,a4   #fch4 ,it is evident from the     
diagrams that in the subaltern moods the
 conclusion is not drawn directly from  
the premisses1 but is an immediate      
inference from the natural conclusion4  
,take for instance ,,aai in the first   
figure4 ,the natural conclusion from    
these premisses is that the minor term  
,c is wholly contained in the major term
 ,a4 ,but instead of drawing this       
conclusion we go on to infer that       
something which is contained in ,c1     
namely some ,c1 is contained in ,a4     
,illustration    ,all ,b is ,a4   ,all  
,c is ,b4   4'4 all ,c is ,a4   4'4 some
 ,c is ,a4  ,similarly in ,,eao in      
figure #a1 instead of arguing that the  
whole of ,c is excluded from ,a1 we draw
 a conclusion which really involves a   
further inference1 namely that part of  
,c is excluded from ,a4    ,illustration

    ,no ,b is ,a4   ,all ,c is ,b4   4'4
 no ,c is ,a4   4'4 some ,c is not ,a4  
#fci4 ,the reason why the canons have   
been expressed in so cumbrous a form is 
to render the validity of all the moods 
in each figure at once apparent from the
 statement4 ,for purposes of general    
convenience they admit of a much more   
compendious mode of expression4   #fdj4 
,the canon of the first figure is known 
as the ,dictum de ,omni et ,nullo--     
,what is true 7distributively7 of a     
whole term is true of all that it       
includes4   #fda4 ,the canon of the     
second figure is known as the ,dictum de
 ,diverse--    ,if one term is contained
 in1 and another excluded from a third  
term1   they are mutually excluded4     
#fdb4 ,the canon of the third figure is 
known as the ,dictum de ,exemplo et de  
,excepto--    ,two terms which contain a
 common part partly agree1 or1 if one   
contains a part which the other does    
not1 they partly differ4   #fdc4 ,the   
canon of the fourth figure has had no   

name assigned to it1 and does not seem  
to admit of any simple expression4      
,another mode of formulating it is as   
follows3--    ,whatever is affirmed of a
 whole term may have partially affirmed 
of   it whatever is included in that    
term 7,bramantip1 ,dimaris71 and        
partially denied of it whatever is      
excluded 7,fesapo72 whatever is         
affirmed of part of a term may have     
partially denied of it whatever   is    
wholly excluded from that term          
7,fresison72 and whatever is denied   of
 a whole term may have wholly denied of 
it whatever is wholly   included in that
 term 7,camenes74   #fdd4 ,from the     
point of view of intension the canons of
 the first three figures may be         
expressed as follows4   #fde4 ,canon of 
the first figure4 ,dictum de ,omni et   
,nullo--    ,an attribute of an         
attribute of anything is an attribute of
 the   thing itself4   #fdf4 ,canon of  
the second figure4 ,dictum de ,diverso--
    ,if a subject has an attribute which

 a class has not1 or vice versa1   the  
subject does not belong to the class4   
#fdg4 ,canon of the third figure4    #a4
 ,dictum de ,exemplo--      ,if a       
certain attribute can be affirmed of any
 portion of the     members of a class1 
it is not incompatible with the         
distinctive     attributes of that      
class4    #b4 ,dictum de ,excepto--     
,if a certain attribute can be denied of
 any portion of the members     of a    
class1 it is not inseparable from the   
distinctive attributes     of that      
class4     ,,chapter ,,xvi4  ,of the    
,special ,uses of the ,four ,figures4   
#fdh4 ,the first figure is useful for   
proving the properties of a thing4      
#fdi4 ,the second figure is useful for  
proving distinctions between things4    
#fej4 ,the third figure is useful for   
proving instances or exceptions4   #fea4
 ,the fourth figure is useful for       
proving the species of a genus4         
,,figure #a4   #feb4    ,b is or is not 
,a4   ,c is ,b4   4'4 ,c is or is not   

,a4  ,we prove that ,c has or has not   
the property ,a by predicating of it ,b1
 which we know to possess or not to     
possess that property4    ,luminous     
objects are material4   ,comets are     
luminous4   4'4 ,comets are material4   
,no moths are butterflies4   ,the       
,death's head is a moth4   4'4 ,the     
,death's head is not a butterfly4       
,,figure ,,ii4   #fec4    ,a is ,b4 ,a  
is not ,b4   ,c is not ,b4 ,c is ,b4    
4'4 ,c is not ,a4 4'4 ,c is not ,a4  ,we
 establish the distinction between ,c   
and ,a by showing that ,a has an        
attribute which ,c is devoid of1 or is  
devoid of an attribute which ,c has4    
,all fishes are cold-blooded4   ,a whale
 is not cold-blooded4   4'4 ,a whale is 
not a fish4    ,no fishes give milk4    
,a whale gives milk4   4'4 ,a whale is  
not a fish4  ,,figure ,,iii4   #fed4    
,b is ,a4 ,b is not ,a4   ,b is ,c4 ,b  
is ,c4   4'4 ,some ,c is ,a4 4'4 ,some  
,c is not ,a4  ,we produce instances of 
,c being ,a by showing that ,c and ,a   

meet1 at all events partially1 in ,b4   
,thus if we wish to produce an instance 
of the compatibility of great learning  
with original powers of thought1 we     
might say    ,sir ,william ,hamilton was
 an original thinker4   ,sir ,william   
,hamilton was a man of great learning4  
4'4 ,some men of great learning are     
original thinkers4  ,or we might urge an
 exception to the supposed rule about   
,scotchmen being deficient in humour    
under the same figure1 thus--    ,sir   
,walter ,scott was not deficient in     
humour4   ,sir ,walter ,scott was a     
,scotchman4   4'4 ,some ,scotchmen are  
not deficient in humour4  ,,figure ,,iv4
   #fee4    ,all ,a is ,b1 ,no ,a is ,b4
   ,all ,b is ,c4 ,all ,b is ,c4   4'4  
,some ,c is ,a 4'4,some ,c is not ,a4   
,we show here that ,a is or is not a    
species of ,c by showing that ,a falls1 
or does not fall1 under the class ,b1   
which itself falls under ,c4 ,thus--    
,all whales are mammals4   ,all mammals 
are warm-blooded4   4'4 ,some           

warm-blooded animals are whales4   ,no  
whales are fishes4   ,all fishes are    
cold-blooded4   4'4 ,some cold-blooded  
animals are not whales4     ,,chapter   
,,xvii4  ,of the ,syllogism with three  
figures4   #fef4 ,it will be remembered 
that in beginning to treat of figure 7  
#efe7 we pointed out that there were    
either four or three ligures possible   
according as the conclusion was assumed 
to be known or not4 ,for1 if the        
conclusion be not known1 we cannot      
distinguish between the major and the   
minor term1 nor1 consequently1 between  
one premiss and another4 ,on this view  
the first and the fourth figures are the
 same1 being that arrangement of the    
syllogism in which the middle term      
occupies a different position in one    
premiss from what it does in the other4 
,we will now proceed to constitute the  
legitimate moods and figures of the     
syllogism irrespective of the           
conclusion4   #feg4 ,when the conclusion
 is set out of sight1 the number of     

possible moods is the same as the number
 of combinations that can be made of the
 four things1 ,a1 ,e1 ,i1 ,o1 taken two 
together1 without restriction as to     
repetition4 ,these are the following    
#af3--    ,,aa   ,,ea   ,,ia   ,,oa     
,,ae  -,,ee-  ,,ie  -,,oe-   ,,ai   ,,ei
  -,,ii- -,,oi-   ,,ao  -,,eo- -,,io-   
-,,oo-  of which seven may be neglected 
as violating the general rules of the   
syllogism1 thus leaving us with nine    
valid moods--    ,,aa4  ,,ae4  ,,ai4    
,,ao4  ,,ea4  ,,ei4  ,,ia4  ,,ie4  ,,oa4
   #feh4 ,we will now put these nine    
moods successively into the three       
figures4 ,by so doing it will become    
apparent how far they are valid in each4
   #fei4 ,let it be premised that       
when the extreme in the premiss that    
stands first is predicate in   the      
conclusion1 we are said to have a       
,direct ,mood2    when the extreme in   
the premiss that stands second is       
predicate in   the conclusion1 we are   
said to have an ,indirect ,mood4   #ffj4

 ,,figure #a4    ,mood ,,aa4   ,all ,b  
is ,a4   ,all ,c is ,b4   4'4 ,all ,c is
 ,a1 or ,some ,a is ,c1 7,barbara       
,bramantip74    ,mood ,,ae4   ,all ,b is
 ,a4   ,no ,c is ,b4   4'4 ,illicit     
,process1 or ,some ,a is not ,c1        
7,fesapo74    ,mood ,,ai4   ,all ,b is  
,a4   ,some ,c is ,b4   4'4 ,some ,c is 
,a1 or ,some ,a is ,c4 7,darii          
,disamis74    ,mood ,,ao4   ,all ,b is  
,a4   ,some ,c is not ,b4   4'4 ,illicit
 ,process1 7,ferio74    ,mood ,,ea4     
,no ,b is ,a4   ,all ,c is ,b4   4'4 ,no
 ,c is ,a1 or ,no ,a is ,c1 7,celarent  
,camenes74    ,mood ,,ei4   ,no ,b is   
,a4   ,some ,c is ,b4   4'4 ,some ,c is 
not ,a1 or ,illicit ,process4    ,mood  
,,ia4   ,some ,b is ,a4   ,all ,c is ,b4
   4'4 ,undistributed ,middle4    ,mood 
,,ie4   ,some ,b is ,c4 ,some ,b is not 
,a4   ,no ,a is ,b4 ,all ,c is ,b4   4'4
 ,illicit ,process1 or ,some ,c is not  
,a1 7,fresison74    ,mood ,,oa4   ,some 
,b is not ,a4   ,all ,c is ,b4   4'4    
,undistributed ,middle4   #ffa4 ,thus we

 are left with six valid moods1 which   
yield four direct conclusions and five  
indirect ones1 corresponding to the four
 moods of the original first figure and 
the five moods of the original fourth1  
which appear now as indirect moods of   
the first figure4   #ffb4 ,but why1 it  
maybe asked1 should not the moods of the
 first figure equally well be regarded  
as indirect moods of the fourth8 ,for   
this reason-that all the moods of the   
fourth figure can be elicited out of    
premisses in which the terms stand in   
the order of the first1 whereas the     
converse is not the case4 ,if1 while    
retaining the quantity and quality of   
the above premisses1 i4 e4 the mood1 we 
were in each case to transpose the      
terms1 we should find that we were left 
with five valid moods instead of six1   
since ,,ai in the reverse order of the  
terms involves undistributed middle2    
and1 though we should have ,celarent    
indirect to ,camenes1 and ,darii to     
,dimaris1 we should never arrive at the 

conclusion of ,barbara or have anything 
exactly equivalent to ,ferio4 ,in place 
of ,barbara1 ,bramantip would yield as  
an indirect mood only the subaltern     
,,aai in the first figure4 ,both ,fesapo
 and ,fresison would result in an       
illicit process1 if we attempted to     
extract the conclusion of ,ferio from   
them as an indirect mood4 ,the nearest  
approach we could make to ,ferio would  
be the mood ,,eao in the first figure1  
which may be elicited indirectly from   
the premisses of ,,camenes1 being       
subaltern to ,,celarent4 ,for these     
reasons the moods of the fourth figure  
are rightly to be regarded as indirect  
moods of the first1 and not vice vers4  
#ffc4 ,,figure ,,ii4     ,mood ,,aa4    
,all ,a is ,b4   ,all ,c is ,b4   4'4   
,undistributed ,middle4    ,mood ,,ae4  
,all ,a is ,b4   ,no ,c is ,b4   4'4 ,no
 ,c is ,a1 or ,no ,a is ,c1 7,camestres 
,cesare74    ,mood ,,ai4   ,all ,a is   
,b4   ,some ,c is ,b4   4'4             
,undistributed ,middle4    ,mood ,,ao4  

,all ,a is ,b4   ,some ,c is not ,b4    
4'4 ,some ,c is not ,a1 7,baroko71 or   
,illicit ,process4    ,mood ,,ea4   ,no 
,a is ,b4   ,all ,c is ,b4   4'4 ,no ,c 
is ,a1 or ,no ,a is ,c1 7,cesare        
,carnestres74     ,mood ,,ei   ,no ,a is
 ,b4   ,some ,c is ,b4   4'4 ,some ,c is
 not ,a1 7,festino71 or ,illicit        
,process4    ,mood ,,ia4   ,some ,a is  
,b4   ,all ,c is ,b4   4'4              
,undistributed ,middle4     ,mood ,,ie4 
,some ,a is ,b4    ,no ,c is ,b4    4'4 
,illicit ,process1 or ,some ,a is not   
,c1 7,festino74     ,mood ,,oa4    ,some
 ,a is not ,b4    ,all ,c is ,b4    4'4 
,illicit ,process1 or ,some ,a is not   
,c1 7,baroko74   #ffd4 ,here again we   
have six valid moods1 which yield four  
direct conclusions corresponding to     
,cesare1 ,,carnestres1 ,,festino and    
,,baroko4 ,the same four are repeated in
 the indirect moods4   #ffe4 ,,figure   
,,iii4    ,mood ,,aa4   ,all ,b is ,a4  
,all ,b is ,c4   4'4 ,some ,c is ,a1 or 
,some ,a is ,c1 7,darapti74    ,mood    

,,ae4   ,all ,b is ,a4   ,no ,b is ,c4  
4'4 ,illicit ,process1 or ,some ,a is   
not ,c1 7,felapton74    ,mood ,,ai4     
,all ,b is ,a1   ,some ,b is ,c4   4'4  
,some ,c is ,a1 or ,some ,a is ,c1      
7,datisi  ,disamis74    ,mood ,,ao4     
,all ,b is ,a4   ,some ,b is not ,c4    
4'4 ,illicit ,process1 ,or ,some ,a is  
not ,c1 7,bokardo74    ,mood ,,ea4   ,no
 ,b is ,a4   ,all ,b is ,c4   4'4 ,some 
,c is not ,a1 7,felapton71 or ,illicit  
,process4    ,mood ,,ei4   ,no ,b is ,a4
   ,some ,b is ,c4   4'4 ,some ,c is not
 ,a1 7,ferison71 or ,illicit ,process4  
,mood ,,ia4   ,some ,b is ,a4   ,all ,b 
is ,c4   4'4 ,some ,c is ,a1 ,or ,some  
,a is ,c1 7,disamis  ,datisi74    ,mood 
,,ie4   ,some ,b is ,a4   ,no ,b is ,c4 
4'4 ,illicit ,process1 or ,some ,a is   
not ,c1 7,ferison74    ,mood ,,qa4      
,some ,b is not ,a4   ,all ,b is ,c4    
4'4 ,some ,c is not ,a1 7,bokardo71 or  
,illicit ,process4   #fff4 ,in this     
figure every mood is valid1 either      
directly or indirectly4 ,we have six    

direct moods1 answering to ,darapti1    
,disamis1 ,datisi1 ,felapton1 ,bokardo  
and ,ferison1 which are simply repeated 
by the indirect moods1 except in the    
case of ,darapti1 which yields a        
conclusion not provided for in the      
mnemonic lines4 ,darapti1 though going  
under one name1 has as much right to be 
considered two moods as ,disamis and    
,datisi4     ,,chapter ,,xviii4  ,of    
,reduction4    #ffg4 ,we revert now to  
the standpoint of the old logicians1 who
 regarded the ,dictum de ,omni et ,nullo
 as the principle of all syllogistic    
reasoning4 ,from this point of view the 
essence of mediate inference consists in
 showing that a special case1 or class  
of cases1 comes under a general rule4   
,but a great deal of our ordinary       
reasoning does not conform to this type4
 ,it was therefore judged necessary to  
show that it might by a little          
manipulation be brought into conformity 
with it4 ,this process is called        
,reduction4   #ffh4 ,reduction is of two

 kinds--    7#a7 ,direct or ,ostensive4 
7#b7 ,indirect or ,ad ,impossibile4     
#ffi4 ,the problem of direct1 or        
ostensive1 reduction is this--    ,given
 any mood in one of the imperfect       
figures 7,,ii1 ,,iii and ,,iv7 how   to 
alter the form of the premisses so as to
 arrive at the same   conclusion in the 
perfect figure1 or at one from which it 
can be   immediately inferred4 ,the     
alteration of the premisses is effected 
by   means of immediate inference and1  
where necessary1 of transposition4      
#fgj4 ,the problem of indirect          
reduction1 or reductio 7per deductionem7
 ad impossibile1 is this--,given any    
mood in one of the imperfect figures1 to
 show by means of a syllogism in the    
perfect figure that its conclusion      
cannot be false4   #fga4 ,the object of 
reduction is to extend the sanction of  
the ,dictum de ,omni et ,nullo to the   
imperfect figures1 which do not         
obviously conform to it4   #fgb4 ,the   
mood required to be reduced is called   

the ,reducend2 that to which it         
conforms1 when reduced1 is called the   
,reduct4    ,direct or ,ostensive       
,reduction4    #fgc4 ,in the ordinary   
form of direct reduction1 the only kind 
of immediate inference employed is      
conversion1 either simple or by         
limitation2 but the aid of permutation  
and of conversion by negation and by    
contraposition may also be resorted to4 
#fgd4 ,there are two moods1 ,baroko and 
,bokardo1 which cannot be reduced       
ostensively except by the employment of 
some of the means last mentioned4       
,accordingly1 before the introduction of
 permutation into the scheme of logic1  
it was necessary to have recourse to    
some other expedient1 in order to       
demonstrate the validity of these two   
moods4 ,indirect reduction was therefore
 devised with a special view to the     
requirements of ,baroko and ,bokardo3   
but the method1 as will be seen1 is     
equally applicable to all the moods of  
the imperfect figures4   #fge4 ,the     

mnemonic lines1 ',barbara1 ,celarent1   
etc41 provide complete directions for   
the ostensive reduction of all the moods
 of the second1 third1 and fourth       
figures to the first1 with the exception
 of ,baroko and ,bokardo4 ,the          
application of them is a mere mechanical
 trick1 which will best be learned by   
seeing the process performed4   #fgf4   
,let it be understood that the initial  
consonant of each name of a figured mood
 indicates that the reduct will be that 
mood which begins with the same letter4 
,thus the ,b of ,bramantip indicates    
that ,bramantip1 when reduced1 will     
become ,barbara4   #fgg4 ,where m       
appears in the name of a reducend1 me   
shall have to take as major that premiss
 which before was minor1 and vice       
versa-in other words1 to transpose the  
premisses1 m stands for mutatio or      
metathesis4   #fgh4 s1 when it follows  
one of the premisses of a reducend1     
indicates that the premiss in question  
must be simply converted2 when it       

follows the conclusion1 as in ,disamis1 
it indicates that the conclusion arrived
 at in the first figure is not identical
 in form with the original conclusion1  
but capable of being inferred from it by
 simple conversion4 ,hence s in the     
middle of a name indicates something to 
be done to the original premiss1 while s
 at the end indicates something to be   
done to the new conclusion4   #fgi4 ,p  
indicates conversion per accidens1 and  
what has just been said of s applies1   
mutatis mutandis1 to p4   #fhj4 k may be
 taken for the present to indicate that 
,baroko and ,bokardo cannot be reduced  
ostensively4   #fha4 ,,figure ,,ii4     
,cesare4               _/  ,celarent4   
,no ,a is ,b4          _/   ,no ,b is   
,a4   ,all ,c is ,b4     _/        ,all 
,c is ,b4   4'4 ,no ,c is ,a4 _/        
4'4 ,no ,c is ,a4    ,camestres4        
_/  ,celarent4   ,all ,a is ,b4         
_/   ,no ,b is ,c4   ,no ,c is ,b4      
_/        ,all ,a is ,b4   4'4 ,no ,c is
 ,a4 _/         4'4 ,no ,a is ,c4       

4'4 ,no ,c is ,a4    ,festino4          
,ferio4   ,no ,a is ,b4               _/
 ,no ,b is ,a4   ,some ,c is ,b4        
,some ,c is ,b4   4'4 ,some ,c is not   
,a4_/      4'4 ,some ,c is not ,a4      
,baroko   #fhb4 ,,figure ,,iii4         
,darapti4              _/   ,darii4     
,all ,b is ,a4         _/    ,all ,b is 
,a4   ,all ,b is ,c4       _/           
,some ,c is ,b4   4'4 ,some ,c is ,a4 _/
        ,some ,c is ,a4    ,disamis4    
_/   ,darii4   ,some ,b is ,a4        _/
    ,all ,b is ,c4   ,all ,b is ,c4     
_/       ,some ,a is ,b4   4'4 ,some ,c 
is ,a4 _/        4'4 ,some ,a is ,c4    
4'4 ,some ,c is ,a4    ,datisi4         
_/ ,darii4   ,all ,b is ,a4         _/  
,all ,b is ,a4   ,some ,b is ,c4      _/
     ,some ,c is ,b4   4'4 ,some ,c is  
,a4 _/      4'4 ,some ,c is ,a4         
,felapton4                 _/ ,ferio4   
,no ,b is ,a4              _/  ,no ,b is
 ,a4   ,all ,b is ,c4           _/      
,some ,c is ,b4   4'4 ,some ,c is       
not-,a4 _/      4'4 ,some ,c is not-,a4 

,bokardo4    ,ferison4                  
_/ ,ferio4   ,no ,b is ,a4              
_/  ,no ,b is ,a4   ,some ,b is ,c4     
_/     ,some ,c is ,b   4'4 ,some ,c is 
not ,a4 _/      4'4 ,some ,c is not ,a4 
#fhc4 ,,figure ,,iv4    ,bramantip4     
_/ ,barbara4   ,all ,a is ,b4        _/ 
,all ,b is ,c4   ,all ,b is ,c4      _/ 
,all ,a is ,b4   44 ,some ,c is ,a4 _/  
44 ,all ,a is ,c4                       
4'4 ,some ,c is ,a4    ,camenes         
,celarent   ,all ,a is ,b        _/ ,no 
,b is ,c4   ,no ,b is ,c4        ,all ,a
 is ,b4   44 ,no ,c is ,a4_/      4'4   
,no ,a is ,c4                        4'4
 ,no ,c is ,a4    ,dimaris4             
,darii4   ,some ,a is ,b4         _/    
,all ,b is ,c4   ,all ,b is ,c4         
,some ,a is ,b4   4'4 ,some ,c is ,a4_/ 
4'4 ,some ,a is ,c4                     
4'4 ,some ,c is ,a4    ,fesapo4         
,ferio4   ,no ,a is ,b4               _/
 ,no ,b is ,a4   ,all ,b is ,c4         
,some ,c is ,b4   4'4 ,some ,c is not   
,a4_/      4'4 ,some ,c is not ,a4      

,fresison4                   ,ferio4    
,no ,a is ,b4               _/ ,no ,b is
 ,a4   ,some ,b is ,c4             ,some
 ,c is ,b4   4'4 ,some ,c is not ,a4_/  
4'4 ,some ,c is not ,a4   #fhd4 ,the    
reason why ,baroko and ,bokardo cannot  
be reduced ostensively by the aid of    
mere conversion becomes plain on an     
inspection of them4 ,in both it is      
necessary1 if we are to obtain the first
 figure1 that the position of the middle
 term should be changed in one premiss4 
,but the premisses of both consist of ,a
 and #j propositions1 of which ,a admits
 only of conversion by limitation1 the  
effect of which would be to produce two 
particular premisses1 while #j does not 
admit of conversion at all1  ,it is     
clear then that the #j proposition must 
cease to be #j before we can get any    
further4 ,here permutation comes to our 
aid2 while conversion by negation       
enables us to convert the ,a            
proposition1 without loss of quantity1  
and to elicit the precise conclusion we 

require out of the reduct of ,boltardo4 
7,baroko7 ,fanoao4            ,ferio4   
,all ,a is ,b4              _/ ,no      
not-,b is ,a4   ,some ,c is not-,b4     
,some ,c is not-,b4   4'4 ,some ,c is   
not-,a4_/      4'4 ,some ,c is not-,a4  
7,bokardo7 ,donamon4          ,darii4   
,some ,b is not-,a4         _/ ,all ,b  
is ,c4   ,all ,b is ,c4                 
,some not-,a is ,b   4'4 ,some ,c is    
not-,a4_/      4'4 ,some not-,a is ,c4  
4'4 ,some ,c is not-,a4   #fhe4 ,in the 
new symbols1 ,fanoao and ,donamon1 pi   
has been adopted as a symbol for        
permutation2 n signifies conversion by  
negation4 ,in ,donamon the first n      
stands for a process which resolves     
itself into permutation followed by     
simple conversion1 the second for one   
which resolves itself into simple       
conversion followed by permutation1     
according to the extended meaning which 
we have given to the term 'conversion by
 negation4' ,if it be thought desirable 
to distinguish these two processes1 the 

ugly symbol ,dopisamospi may be adopted 
in place of ,donamon4   #fhf4 ,the      
foregoing method1 which may be called   
,reduction by ,negation1 is no less     
applicable to the other moods of the    
second figure than to ,baroko4 ,the     
symbols which result from providing for 
its application would make the second of
 the mnemonic lines run thus--          
,benarepi1 ,canepie1 ,denilopi1 ,fanopio
 secundae4   #fhg4 ,the only other      
combination of mood and figure in which 
it will be found available is ,camenes1 
whose name it changes to ,canene4       
#fhh4    7,cesare7 ,benarea4            
,barbara4   ,no ,a is ,b4               
_/ ,all ,b is not-,a4   ,all ,c is ,b4  
,all ,c is ,b4   4'4 ,no ,c is ,a4      
_/      4'4 ,all ,c is not-,a4          
4'4 ,no ,c is ,a4    7,camestres7       
,canepie4      ,celarent4   ,all ,a is  
,b4              _/ ,no not-,b is ,a4   
,no ,c is ,b4               ,all ,c is  
not-,b4   4'4 ,no ,c is ,a4      _/     
4'4 ,no ,c is ,a4    7,festino7         

,denilopi4       ,darii4   ,no ,a is ,b4
               _/ ,all ,b is not-,a4    
,some ,c is ,b4             ,some ,c is 
,b4   4'4 ,some ,c is not ,a4_/      4'4
 ,some ,c is not-,a4                    
4'4 ,some ,c is not ,a4    7,camenes7   
,canene4           ,celarent4   ,all ,a 
is ,b4              _/ ,no not-,b is ,a4
   ,no ,b is ,c4               ,all ,c  
is not-,b4   4'4 ,no ,c is ,a4      _/  
4'4 ,no ,c is ,a4   #fhi4 ,the following
 will serve as a concrete instance of   
,canepie reduced to the first figure4   
,all things of which we have a perfect  
idea are perceptions4   ,a substance is 
not a perception4   4'4 ,a substance is 
not a thing of which we have a perfect  
idea4  ,when brought into ,celarent this
 becomes--    ,no not-perception is a   
thing of which we have a perfect idea4  
,a substance is a not-perception4   4'4 
,no substance is a thing of which we    
have a perfect idea4   #fij4 ,we may    
also bring it1 if we please1 into       
,barbara1 by permuting the major premiss

 once more1 so as to obtain the         
contrapositive of the original--    ,all
 not-perceptions are things of which we 
have an imperfect idea4   ,all          
substances are not-perceptions4   4'4   
,all substances are things of which we  
have an imperfect idea4    ,indirect    
,reduction4    #fia4 ,we will apply this
 method to ,baroko4    ,all ,a is ,b4   
,all fishes are oviparous4   ,some ,c is
 not ,b4      ,some marine animals are  
not oviparous4   4'4 ,some ,c is not ,a4
  4'4 ,some marine animals are not      
fishes4   #fib4 ,the reasoning in such a
 syllogism is evidently conclusive3 but 
it does not conform1 as it stands1 to   
the first figure1 nor 7permutation      
apart7 can its premisses be twisted into
 conformity with it4 ,but though we     
cannot prove the conclusion true in the 
first figure1 we can employ that figure 
to prove that it cannot be false1 by    
showing that the supposition of its     
falsity would involve a contradiction of
 one of the original premisses1 which   

are true ex hypothesi4   #fic4 ,if      
possible1 let the conclusion ',some ,c  
is not ,a' be false4 ,then its          
contradictory ',all ,c is ,a' must be   
true4 ,combining this as minor with the 
original major1 we obtain premisses in  
the first figure1    ,all ,a is ,b1     
,all fishes are oviparous1   ,all ,c is 
,a1   ,all marine animals are fishes1   
which lead to the conclusion    ,all ,c 
is ,b1   ,all marine animals are        
oviparous4  ,but this conclusion        
conflicts with the original minor1      
',some ,c is not ,b1' being its         
contradictory4 ,but the original minor  
is ex hypothesi true4 ,therefore the new
 conclusion is false4 ,therefore it must
 either be wrongly drawn or else one or 
both of its premisses must be false4    
,but it is not wrongly drawn2 since it  
is drawn in the first figure1 to which  
the ,dictum de ,omni et ,nullo applies4 
,therefore the fault must lie in the    
premisses4 ,but the major premiss1 being
 the same with that of the original     

syllogism1 is ex hypothesi true4        
,therefore the minor premiss1 ',all ,c  
is ,a1' is false4 ,but this being false1
 its contradictory must be true4 ,now   
its contradictory is the original       
conclusion1 ',some ,c is not ,a1' which 
is therefore proved to be true1 since it
 cannot be false4   #fid4 ,it is        
convenient to represent the two         
syllogisms in juxtaposition thus--      
,baroko4                  ,barbara4     
,all ,a is ,b4              ,all ,a is  
,b4   ,some ,c is not ,b4     _/  ,all  
,c is ,a4   4'4 ,some ,c is not ,a4 _/  
,all ,c is ,b4   #fie4 ,the lines       
indicate the propositions which conflict
 with one another4 ,the initial         
consonant of the names ,baroko and      
,eokardo indicates that the indirect    
reduct will be ,barbara4 ,the k         
indicates that the ,o proposition1 which
 it follows1 is to be dropped out in the
 new syllogism1 and its place supplied  
by the contradictory of the old         
conclusion4   #fif4 ,in ,bokardo the two

 syllogisms will stand thus--           
,bokardo4                ,barbara4      
,some ,b is not ,a4     _/ ,all ,c is   
,a4   ,all ,b is ,c4          ,x  ,all  
,b is ,c4   4'4 ,some ,c is not ,a4_/   
4'4 ,all ,b is ,a4   #fig4 ,the method  
of indirect reduction1 though invented  
with a special view to ,baroko and      
,bokardo1 is applicable to all the moods
 of the imperfect figures4 ,the         
following modification of the mnemonic  
lines contains directions for performing
 the process in every case3--,barbara1  
,celarent1 ,darii1 ,ferioque prioris2   
,felake1 ,dareke1 ,celiko1 ,baroko      
secundae2 ,tertia ,cakaci1 ,cikari1     
,fakini1 ,bekaco1 ,bokardo1 ,dekilon    
habet2 quarta insuper addit ,cakapi1    
,daseke1 ,cikasi1 ,cepako1 ,ceskon4     
#fih4 ,the c which appears in two moods 
of the third figure1 ,cakaci and        
,bekaco1 signifies that the new         
conclusion is the contrary1 instead of1 
as usual1 the contradictory of the      
discarded premiss4   #fii4 ,the letters 

s and p1 which appear only in the fourth
 figure1 signify that the new conclusion
 does not conflict directly with the    
discarded premiss1 but with its         
converse1 either simple or per accidens1
 as the case may be4   #gjj4 l1 n and r 
are meaningless1 as in the original     
lines4     ,,chapter ,,xix4  ,of        
,immediate ,inference as applied to     
,complex ,propositions4    #gja4 ,so far
 we have treated of inference1 or       
reasoning1 whether mediate or immediate1
 solely as applied to simple            
propositions4 ,but it will be remembered
 that we divided propositions into      
simple and complex4 ,i t becomes        
incumbent upon us therefore to consider 
the laws of inference as applied to     
complex propositions4 ,inasmuch however 
as every complex proposition is         
reducible to a simple one1 it is evident
 that the same laws of inference must   
apply to both4   #gjb4 ,we must first   
make good this initial statement as to  
the essential identity underlying the   

difference of form between simple and   
complex propositions4   #gjc4 ,complex  
propositions are either ,conjunctive or 
,disjunctive 7 #bad74   #gjd4           
,conjunctive propositions may assume any
 of the four forms1 ,a1 ,e1 ,i1 ,o1 as  
follows--    7,a7 ,if ,a is ,b1 ,c is   
always ,d4   7,e7 ,if ,a is ,b1 ,c is   
never ,d4   7,i7 ,if ,a is ,b1 ,c is    
sometimes ,d4   7,o7 ,if ,a is ,b1 ,c is
 sometimes not ,d4   #gje4 ,these admit 
of being read in the form of simple     
propositions1 thus--    7,a7 ,if ,a is  
,b1 ,c is always ,d  ,all cases of ,a   
being ,b are cases of ,c   being ,d4    
7,every ,,ab is a ,,cd47    7,e7 ,if ,a 
is ,b1 ,c is never ,d  ,no cases of ,a  
being ,b are cases of ,c   being ,d4    
7,no ,,ab is a ,,cd47    7,i7 ,if ,a is 
,b1 ,c is sometimes ,d  ,some cases of  
,a being ,b are cases   of ,c being ,d4 
7,some ,,ab's are ,,cd's47    7,o7 ,if  
,a is ,b1 ,c is sometimes not ,d  ,some 
cases of ,a being ,b are   not cases of 
,c being ,d4  7,some ,,ab's are not     

,,cd's47   #gjf4 ,or1 to take concrete  
examples1    7,a7 ,if kings are         
ambitious1 their subjects always suffer4
    ,all cases of ambitious kings are   
cases of subjects suffering4    7,e7 ,if
 the wind is in the south1 the river    
never freezes4    ,no cases of wind in  
the south are cases of the river        
freezing4    7,i7 ,if a man plays       
recklessly1 the luck sometimes goes     
against him4    ,some cases of reckless 
playing are cases of going against one4 
7,o7 ,if a novel has merit1 the public  
sometimes do not buy it4    ,some cases 
of novels with merit are not cases of   
the public buying4   #gjg4 ,we have seen
 already that the disjunctive differs   
from the conjunctive proposition in     
this1 that in the conjunctive the truth 
of the antecedent involves the truth of 
the consequent1 whereas in the          
disjunctive the falsity of the          
antecedent involves the truth of the    
consequent4  ,the disjunctive           
proposition therefore    ,either ,a is  

,b or ,c is ,d  may be reduced to a     
conjunctive    ,if ,a is not ,b1 ,c is  
,d1  and so to a simple proposition with
 a negative term for subject4    ,all   
cases of ,a not being ,b are cases of ,c
 being ,d4   7,every not-,,ab is a      
,,cd47   #gjh4 ,it is true that the     
disjunctive proposition1 more than any  
other form1 except ,u1 seems to convey  
two statements in one breath4 ,yet it   
ought not1 any more than the ,e         
proposition1 to be regarded as conveying
 both with equal directness4 ,the       
proposition ',no ,a is ,b' is not       
considered to assert directly1 but only 
implicitly1 that ',no ,b is ,a4' ,in the
 same way the form ',either ,a is ,b or 
,c is ,d' ought to be interpreted as    
meaning directly no more than this1 ',if
 ,a is not ,b1 ,c is ,d4' ,it asserts   
indeed by implication also that ',if ,c 
is not ,d1 ,a is ,b4' ,but this is an   
immediate inference1 being1 as we shall 
presently see1 the contrapositive of the
 original4 ,when we say ',so and so is  

either a knave or a fool1' what we are  
directly asserting is that1 if he be not
 found to be a knave1 he will be found  
to be a fool4 ,by implication we make   
the further statement that1 if he be not
 cleared of folly1 he will stand        
condemned of knavery4 ,this inference is
 so immediate that it seems             
indistinguishable from the former       
proposition3 but since the two members  
of a complex proposition play the part  
of subject and predicate1 to say that   
the two statements are identical would  
amount to asserting that the same       
proposition can have two subjects and   
two predicates4 ,from this point of view
 it becomes clear that there is no      
difference but one of expression between
 the disjunctive and the conjunctive    
proposition4  ,the disjunctive is merely
 a peculiar way of stating a conjunctive
 proposition with a negative antecedent4
   #gji4 ,conversion of ,complex        
,propositions4    ,a  _/ ,if ,a is ,b1  
,c is always ,d4       4'4 ,if ,c is ,d1

 ,a is sometimes ,b4    ,e  _/ ,if ,a is
 ,b1 ,c is never ,d4       4'4 ,if ,c is
 ,d1 ,a is never ,b4    ,i  _/ ,if ,a is
 ,s1 ,c is sometimes ,d4       4'4 ,if  
,c is ,d1 ,a is sometimes ,b4   #gaj4   
,exactly the same rules of conversion   
apply to conjunctive as to simple       
propositions4   #gaa4 ,a can only be    
converted per accidens1 as above4  ,the 
original proposition    ',if ,a is ,b1  
,c is always ,d'  is equivalent to the  
simple proposition    ',all cases of ,a 
being ,b are cases of ,c being ,d4'     
,this1 when converted1 becomes    ',some
 cases of ,c being ,d are cases of ,a   
being ,b1'  which1 when thrown back into
 the conjunctive form1 becomes    ',if  
,c is ,d1 ,a is sometimes ,b4'   #gab4  
,this expression must not be            
misunderstood as though it contained any
 reference to actual existence4  ,the   
meaning might be better conveyed by the 
form    ',if ,c is ,d1 ,a may be ,b4'   
,but it is perhaps as well to retain the
 other1 as it serves to emphasize the   

fact that formal logic is concerned only
 with the connection of ideas4   #gac4  
,a concrete instance will render the    
point under discussion clearer4 ,the    
example we took before of an ,a         
proposition in the conjunctive form--   
',if kings are ambitious1 their subjects
 always suffer'  may be converted into  
',if subjects suffer1 it may be that    
their kings are ambitious1'  i4e4 among 
the possible causes of suffering on the 
part of subjects is to be found the     
ambition of their rulers1 even if every 
actual case should be referred to some  
other cause4 ,it is in this sense only  
that the inference is a necessary one4  
,but then this is the only sense which  
formal logic is competent to recognise4 
,to judge of conformity to fact is no   
part of its province4 ,from ',every ,,ab
 is a ,,cd' it follows that ' ,some     
,,cd's are ,,ab's' with exactly the same
 necessity as that with which ',some ,b 
is ,a' follows from ',all ,a is ,b4' ,in
 the latter case also neither           

proposition may at all conform to fact4 
,from ',all centaurs are animals' it    
follows necessarily that ',some animals 
are centaurs'3 but as a matter of fact  
this is not true at all4   #gad4 ,the ,e
 and the ,i proposition may be converted
 simply1 as above4   #gae4 ,o cannot be 
converted at all4 ,from the proposition 
',if a man runs a race1 he sometimes    
does not win it1'  it certainly does not
 follow that    ',if a man wins a race1 
he sometimes does not run it4'   #gaf4  
,there is a common but erroneous notion 
that all conditional propositions are to
 be regarded as affirmative4 ,thus it   
has been asserted that1 even when we say
 that ',if the night becomes cloudy1    
there will be no dew1' the proposition  
is not to be regarded as negative1 on   
the ground that what we affirm is a     
relation between the cloudiness of night
 and the absence of dew4 ,this is a     
possible1 but wholly unnecessary1 mode  
of regarding the proposition4 ,it is    
precisely on a par with ,hobbes's theory

 of the copula in a simple proposition  
being always affirmative4 ,it is true   
that it may always be so represented at 
the cost of employing a negative term2  
and the same is the case here4   #gag4  
,there is no way of converting a        
disjunctive proposition except by       
reducing it to the conjunctive form4    
#gah4 ,permutation of ,complex          
,propositions4    7,a7 ,if ,a is ,b1 ,c 
is always ,d4       4'4 ,if ,a is ,b1 ,c
 is never not-,d4 7,e7    7,e7 ,if ,a is
 ,b1 ,c is never ,d4       4'4 ,if ,a is
 ,b1 ,c is always not-,d4 7,a7    7,i7  
,if ,a is ,b1 ,c is sometimes ,d4       
4'4 ,if ,a is ,b1 ,c is sometimes not   
not-,d4 7,o7    7,o7 ,if ,a is ,b1 ,c is
 sometimes not ,d4       4'4 ,if ,a is  
,b1 ,c is sometimes not-,d4 7,i7   #gai4
    7,a7 ,if a mother loves her         
children1 she is always kind to them4   
4'4 ,if a mother loves her children1 she
 is never unkind to       them4 7,e7    
7,e7 ,if a man tells lies1 his friends  
never trust him4       4'4 ,if a man    

tells lies1 his friends always distrust 
him4 7,a7    7,i7 ,if strangers are     
confident1 savage dogs are sometimes    
friendly4       4'4 ,if strangers are   
confident1 savage dogs are sometimes not
       unfriendly4 7,o7    7,o7 ,if a   
measure is good1 its author is sometimes
 not popular4       4'4 ,if a measure is
 good1 its author is sometimes          
unpopular4 7,i7   #gbj4 ,the disjunctive
 proposition may be permuted as it      
stands without being reduced to the     
conjunctive form4    ,either ,a is ,b or
 ,c is ,d4   4'4 ,either ,a is ,b or ,c 
is not not-,d4    ,either a sinner must 
repent or he will be damned4   4'4      
,either a sinner must repent or he will 
not be saved4   #gba4 ,conversion by    
,negation of ,complex ,propositions4    
7,a7 ,if ,a is ,b1 ,c is always ,d4     
4'4 ,if ,c is not-,d1 ,a is never ,b4   
7,e7    7,e7 ,if ,a is ,b1 ,c is never  
,d4       4'4 ,if ,c is ,d1 ,a is always
 not-,b4 7,a7    7,i7 ,if ,a is ,b1 ,c  
is sometimes ,d4       4'4 ,if ,c is ,d1

 ,a is sometimes not not-,b4 7,o7       
7,o7 ,if ,a is ,b1 ,c is sometimes not  
,d4       4'4 ,if ,c is not-,d1 ,a is   
sometimes ,b4 7,i7    7,e per acc47 ,if 
,a is ,b1 ,c is never ,d4       4'4 ,if 
,c is not-,d1 ,a is sometimes ,b4 7,i7  
7,a per ace47 ,if ,a is ,b1 ,c is always
 ,d4       4'4 ,if ,c is ,d1 ,a is      
sometimes not not-,d4 7,o7   #gbb4      
7,a7 ,if a man is a smoker1 he always   
drinks4       4'4 ,if a man is a total  
abstainer1 he never smokes4 7,e7    7,e7
 ,if a man merely does his duty1 no one 
ever thanks him4       4'4 ,if people   
thank a man1 he has always done more    
than his       duty4 7,a7    7,i7 ,if a 
statesman is patriotic1 he sometimes    
adheres to a party4       4'4 ,if a     
statesman adheres to a party1 he is     
sometimes not       unpatriotic4 7,o7   
7,o7 ,if a book has merit1 it sometimes 
does not sell4       4'4 ,if a book     
fails to sell1 it sometimes has merit4  
7,i7    7,e per acc47 ,if the wind is   
high1 rain never falls4       4'4 ,if   

rain falls1 the wind is sometimes high4 
7,i7    7,a per acc47 ,if a thing is    
common1 it is always cheap4       4'4   
,if a thing is cheap1 it is sometimes   
not uncommon4 7,o7   #gbc4 ,when applied
 to disjunctive propositions1 the       
distinctive features of conversion by   
negation are still discernible4 ,in each
 of the following forms of inference the
 converse differs in quality from the   
convertend and has the contradictory of 
one of the original terms 7 #eae74      
#gbd4    7,a7 ,either ,a is ,b or ,c is 
always ,d4       4'4 ,either ,c is ,d or
 ,a is never not-,b4 7,e7    7,e7       
,either ,a is ,b or ,c is never ,d4     
4'4 ,either ,c is not-,d or ,a is always
 ,b4 7,a7    7,i7 ,either ,a is ,b or ,c
 is sometimes ,d4       4'4 ,either ,c  
is not-,d or ,a is sometimes not ,b4    
7,o7    7,o7 ,either ,a is ,b or ,c is  
sometimes not ,d4       4'4 ,either ,c  
is ,d or ,a is sometimes not-,b4 7,i7   
#gbe4    7,a7 ,either miracles are      
possible or every ancient historian is  

untrustworthy4       4'4 ,either ancient
 historians are untrustworthy or        
miracles are       not impossible4 7,e7 
7,e7 ,either the tide must turn or the  
vessel can not make the port4       4'4 
,either the vessel cannot make the port 
or the tide must       turn4 7,a7       
7#a7 ,either he aims too high or the    
cartridges are sometimes bad4       4'4 
,either the cartridges are not bad or he
 sometimes does not       aim too high4 
7#j7    7,o7 ,either care must be taken 
or telegrams will sometimes not be      
correct4       4'4 ,either telegrams are
 correct or carelessness is sometimes   
shown4 7#a7   #gbf4 ,in the above       
examples the converse of ,e looks as if 
it had undergone no change but the mere 
transposition of the alternative4 ,this 
appearance arises from mentally reading 
the ,e as an ,a proposition3 but1 if it 
were so taken1 the result would be its  
contrapositive1 and not its converse by 
negation4   #gbg4 ,the converse of ,i is
 a little difficult to grasp4  ,it      

becomes easier if we reduce it to the   
equivalent conjunctive--    ',if the    
cartridges are bad1 he sometimes does   
not aim too high4'  ,here1 as elsewhere1
 'sometimes' must not be taken to mean  
more than 'it may be that4'   #gbh4     
,conversion by ,contraposition of       
,complex ,propositions4  ,as applied to 
conjunctive propositions conversion by  
contraposition assumes the following    
forms--    7,a7 ,if ,a is ,b1 ,c is     
always ,d4       4'4 ,if ,c is not-,d1  
,a is always not-,b4    7,o7 ,if ,a is  
,b1 ,c is sometimes not ,d4       4'4   
,if ,c is not-,d1 ,a is sometimes not   
not-,b4    7,a7 ,if a man is honest1 he 
is always truthful4       4'4 ,if a man 
is untruthful1 he is always dishonest4  
7,o7 ,if a man is hasty1 he is sometimes
 not malevolent4       4'4 ,if a man is 
benevolent1 he is sometimes not unhasty4
   #gbi4 ,as applied to disjunctive     
propositions conversion by              
contraposition consists simply in       
transposing the two alternatives4       

7,a7 ,either ,a is ,b or ,c is ,d4      
4'4 ,either ,c is ,d or ,a is ,b4  ,for1
 when reduced to the conjunctive shape1 
the reasoning would run thus--    ,if ,a
 is not ,b1 ,c is ,d4   4'4 ,if ,c is   
not ,d1 ,a is ,b4  which is the same in 
form as    ,all not-,a is ,b4   4'4 ,all
 not-,b is ,a4  ,similarly in the case  
of the ,o proposition    7,o7 ,either ,a
 is ,b or ,c is sometimes not ,d4       
4'4 ,either ,c is ,d or ,a is sometimes 
not ,b4   #gcj4 ,on comparing these     
results with the converse by negation of
 each of the same propositions1 ,a and  
#j1 the reader will see that they differ
 from them1 as was to be expected1 only 
in being permuted4 ,the validity of the 
inference may be tested1 both here and  
in the case of conversion by negation1  
by reducing the disjunctive proposition 
to the conjunctive1 and so to the simple
 form1 then performing the process as in
 simple propositions1 and finally       
throwing the converse1 when so obtained1
 back into the disjunctive form4 ,we    

will show in this manner that the above 
is really the contrapositive of the #j  
proposition4    7,o7 ,either ,a is ,b or
 ,c is sometimes not ,d4     ,if ,a is  
not ,b1 ,c is sometimes not ,d4         
,some cases of ,a not being ,b are not  
cases of ,c being ,d4 7,some ,a is   not
 ,b47     ,some cases of ,c not being ,d
 are not cases of ,a being ,b4 7,some   
not-,b is not not-,a47     ,if ,c is not
 ,d1 ,a is sometimes not ,b4     ,either
 ,c is ,d or ,a is sometimes not ,b4    
,,chapter ,,xx4  ,of ,complex           
,syllogisms4    #gca4 ,a ,complex       
,syllogism is one which is composed1 in 
whole or part1 of complex propositions4 
#gcb4 ,though there are only two kinds  
of complex proposition1 there are three 
varieties of complex syllogism4  ,for we
 may have    7#a7 a syllogism in which  
the only kind of complex proposition    
employed is the conjunctive2    7#b7 a  
syllogism in which the only kind of     
complex proposition   employed is the   
disjunctive2    7#c7 a syllogism which  

has one premiss conjunctive and the     
other   disjunctive4  ,the chief        
instance of the third kind is that known
 as the ,dilemma4                       
,syllogism                              
,simple                                 
,complex   7,categorical7               
7,conditional7                          
,conjunctive          ,disjunctive      
,dilemma                7,hypothetical7 
,the ,conjunctive ,syllogism4    #gcc4  
,the ,conjunctive ,syllogism has one or 
both premisses conjunctive propositions3
 but if only one is conjunctive1 the    
other must be a simple one4   #gcd4     
,where both premisses are conjunctive1  
the conclusion will be of the same      
character2 where only one is            
conjunctive1 the conclusion will be a   
simple proposition4   #gce4 ,of these   
two kinds of conjunctive syllogisms we  
will first take that which consists     
throughout of conjunctive propositions4 
,the ,wholly ,conjunctive ,syllogism4   
#gcf4 ,wholly conjunctive syllogisms do 

not differ essentially from simple ones1
 to which they are immediately          
reducible4 ,they admit of being         
constructed in every mood and figure1   
and the moods of the imperfect figures  
may be brought into the first by        
following the ordinary rules of         
reduction4 ,for instance--      ,cesare4
                              ,celarent4
    ,if ,a is ,b1 ,c is never ,d4       
_/ ,if ,c is ,d1 ,a is never ,b4   ,if  
,e is ,f1 ,c is always ,d4         ,if  
,e is ,f1 ,c is always ,d4   4'4 ,if ,e 
is ,f1 ,a is never ,b4 _/      4'4 ,if  
,e is ,f1 ,a is never ,b4    ,if it is  
day1 the stars never shine4   _/,if the 
stars shine1 it is never day4   ,if it  
is night1 the stars always     _/ ,if it
 is night1 the stars always   shine4    
_/  shine4   4'4 ,if it is night1 it is 
never day _/   4'4 ,if it is night1 it  
is never day4      ,disamis4            
,darii4   ,if ,c is ,d1 ,a is sometimes 
,b4      _/ ,if ,c is ,d1 ,e is always  
,f4   ,if ,c is ,d1 ,e is always ,f4    

,if ,a is ,b1 ,c is sometimes ,d4   ,if 
,e is ,f1 ,a is sometimes ,b4 _/        
4'4 ,if ,a is ,b1 ,e is sometimes ,f4   
4'4 ,if ,e is ,f1 ,a is sometimes ,b4   
,if she goes1 ,i sometimes go4          
_/ ,if she goes1 he always goes1   ,if  
she goes1 he always goes4         ,if ,i
 go1 she sometimes goes4   4'4 ,if he   
goes1 ,i sometimes go4 _/      4'4 ,if  
,i go1 he sometimes goes4               
4'4 ,if he goes1 ,i sometimes go4       
,the ,partly ,conjunctive ,syllogism4   
#gcg4 ,it is this kind which is usually 
meant when the ,conjunctive or          
,hypothetical ,syllogism is spoken of4  
#gch4 ,of the two premisses1 one        
conjunctive and one simple1 the         
conjunctive is considered to be the     
major1 and the simple premiss the minor4
 ,for the conjunctive premiss lays down 
a certain relation to hold between two  
propositions as a matter of theory1     
which is applied in the minor to a      
matter of fact4   #gci4 ,taking a       
conjunctive proposition as a major      

premiss1 there are four simple minors   
possible4 ,for we may either assert or  
deny the antecedent or the consequent of
 the conjunctive4        ,constructive  
,mood4                ,destructive      
,mood4   7#a7 ,if ,a is ,b1 ,c is ,d4   
7#b7 ,if ,a is ,b1 ,c is ,d4       ,a is
 ,b4                           ,c is not
 ,d4       4'4 ,c is ,d4                
4'4 ,a is not ,b4    7#c7 ,if ,a is ,b1 
,c is ,d4            7#d7 ,if ,a is ,b1 
,c is ,d4       ,a is not ,b4           
,c is ,d4       ,no conclusion4         
,no conclusion4   #gdj4 ,when we take as
 a minor ',a is not ,b ' 7#c71 it is    
clear that we can get no conclusion4    
,for to say that ,c is ,d whenever ,a is
 ,b gives us no right to deny that ,c   
can be ,d in the absence of that        
condition4 ,what we have predicated has 
been merely inclusion of the case ,,ab  
in the case ,,cd4  ,illustration   #gda4
 ,again1 when we take as a minor1 ',c is
 ,d' 7#d71 we can get no universal      
conclusion4 ,for though ,a being ,b is  

declared to involve as a consequence ,c 
being ,d1 yet it is possible for ,c to  
be ,d under other circumstances1 or from
 other causes4 ,granting the truth of   
the proposition ',if the sky falls1 we  
shall catch larks1' it by no means      
follows that there are no other         
conditions under which this result can  
be attained4   #gdb4 ,from a            
consideration of the above four cases we
 elicit the following    ,canon of the  
,conjunctive ,syllogism4   ,to affirm   
the antecedent is to affirm the         
consequent1 and to deny the consequent  
is to deny the antecedent3 but from     
denying the antecedent or affirming the 
consequent no conclusion follows4       
#gdc4 ,there is a case1 however1 in     
which we can legitimately deny the      
antecedent and affirm the consequent of 
a conjunctive proposition1 namely1 when 
the relation predicated between the     
antecedent and the consequent is not    
that of inclusion but of                
coincidence--where in fact the          

conjunctive proposition conforms to the 
type u4  ,for example--    ,denial of   
the ,antecedent4   ,if you repent1 then 
only are you forgiven4   ,you do not    
repent4   4'4 ,you are not forgiven4    
,affirmation of the ,consequent4   ,if  
you repent1 then only are you forgiven4 
,you are forgiven4   4'4 ,you repent4   
,,chapter ,,xxi4  ,of the ,reduction of 
the ,partly ,conjunctive ,syllogism4    
#gdd4 ,such syllogisms as those just    
treated of1 if syllogisms they are to be
 called1 have a major and a middle term 
visible to the eye1 but appear to be    
destitute of a minor4 ,the missing minor
 term is however supposed to be latent  
in the transition from the conjunctive  
to the simple form of proposition4 ,when
 we say ',a is ,b1' we are taken to     
mean1 ',as a matter of fact1 ,a is ,b'  
or ',the actual state of the case is    
that ,a is ,b4' ,the insertion therefore
 of some such expression as ',the case  
in hand1' or ',this case1' is1 on this  
view1 all that is wanted to complete the

 form of the syllogism4 ,when reduced in
 this manner to the simple type of      
argument1 it will be found that the     
constructive conjunctive conforms to the
 first figure and the destructive       
conjunctive to the second4              
,constructive ,mood4    ,barbara4    ,if
 ,a is ,b1 ,c is ,d4      _/ ,all cases 
of ,a being ,b are cases of             
_/    ,c being ,d4   ,a is ,b4          
_/     ,this is a case of ,a being ,b4  
4'4 ,c is ,d4        _/      4'4 ,this  
is a case of ,c being ,d4               
,destructive ,mood4     ,camestres4     
,if ,a is ,b1 ,c is ,d4      _/ ,all    
cases of ,a being ,b are cases of       
_/    ,c being ,d4   ,c is not ,d4      
_/     ,this is not a case of ,c being  
,d4   4'4 ,a is not ,b4    _/      4'4  
,this is not a case of ,a being ,b4     
#gde4 ,it is apparent from the position 
of the middle term that the constructive
 conjunctive must fall into the first   
figure and the destructive conjunctive  
into the second4  ,there is no reason1  

however1 why they should be confined to 
the two moods1 ,barbara and ,carnestres4
 ,if the inference is universal1 whether
 as general or singular1 the mood is    
,barbara or ,carnestres2 if it is       
particular1 the mood is ,darii or       
,baroko4    ,barbara4                   
,camestres4   ,if ,a is ,b1 ,c is always
 ,d4       ,if ,a is ,b1 ,c is always   
,d4       ,a is always ,b4              
,c is never ,d4                    4'4  
,c is always ,d4              4'4 ,a is 
never ,b4                               
,if ,a is ,b1 ,c is always ,d4   _/     
,if ,a is ,b1 ,c is always ,d4      _/  
,a is in this case ,b4       _/     ,c  
is not in this case ,d4      _/   4'4 ,c
 is in this case ,d4  _/      4'4 ,a is 
not in this case ,b4 _/    ,darii4      
,baroko4    ,if ,a is ,b1 ,c is always  
,d4        ,if ,a is ,b1 ,c is never ,d4
   ,a is sometimes ,b4                ,c
 is sometimes not ,d4   4'4 ,c is       
sometimes ,d4            4'4 ,a is      
sometimes not ,b4   #gdf4 ,the remaining

 moods of the first and second figure   
are obtained by taking a negative       
proposition as the consequent in the    
major premiss4    ,celarent4            
,ferio4   ,if ,a is ,b1 ,c is never ,d4 
,if ,a is ,b1 ,c is never ,d4   ,a is   
always ,b4                 ,a is        
sometimes ,b4   4'4 ,c is never ,d4     
4'4 ,c is sometimes not ,d4    ,cesare4 
,festino4   ,if ,a is ,b1 ,c is never   
,d4       ,if ,a is ,b1 ,c is never ,d4 
,c is always ,d4                 ,c is  
sometimes ,d4   4'4 ,a is never ,b4     
4'4 ,a is sometimes not ,b4   #gdg4 ,as 
the partly conjunctive syllogism is thus
 reducible to the simple form1 it       
follows that violations of its laws must
 correspond with violations of the laws 
of simple syllogism4 ,by our throwing   
the illicit moods into the simple form  
it will become apparent what fallacies  
are involved in them4    ,denial of     
,anteceded4    ,if ,a is ,b1 ,c is ,d4  
_/ ,all cases of ,a being ,b are cases  
of ,c                         _/        

being ,d4   ,a is not ,b4         _/    
,this is not a case of ,a being ,b4     
4'4 ,c is not ,d4    _/      4'4 ,this  
is not a case of ,c being ,d4  ,here we 
see that the denial of the antecedent   
amounts to illicit process of the major 
term4   #gdha ,affirmation of           
,consequent4    ,if ,a is ,b1 ,c is ,d4 
_/ ,all ,cases of ,a being ,b are cases 
of ,c                              being
 ,d4   ,c is ,d4            _/          
,this is a case of ,c being ,d4  ,here  
we see that the affirmation of the      
consequent amounts to undistributed     
middle4   #gdi4 ,if we confine ourselves
 to the special rules of the four       
figures1 we see that denial of the      
antecedent involves a negative minor in 
the first figure1 and affirmation of the
 consequent two affirmative premisses in
 the second4 ,or1 if the consequent in  
the major premiss were itself negative1 
the affirmation of it would amount to   
the fallacy of two negative premisses4  
,thus--    ,if ,a is ,b1 ,c is not ,d4  

_/ ,no cases of ,a being ,b are cases of
 ,c                                     
being ,d4   ,c is not ,d4            _/ 
,this is not a case of ,c being ,d4     
#gej4 ,the positive side of the canon of
 the conjunctive syllogism--',to affirm 
the antecedent is to affirm the         
consequent1' corresponds with the       
,dictum de ,omni4 ,for whereas something
 7viz4 ,c being ,d7 is affirmed in the  
major of all conceivable cases of ,a    
being ,b1 the same is affirmed in the   
conclusion of something which is        
included therein1 namely1 'this case1'  
or 'some cases1' or even 'all actual    
cases4'   #gea4 ,the negative side--'to 
deny the consequent is to deny the      
antecedent'--corresponds with the       
,dictum de ,diverse 7 #fdc74 ,for       
whereas in the major all conceivable    
cases of ,a being ,b are included in ,c 
being ,d1 in the minor 'this case1' or  
'some cases1' or even 'all actual cases'
 of ,c being ,d1 are excluded from the  
same notion4   #geb4 ,the special       

characteristic of the partly conjunctive
 syllogism lies in the transition from  
hypothesis to fact4  ,we might lay down 
as the appropriate axiom of this form of
 argument1 that ',what is true in the   
abstract is true--in the concrete1' or  
',what is true in theory is also true in
 fact1' a proposition which is apt to be
 neglected or denied4 ,but this does not
 vitally distinguish it from the        
ordinary syllogism4 ,for though in the  
latter we think rather of the transition
 from a general truth to a particular   
application of it1 yet at bottom a      
general truth is nothing but a          
hypothesis resting upon a slender basis 
of observed fact4 ,the proposition ',a  
is ,b' may be expressed in the form ',if
 ,a is1 ,b is4' ,to say that ',all men  
are mortal' may be interpreted to mean  
that ',if we find in any subject the    
attributes of humanity1 the attributes  
of mortality are sure to accompany      
them4'     ,,chapter ,,xxii4  ,of the   
,partly ,conjunctive ,syllogism regarded

 as an ,immediate ,inference4    #gec4  
,it is the assertion of fact in the     
minor premiss1 where we have the        
application of an abstract principle to 
a concrete instance1 which alone        
entitles the partly conjunctive         
syllogism to be regarded as a syllogism 
at all4  ,apart from this the forms of  
semi-conjunctive reasoning run at once  
into the moulds of immediate inference4 
#ged4 ,the constructive mood will then  
be read in this way--    ,if ,a is ,b1  
,c is ,d1   4'4 ,a being ,b1 ,c is ,d4  
reducing itself to an instance of       
immediate inference by subaltern        
opposition--    ,every case of ,a being 
,b1 is a case of ,c being ,d4   4'4     
,some particular case of ,a being ,b is 
a case of ,c being ,d4   #gee4 ,again1  
the destructive conjunctive will read as
 follows--    ,if ,a is ,b1 ,c is ,d1   
4'4 ,c not being ,d1 ,a is not ,b4      
which is equivalent to    ,all cases of 
,a being ,b are cases of ,c being ,d4   
4'4 ,whatever is not a case of ,c being 

,d is not a case of ,a being ,b4   4'4  
,some particular case of ,c not being ,d
 is not a case of ,a being   ,b4  ,but  
what is this but an immediate inference 
by contraposition1 coming under the     
formula    ,all ,a is ,b1   4'4 ,all    
not-,b is not-,a1  and followed by      
,subalternation8   #gef4 ,the fallacy of
 affirming the consequent becomes by    
this mode of treatment an instance of   
the vice of immediate inference known as
 the simple conversion of an ,a         
proposition4 ',if ,a is ,b1 ,c is ,d' is
 not convertible with ',if ,c is ,d1 ,a 
is ,b' any more than ',all ,a is ,b' is 
convertible with ',all ,b is ,a4'       
#geg4 ,we may however argue in this way 
,if ,a is ,b1 ,c is ,d1   ,c is ,d1     
4'4 ,a may be ,b1  which is equivalent  
to saying1    ,when ,a is ,b1 ,c is     
always ,d1   4'4 ,when ,c is ,d1 ,a is  
sometimes ,b1  and falls under the      
legitimate form of conversion of ,a per 
accidens--    ,all cases of ,a being ,b 
are cases of ,c being ,d4   4'4 ,some   

cases of ,c being ,d are cases of ,a    
being ,b4   #geh4 ,the fallacy of       
denying the antecedent assumes the      
following form--    ,if ,a is ,b1 ,c is 
,d1   4'4 ,if ,a is not ,b1 ,c is not   
,d1  equivalent to--    ,all cases of ,a
 being ,b are cases of ,c being ,d4     
4'4 ,whatever is not a case of ,a being 
,b is not a case of ,c being ,d4  ,this 
is the same as to argue--    ,all ,a is 
,b1   4'4 ,all not-,a is not-,b1  an    
erroneous form of immediate inference   
for which there is no special name1 but 
which involves the vice of simple       
conversion of ,a1 since ',all not-,a is 
not-,b' is the contrapositive1 not of   
',all ,a is ,b1' but of its simple      
converse ',all ,b is ,a4'   #gei4 ,the  
above-mentioned form of immediate       
inference1 however 7namely1 the         
employment of contraposition without    
conversion71 is valid in the case of the
 ,u proposition2 and so also is simple  
conversion4 ,accordingly we are able1 as
 we have seen1 in dealing with a        

proposition of that form1 both to deny  
the antecedent and to assert the        
consequent with impunity--    ,if ,a is 
,b1 then only ,c is ,d1   4'4 ,a not    
being ,b1 ,c is not ,d2  and again1 ,c  
being ,d1 ,a must be ,b4     ,,chapter  
,,xxiii4  ,of the ,disjunctive          
,syllogism4    #gfj4 ,roughly speaking1 
a ,disjunctive ,syllogism results from  
the combination of a disjunctive with a 
simple premiss4 ,as in the preceding    
form1 the complex proposition is        
regarded as the major premiss1 since it 
lays down a hypothesis1 which is applied
 to fact in the minor4   #gfa4 ,the     
,disjunctive ,syllogism may be exactly  
defined as follows--    ,a complex      
syllogism1 which has for its major      
premiss a disjunctive   proposition1    
either the antecedent or consequent of  
which is in the   minor premiss simply  
affirmed or denied4   #gfb4 ,thus there 
are four types of disjunctive syllogism 
possible4  ,constructive ,moods4    7#a7
 ,either ,a is ,b or ,c is ,d4 7#b7     

,either ,a is ,b or ,c is ,d4       ,a  
is not ,b4                  ,c is not   
,d4       4'4 ,c is ,d4                 
4'4 ,a is ,b4    ,either death is       
annihilation or we are immortal4        
,death is not annihilation4   4'4 ,we   
are immortal4    ,either the water is   
shallow or the boys will be drowned4    
,the boys are not drowned4   4'4 ,the   
water is shallow4  ,destructive ,moods4 
7#c7 ,either ,a is ,b or ,c is ,d4 7#d7 
,either ,a is ,b or ,c is ,d4       ,a  
is ,b4                      ,c is ,d4   
4'4 ,c is not ,d4              4'4 ,a is
 not ,b4   #gfc4 ,of these four1        
however1 it is only the constructive    
moods that are formally conclusive4 ,the
 validity of the two destructive moods  
is contingent upon the kind of          
alternatives selected4 ,if these are    
such as necessarily to exclude one      
another1 the conclusion will hold1 but  
not otherwise4 ,they are of course      
mutually exclusive whenever they embody 
the result of a correct logical         

division1 as ',triangles are either     
equilateral1 isosceles or scalene4'     
,here1 if we affirm one of the members1 
we are justified in denying the rest4   
,when the major thus contains the       
dividing members of a genus1 it may more
 fitly be symbolized under the formula1 
',a is either ,b or ,c4' ,but as this   
admits of being read in the shape1      
',either ,a is ,b or ,a is ,c1' we      
retain the wider expression which       
includes it4 ,any knowledge1 however1   
which we may have of the fact that the  
alternatives selected in the major are  
incompatible must come to us from       
material sources2 unless indeed we have 
confined ourselves to a pair of         
contradictory terms 7,a is either ,b or 
not-,b74 ,there can be nothing in the   
form of the expression to indicate the  
incompatibility of the alternatives1    
since the same form is employed when the
 alternatives are palpably compatible4  
,when1 for instance1 we say1 ',a        
successful student must be either       

talented or industrious1' we do not at  
all mean to assert the positive         
incompatibility of talent and industry  
in a successful student1 but only the   
incompatibility of their negatives--in  
other words1 that1 if both are absent1  
no student can be successful4           
,similarly1 when it is said1 ',either   
your play is bad or your luck is        
abominable1' there is nothing in the    
form of the expression to preclude our  
conceiving that both may be the case4   
#gfd4 ,there is no limit to the number  
of members in the disjunctive major4    
,but if there are only two alternatives1
 the conclusion will be a simple        
proposition2 if there are more than two1
 the conclusion will itself be a        
disjunctive4 ,thus--    ,either ,a is ,b
 or ,c is ,d or ,e is ,f or ,g is ,h4   
,e is not ,f4   4'4 ,either ,a is ,b or 
,c is ,d or ,g is ,h4   #gfe4 ,the      
,canon of the ,disjunctive ,syllogism   
may be laid down as follows--    ,to    
deny one member is to affirm the rest1  

either simply or   disjunctively2 but   
from affirming any member nothing       
follows4     ,,chapter ,,xxiv4  ,of the 
,reduction of the ,disjunctive          
,syllogism4   #gff4 ,we have seen that  
in the disjunctive syllogism the two    
constructive moods alone are formally   
valid4 ,the first of these1 namely1 the 
denial of the antecedent1 will in all   
cases give a simple syllogism in the    
first figure2 the second of them1       
namely1 the denial of the consequent1   
will in all cases give a simple         
syllogism in the second figure4         
,denial of ,antecedent  ,barbara4       
,either ,a is ,b or ,c is ,d4     ,a is 
not ,b4     4'4,c is ,d    is equal to  
,if ,a is not ,b1 ,c is ,d4     ,a is   
not ,b4     4'4 ,c is ,d4    is equal to
      ,all cases of ,a not being ,b are 
cases of ,c being ,d4     ,this is a    
case of ,a not being ,b4     4'4 ,this  
is a case of ,c being ,d4     ,denial of
 ,consequent  ,camestres4      ,either  
,a is ,e or ,c is ,d4     ,c is not ,d4 

4'4 ,a is ,b4    is equal to      ,if ,a
 is not ,b1 ,c is ,d4     ,c is not ,d4 
4'4 ,a is ,b4    is equal to      ,all  
cases of ,a not being ,b are cases of ,c
 being ,d4     ,this is not a case of ,c
 being ,d4     4'4 ,this is not a case  
of ,a being ,b4   #gfg4 ,the other moods
 of the first and second figures can be 
obtained by varying the quality of the  
antecedent and consequent in the major  
premiss and reducing the quantity of the
 minor4   #gfh4 ,the invalid destructive
 moods correspond with the two invalid  
types of the partly conjunctive         
syllogism1 and have the same fallacies  
of simple syllogism underlying them4    
,affirmation of the antecedent of a     
disjunctive is equivalent to the        
semi-conjunctive fallacy of denying the 
antecedent1 and therefore involves the  
ordinary syllogistic fallacy of illicit 
process of the major4  ,affirmation of  
the consequent of a disjunctive is      
equivalent to the same fallacy in the   
semi-conjunctive form1 and therefore    

involves the ordinary syllogistic       
fallacy of undistributed middle4        
,affirmation of ,antecedent  ,illicit   
,major4      ,either ,a is ,b or ,c is  
,d4     ,a is ,b4     4'4 ,c is not ,d4 
is equal to      ,if ,a is not ,b1 ,c is
 ,d4     ,a is ,b4     4'4 ,c is not ,d4
    is equal to      ,all cases of ,a   
not being ,b are cases of ,c being ,d4  
,this is not a case of ,a not being ,b4 
4'4 ,this is not a case of ,c not being 
,d4     ,affirmation of ,consequent     
,undistributed ,middle4      ,either ,a 
is ,b or ,c is ,d4     ,c is ,d4    is  
equal to      ,if ,a is not ,b1 ,c is   
,d4     ,c is ,d4    is equal to        
,all cases of ,a not being ,b are cases 
of ,c being ,d4     ,this is a case of  
,c being ,d4   #gfi4 ,so far as regards 
the consequent1 the two species of      
complex reasoning hitherto discussed are
 identical both in appearance and       
reality4 ,the apparent difference of    
procedure in the case of the antecedent1
 namely1 that it is affirmed in the     

partly conjunctive1 but denied in the   
disjunctive syllogism1 is due merely to 
the fact that in the disjunctive        
proposition the truth of the consequent 
is involved in the falsity of the       
antecedent1 so that the antecedent being
 necessarily negative1 to deny it in    
appearance is in reality to assert it4  
,,chapter ,,xxv4  ,the ,disjunctive     
,syllogism regarded as an ,immediate    
,inference4    #ggj4 ,if no stress be   
laid on the transition from disjunctive 
hypothesis to fact1 the disjunctive     
syllogism will run with the same        
facility as its predecessor into the    
moulds of immediate inference4   #gga4  
,denial of ,antecedent4                 
,subalternation4    ,either ,a is ,b or 
,c is ,d1       ,every case of ,a not   
being ,b                                
is a case of ,c being ,d4   4'4 ,a not  
being ,b1 ,c is ,d4     4'4 ,some case  
of ,a not being ,b                      
is a case of ,c being ,d4   #ggb4       
,denial of ,consequent4      ,conversion

 by ,contraposition                     
,subalternation4    ,either ,a is ,b or 
,c is ,d4       ,all cases of ,a not    
being ,b                                
are cases of ,c being ,d4   4'4 ,c not  
being ,d1 ,a is ,b      4'4 ,all cases  
of ,c not being ,d are                  
cases of ,a being ,b4                   
4'4 ,some case of ,c not being ,d is    
a case of ,a being ,b4   #ggc4          
,similarly the two invalid types of     
disjunctive syllogism will be found to  
coincide with fallacies of immediate    
inference4   #ggd4    ,affirmation of   
,antecedent4   ,contraposition without  
,conversion4    ,either ,a is ,b or ,c  
is ,d4         ,all cases of ,a not     
being ,b are                            
cases of ,c being ,d4   4'4 ,a being ,b1
 ,c is not ,d        4'4 ,all cases of  
,a being ,b are                         
cases of ,c not being ,d4   #gge4 ,the  
affirmation of the antecedent thus comes
 under the formula--    ,all not-,a is  
,b1   4'4 ,all ,a is not-,b1  a form of 

inference which cannot hold except where
 ,a and ,b are known to be incompatible4
 ,who1 for instance1 would assent to    
this8--    ,all non-boating men play    
cricket4   4'4 ,all boating men are     
non-cricketers4   #ggf4    ,affirmation 
of ,consequent4   ,simple ,conversion of
 ,a4    ,either ,a is ,b or ,c is ,d4   
,all cases of ,a not being ,b are       
cases of ,c being ,d4   4'4,c being ,d1 
,a is not ,b4         4'4 ,all cases of 
,c being ,d are                         
cases of ,a not being ,b4   #ggg4 ,we   
may however argue in this way--         
,conversion of ,a per accidens4         
,either ,a is ,b or ,c is ,d4           
,all cases of ,a not being ,b           
are cases of ,c being ,d4   4'4 ,c being
 ,d1 ,a is sometimes ,b4   4'4 ,some    
cases of ,c being ,d are                
cases of ,a not being ,b4    ,the men   
who pass this examination must have     
either talent or industry4   4'4        
,granting that they are industrious1    
they may be without talent4             

,,chapter ,,xxvi4  ,of the ,mixed ,form 
of ,complex ,syllogism4    #ggh4 ,under 
this head are included all syllogisms in
 which a conjunctive is combined with a 
disjunctive premiss4 ,the best known    
form is    ,the ,dilemma4    #ggi4 ,the 
,dilemma may be defined as--    ,a      
complex syllogism1 having for its major 
premiss a conjunctive   proposition with
 more than one antecedent1 or more than 
one   consequent1 or both1 which        
7antecedent or consequent7 the minor    
premiss disjunctively affirms or denies4
   #ghj4 ,it will facilitate the        
comprehension of the dilemma1 if the    
following three points are borne in     
mind--    7#a7 that the dilemma conforms
 to the canon of the partly conjunctive 
syllogism1 and therefore a valid        
conclusion can be obtained only by      
affirming the antecedent or denying the 
consequent2    7#b7 that the minor      
premiss must be disjunctive2    7#c7    
that if only the antecedent be more than
 one1 the conclusion   will be a simple 

proposition2 but if both antecedent and 
consequent   be more than one1 the      
conclusion will itself be disjunctive4  
#gha4 ,the dilemma1 it will be seen1    
differs from the partly conjunctive     
syllogism chiefly in the fact of having 
a disjunctive affirmation of the        
antecedent or denial of the consequent  
in the minor1 instead of a simple one4  
,it is this which constitutes the       
essence of the dilemma1 and which       
determines its possible varieties4 ,for 
if only the antecedent or only the      
consequent be more than one1 we must1 in
 order to obtain a disjunctive minor1   
affirm the antecedent or deny the       
consequent respectively2 whereas1 if    
there be more than one of both1 it is   
open to us to take either course4 ,this 
gives us four types of dilemma4   #ghb4 
7#a74 ,simple ,constructive4      ,if ,a
 is ,b or ,c is ,d1 ,e is ,f4           
,either ,a is ,b or ,c is ,d4     4'4 ,e
 is ,f4    7#b74 ,simple ,destructive4  
,if ,a is ,b1 ,c is ,d and ,e is ,f4    

,either ,c is not ,d or ,e is not ,f4   
4'4 ,a is not ,b4    7#c74 ,complex     
,constructive4      ,if ,a is ,b1 ,c is 
,d2 and if ,e is ,f1 ,g is ,h4          
,either ,a is ,b or ,e is ,f4     4'4   
,either ,c is ,d or ,g is ,h4    7#d74  
,complex ,destructive4      ,if ,a is   
,b1 ,c is ,d2 and if ,e is ,f1 ,g is ,h4
     ,either ,c is not ,d or ,g is not  
,h4     4'4 ,either ,a is not ,b or ,e  
is not ,f4   #ghc4    7#a74 ,simple     
,constructive4      ,if she sinks or if 
she swims1 there will be an end of her4 
,she must either sink or swim4     4'4  
,there will be an end of her4    7#b74  
,simple ,destructive4      ,if ,i go to 
,town1 ,i must pay for my ticket and pay
 my hotel bill4     ,either ,i cannot   
pay for my ticket or ,i cannot pay my   
hotel bill4     4'4 ,i cannot go to     
,town4    7#c74 ,complex ,constructive4 
,if ,i stay in this room1 ,i shall be   
burnt to death1 and if ,i jump     out  
of the window1 ,i shall break my neck4  
,i must either stay in the room or jump 

out of the window4     4'4 ,i must      
either be burnt to death or break my    
neck4    7#d74 ,complex ,destructive4   
,if he were clever1 he would see his    
mistake2 and     if he were candid1 he  
would acknowledge it4     ,either he    
does not see his mistake or he will not 
acknowledge it4     4'4 ,either he is   
not clever or he is not candid4   #ghd4 
,it must be noticed that the simple     
destructive dilemma would not admit of a
 disjunctive consequent4 ,if we said1   
,if ,a is ,b1 either ,c is ,d or ,e is  
,f1   ,either ,c is not ,d or ,e is not 
,f1  we should not be denying the       
consequent4 ,for ',e is not ,f' would   
make it true that ,c is ,d1 and ',c is  
not ,d' would make it true that ,e is   
,f2 so that in either case we should    
have one of the alternatives true1 which
 is just what the disjunctive form      
',either ,c is ,d or ,e is ,f' insists  
upon4   #ghe4 ,in the case of the       
complex constructive dilemma the several
 members1 instead of being              

distributively assigned to one another1 
may be connected together as a          
whole--thus--    ,if either ,a is ,b or 
,e is ,f1 either ,c is ,d or ,g is ,h4  
,either ,a is ,b or ,e is ,f4   4'4     
,either ,c is ,d or ,g is ,h4  ,in this 
shape the likeness of the dilemma to the
 partly conjunctive syllogism is more   
immediately recognisable4  ,the major   
premiss in this shape is vaguer than in 
the former4 ,for each antecedent has now
 a disjunctive choice of consequents1   
instead of being limited to one4 ,this  
vagueness1 however1 does not affect the 
conclusion4 ,for1 so long as the        
conclusion is established1 it does not  
matter from which members of the major  
its own members flow4   #ghf4 ,it must  
be carefully noticed that we cannot     
treat the complex destructive dilemma in
 the same way4    ,if either ,a is ,b or
 ,e is ,f1 either ,c is ,d or ,g is ,h4 
,either ,c is not ,d or ,g is not ,h4   
,since the consequents are no longer    
connected individually with the         

antecedents1 a disjunctive denial of    
them leaves it still possible for the   
antecedent as a whole to be true4 ,for  
',c is not ,d' makes it true that ,g is 
,h1 and ',g is not ,h' makes it true    
that ,c is ,d4 ,in either case then one 
is true1 which is all that was demanded 
by the consequent of the major4 ,hence  
the consequent has not really been      
denied4   #ghg4 ,for the sake of        
simplicity we have limited the examples 
to the case of two antecedents or       
consequents4  ,but we may have as many  
of either as we please1 so as to have a 
,trilemma1 a ,tetralemma1 and so on4    
,,trilemma4    ,if ,a is ,b1 ,c is ,d2  
and if ,e is ,f1 ,g is ,h2 and if ,k is 
,l1 ,m is ,n4   ,either ,a is ,b or ,e  
is ,f or ,k is ,l4   4'4 ,either ,c is  
,d or ,g is ,h or ,k is ,l4   #ghh4     
,having seen what the true dilemma is1  
we shall now examine some forms of      
reasoning which resemble dilemmas       
without being so4   #ghi4 ,this1 for    
instance1 is not a dilemma--    ,if ,a  

is ,b or if ,e is ,f1 ,c is ,d4   ,but  
,a is ,b and ,e is ,f4   4'4 ,c is ,d4  
,if he observes the sabbath or if he    
refuses to eat pork1 he is a   ,jew4    
,but he both observes the sabbath and   
refuses to eat pork4   4'4 ,he is a     
,jew4  ,what we have here is a          
combination of two partly conjunctive   
syllogisms with the same conclusion1    
which would have been established by    
either of them singly4  ,the proof is   
redundant4   #gij4 ,neither is the      
following a dilemma--    ,if ,a is ,b1  
,c is ,d and ,e is ,f4   ,neither ,c is 
,d nor ,e is ,f4   4'4 ,a is not ,b4    
,if this triangle is equilateral1 its   
sides and its angles will be   equal4   
,but neither its sides nor its angles   
are equal4   4'4 ,it is not equilateral4
  ,this is another combination of two   
conjunctive syllogisms1 both pointing to
 the same conclusion4 ,the proof is     
again redundant4 ,in this case we have  
the consequent denied in both1 whereas  
in the former we had the antecedent     

affirmed4 ,it is only for convenience   
that such arguments as these are thrown 
into the form of a single syllogism4    
,their real distinctness may be seen    
from the fact that we here deny each    
proposition separately1 thus making two 
independent statements--,c is not ,d and
 ,e is not ,f4 ,but in the true instance
 of the simple destructive dilemma1 what
 we deny is not the truth of the two    
propositions contained in the           
consequent1 but their compatibility2 in 
other words we make a disjunctive       
denial4   #gia4 ,nor yet is the         
following a dilemma--    ,if ,a is ,b1  
either ,c is ,d or ,e is ,f4   ,neither 
,c is ,d nor ,e is ,f4   4'4 ,a is not  
,b4    ,if the barometer falls there    
will be either wind or rain4   ,there is
 neither wind nor rain4   4'4 ,the      
barometer has not fallen4  ,what we have
 here is simply a conjunctive major with
 the consequent denied in the minor4 ,in
 the consequent of the major it is      
asserted that the two propositions1 ',c 

is ,d' and ',e is ,f' cannot both be    
false2 and in the minor this is denied  
by the assertion that they are both     
false4   #gib4 ,a dilemma is said to be 
rebutted or retorted1 when another      
dilemma is made out proving an opposite 
conclusion4 ,if the dilemma be a sound  
one1 and its premisses true1 this is of 
course impossible1 and any appearance of
 contradiction that may present itself  
on first sight must vanish on           
inspection4 ,the most usual mode of     
rebutting a dilemma is by transposing   
and denying the consequents in the      
major--    ,if ,a is ,b1 ,c is ,d2 and  
if ,e is ,f1 ,g is ,h4   ,either ,a is  
,b or ,e is ,f4   4'4 ,either ,c is ,d  
or ,g is ,h4  ,the same rebutted--      
,if ,a is ,b1 ,g is not ,h2 and if ,e is
 ,f1 ,c is not ,d4   ,either ,a is ,b or
 ,e is ,f4   4'4 ,either ,g is not ,h or
 ,c is not ,d4      ,either ,c is not ,d
 or ,g is not ,h4   #gic4 ,under this   
form comes the dilemma addressed by the 
,athenian mother to her son--',do not   

enter public life3 for1 if you say what 
is just1 men will hate you2 and1 if you 
say what is unjust1 the gods will hate  
you' to which the following retort was  
made--',i ought to enter public life3   
for1 if #a say what is just1 the gods   
will love me2 and1 if #a say what is    
unjust1 men will love me4' ,but the two 
conclusions here are quite compatible4  
,a man must1 on the given premisses1 be 
both hated and loved1 whatever course he
 takes4 ,so far indeed are two          
propositions of the form    ,either ,c  
is ,d or ,g is ,h1   and ,either ,c is  
not ,d or ,g is not ,h1  from being     
incompatible1 that they express         
precisely the same thing when           
contradictory alternatives have been    
selected1 e4g4--    ,either a triangle  
is equilateral or non-equilateral4      
,either a triangle is non-equilateral or
 equilateral4   #gid4 ,equally illusory 
is the famous instance of rebutting a   
dilemma contained in the story of       
,protagoras and ,euathlus 7,aul4 ,gell4 

,noct4 ,alt4 v4 #aj71 ,euathlus was a   
pupil of ,protagoras in rhetoric4 ,he   
paid half the fee demanded by his       
preceptor before receiving lessons1 and 
agreed to pay the remainder when he won 
his first case4  ,but as he never       
proceeded to practise at the bar1 it    
became evident that he meant to bilk his
 tutor4 ,accordingly ,protagoras himself
 instituted a law-suit against him1 and 
in the preliminary proceedings before   
the jurors propounded to him the        
following dilemma--',most foolish young 
man1 whatever be the issue of this suit1
 you must pay me what ,i claim3 for1 if 
the verdict be given in your favour1 you
 are bound by our bargain2 and if it be 
given against you1 you are bound by the 
decision of the jurors4'  ,the pupil1   
however1 was equal to the occasion1 and 
rebutted the dilemma as follows4 ',most 
sapient master1 whatever be the issue of
 this suit1 ,i shall not pay you what   
you claim3 for1 if the verdict be given 
in my favour1 ,i am absolved by the     

decision of the jurors2 and1 if it be   
given against me1 ,i am absolved by our 
bargain4' ,the jurors are said to have  
been so puzzled by the conflicting      
plausibility of the arguments that they 
adjourned the case till the ,greek      
,kalends4 ,it is evident1 however1 that 
a grave injustice was thus done to      
,protagoras4 ,his dilemma was really    
invincible4 ,in the counter-dilemma of  
,euathlus we are meant to infer that    
,protagoras would actually lose his fee1
 instead of merely getting it in one way
 rather than another4 ,in either case he
 would both get and lose his fee1 in the
 sense of getting it on one plea1 and   
not getting it on another3 but in       
neither case would he actually lose it4 
#gie4 ,if a dilemma is correct in form1 
the conclusion of course rigorously     
follows3 but a material fallacy often   
underlies this form of argument in the  
tacit assumption that the alternatives  
offered in the minor constitute an      
exhaustive division4 ,thus the dilemma  

',if pain is severe1 it will be brief2  
and if it last long it will be slight1' 
c41 leaves out of sight the unfortunate 
fact that pain may both be severe and of
 long continuance4 ,again the following 
dilemma--    ,if students are idle1     
examinations are unavailing2 and1 if    
they are industrious1 examinations are  
superfluous1   ,students are either idle
 or industrious1   4'4 ,examinations are
 either unavailing or superfluous1  is  
valid enough1 so far as the form is     
concerned4 ,but the person who used it  
would doubtless mean to imply that      
students could be exhaustively divided  
into the idle and the industrious4 ,no  
deductive conclusion can go further than
 its premisses2 so that all that the    
above conclusion can in strictness be   
taken to mean is that examinations are  
unavailing1 when students are idle1 and 
superfluous1 when they are              
industrious--which is simply a          
reassertion as a matter of fact of what 
was previously given as a pure          

hypothesis4     ,,chapter ,,xxvii4  ,of 
the ,reduction of the ,dilemma4    #gif4
 ,as the dilemma is only a peculiar     
variety of the partly conjunctive       
syllogism1 we should naturally expect to
 find it reducible in the same way to   
the form of a simple syllogism4 ,and    
such is in fact the case4 ,the          
constructive dilemma conforms to the    
first figure and the destructive to the 
second4    #a7 ,simple ,constructive    
,dilemma4                               
,barbara4   ,if ,a is ,b or if ,e is ,f1
 ,c is ,d4   ,all cases of either ,a    
being ,b or ,e                          
being ,f are cases of ,c being ,d4      
,either ,a is ,b or ,e is ,f4           
,all actual cases are cases of either   
,a being ,b ,,op ,e being ,f4   4'4 ,c  
is ,d4                       4'4 ,all   
actual cases are cases of ,c            
being ,d4    7#b7 ,simple ,destructive4 
,camstres4   ,if ,a is ,b1 ,c is ,d and 
,e is ,f4      ,all cases of ,a being ,b
 are cases of                           

,c being ,d and ,e being ,f4   ,either  
,c is not ,d or ,e is not ,f4   ,no     
actual cases are cases of ,c being      
,d and ,e being ,f4   4'4 ,a is not ,b4 
4'4 ,no actual cases are cases of ,a    
being ,b4    7#c7 ,complex              
,constructive4                          
,barbara4   ,if ,a is ,b1 ,c is ,d2 and 
if ,e is ,f1     ,all cases of either ,a
 being ,b or      ,g is ,h4             
being ,f are cases of either ,c being   
,d or ,g being ,h4   ,either ,a is ,b or
 ,e is ,f4              ,all actual     
cases are cases of either ,a            
being ,b or ,e being ,f4   4'4 ,either  
,c is ,d or ,g is ,h4          4'4 ,all 
actual cases are cases of either ,c     
being ,d or ,g being ,h4    7#d7        
,complex ,destructive4    ,if ,a is ,b1 
,c is ,d2 and if ,e is ,f1   ,all cases 
of ,a being ,b and ,e being ,f   ,g is  
,h4                                are  
cases of ,c being ,d and ,g             
being ,h4   ,either ,c is not ,d ,or ,g 
is           ,no actual cases are cases 

of ,c being      not ,h                 
,d and ,g being ,h4   ,either ,a is not 
,b or ,e is           ,no actual cases  
are cases of ,a being   not ,f4         
,b and ,e being ,f4   #gig4 ,there is   
nothing to prevent our having ,darii1   
instead of ,barbara1 in the constructive
 form1 and ,baroko1 instead of          
,camestres1 in the destructive4 ,as in  
the case of the partly conjunctive      
syllogism the remaining moods of the    
first and second figure are obtained by 
taking a negative proposition as the    
consequent of the major premiss1 e4g4-- 
,simple ,constructive4                  
,celarent or ,ferio4   ,if ,a is ,b or  
if ,e is ,f1 ,c is not ,d  ,no cases of 
either ,a being ,b or ,e                
being ,f are cases of ,c being ,d4      
,either ,a is ,b or ,e is ,f4           
,all 7or some7 actual cases are cases of
                                        
either ,a being ,b or ,e being ,f   4'4 
,c is not ,d4                     4'4   
,all 7or some7 actual cases are not     

cases of ,c being ,d4     ,,chapter     
,,xxviii4  ,of the ,dilemma regarded as 
an ,immediate ,inference4    #gih4 ,like
 the partly conjunctive syllogism1 the  
dilemma can be expressed under the forms
 of immediate inference4  ,as before1   
the conclusion in the constructive type 
resolves itself into the subalternate of
 the major itself1 and in the           
destructive type into the subalternate  
of its contrapositive4  ,the simple     
constructive dilemma1 for instance1 may 
be read as follows--    ,if either ,a is
 ,b or ,e is ,f1 ,c is ,d1   4'4 ,either
 ,a being ,b or ,e being ,f1 ,c is ,d1  
which is equivalent to    ,every case of
 either ,a being ,b or ,e being ,f is a 
case of ,c being ,d4   4'4 ,some case of
 either ,a being ,b or ,e being ,f is a 
case of ,c being ,d4  ,the descent here 
from 'every' to 'some' takes the place  
of the transition from hypothesis to    
fact4   #gii4 ,again the complex        
destructive may be read thus--    ,if ,a
 is ,b1 ,c is ,d2 and if ,e is ,f1 ,g is

 ,h1   4'4 ,it not being true that ,c is
 ,d and ,g is ,h1 it is not       true  
that ,a is ,b and ,e is ,f1  which may  
be resolved into two steps of immediate 
inference1 namely1 conversion by        
contraposition followed by              
subalternation--    ,all cases of ,a    
being ,b and ,e being ,f are cases of ,c
 being ,d and ,g   being ,h4   4'4      
,whatever is not a case of ,c being ,d  
and ,g being ,h is not a case   of ,a   
being ,b and ,e being ,f4   4'4 ,some   
case which is not one of ,c being ,d and
 ,g being ,h is not a   case of ,a being
 ,b and ,e being ,f4     ,,chapter      
,,xxix4  ,of ,trains of ,reasoning4     
#hjj4 ,the formal logician is only      
concerned to examine whether the        
conclusion duly follows from the        
premisses3 he need not concern himself  
with the truth or falsity of his data4  
,but the premisses of one syllogism may 
themselves be conclusions deduced from  
other syllogisms1 the premisses of which
 may in their turn have been established

 by yet earlier syllogisms4 ,when       
syllogisms are thus linked together we  
have what is called a ,train of         
,reasoning4   #hja4 ,it is plain that   
all truths cannot be established by     
reasoning4 ,for the attempt to do so    
would involve us in an infinite regress1
 wherein the number of syllogisms       
required would increase at each step in 
a geometrical ratio4 ,to establish the  
premisses of a given syllogism we should
 require two preceding syllogisms2 to   
establish their premisses1 four2 at the 
next step backwards1 eight2 at the next1
 sixteen2 and so on ad infinitum4 ,thus 
the very possibility of reasoning       
implies truths that are known to us     
prior to all reasoning2 and1 however    
long a train of reasoning may be1 we    
must ultimately come to truths which are
 either self-evident or are taken for   
granted4   #hjb4 ,any syllogism which   
establishes one of the premisses of     
another is called in reference to that  
other a ,pro-syllogism1 while a         

syllogism which has for one of its      
premisses the conclusion of another     
syllogism is called in reference to that
 other an ,epi-syllogism4    ,the       
,epicheirema4    #hjc4 ,the name        
,epicheirema is given to a syllogism    
with one or both of its premisses       
supported by a reason4  ,thus the       
following is a double epicheirema--     
,all ,b is ,a1 for it is ,e4   ,all ,c  
is ,b1 for it is ,f4   4'4 ,all ,c is   
,a4    ,all virtue is praiseworthy1 for 
it promotes the general welfare4        
,generosity is a virtue1 for it prompts 
men to postpone self to others4   4'4   
,generosity is praiseworthy4   #hjd4 ,an
 epicheirema is said to be of the first 
or second order according as the major  
or minor premiss is thus supported4 ,the
 double epicheirema is a combination of 
the two orders4   #hje4 ,an epicheirema1
 it will be seen1 consists of one       
syllogism fully expressed together with 
one1 or1 it may be1 two enthymemes 7    
#eeg74 ,in the above instance1 if the   

reasoning which supports the premisses  
were set forth at full length1 we should
 have1 in place of the enthymemes1 the  
two following pro-syllogisms--    7i7   
,all ,e is ,a4       ,all ,b is ,e4     
4'4 ,all ,b is ,a4    ,whatever promotes
 the general welfare is praiseworthy4   
,every virtue promotes the general      
welfare4    4'4 ,every virtue is        
praiseworthy4    7#b7 ,all ,f is ,b4    
,all ,c is ,f4        4'4 ,all ,c is ,b4
    ,whatever prompts men to postpone   
self to others is a virtue4             
,generosity prompts men to postpone self
 to others4    4'4 ,generosity is a     
virtue4   #hjf4 ,the enthymemes in the  
instance above given are both of the    
first order1 having the major premiss   
suppressed4  ,but there is nothing to   
prevent one or both of them from being  
of the second order--    ,all ,b is ,a1 
because all ,f is4   ,all ,c is ,b1     
because all ,f is4   4'4 ,all ,c is ,a4 
,all ,mahometans are fanatics1 because  
all ,monotheists are4   ,these men are  

,mahometans1 because all ,persians are4 
4'4 ,these men are fanatics4  ,here it  
is the minor premiss in each syllogism  
that is suppressed1 namely1    7#a7 ,all
 ,mahometans are ,monotheists4    7#b7  
,these men are ,persians4    ,the       
,sorites4    #hjg4 ,the ,sorites is the 
neatest and most compendious form that  
can be assumed by a train of reasoning4 
#hjh4 ,it is sometimes more             
appropriately called the chain-argument1
 and map be defined as--    ,a train of 
reasoning1 in which one premiss of each 
epi-syllogism is   supported by a       
pro-syllogism1 the other being taken for
 granted4  ,this is its inner essence4  
#hji4 ,in its outward form it may be    
described as--,a series of propositions1
 each of which has one term in common   
with that which preceded it1 while in   
the conclusion one of the terms in the  
last proposition becomes either subject 
or predicate to one of the terms in the 
first4   #haj4 ,a sorites may be        
either--    7#a7 ,progressive1    or    

7#b7 ,regressive4  ,progressive         
,sorites4    ,all ,a is ,b4   ,all ,b is
 ,c4   ,all ,c is ,d4   ,all ,d is ,e4  
4'4 ,all ,a is ,e4  ,regressive         
,sorites4    ,all ,d is ,e4   ,all ,c is
 ,d4   ,all ,b is ,c4   ,all ,a is ,b4  
4'4 ,all ,a is ,e4   #haa4 ,the usual   
form is the progressive2 so that the    
sorites is commonly described as a      
series of propositions in which the     
predicate of each becomes the subject of
 the next1 while in the conclusion the  
last predicate is affirmed or denied of 
the first subject4 ,the regressive form1
 however1 exactly reverses these        
attributes2 and would require to be     
described as a series of propositions1  
in which the subject of each becomes the
 predicate of the next1 while in the    
conclusion the first predicate is       
affirmed or denied of the last subject4 
#hab4 ,the regressive sorites1 it will  
be observed1 consists of the same       
propositions as the progressive one1    
only written in reverse order4 ,why     

then1 it may be asked1 do we give a     
special name to it1 though we do not    
consider a syllogism different1 if the  
minor premiss happens to precede the    
major8 ,it is because the sorites is not
 a mere series of propositions1 but a   
compressed train of reasoning2 and the  
two trains of reasoning may be resolved 
into their component syllogisms in such 
a manner as to exhibit a real difference
 between them4   #hac4 ,the ,progressive
 ,sorites is a train of reasoning in    
which the minor premiss of each         
epi-syllogism is supported by a         
pro-syllogism1 while the major is taken 
for granted4   #had4 ,the ,regressive   
,sorites is a train of reasoning in     
which the major premiss of each         
epi-syllogism is supported by a         
pro-syllogism1 while the minor is taken 
for granted4    ,progressive ,sorites4  
7i7 ,all ,b is ,c4       ,all ,a is ,b4 
4'4 ,all ,a is ,c4    7#b7 ,all ,c is   
,d4       ,all ,a is ,c4       4'4 ,all 
,a is ,d4    7#c7 ,all ,d is ,e4        

,all ,a is ,d4       4'4 ,all ,a is ,e4 
,regressive ,sorites4   7#a7 ,all ,d is 
,e4       ,all ,c is ,d4       4'4 ,all 
,c is ,e4    7#b7 ,all ,c is ,e4        
,all ,b is ,c4       4'4 ,all ,b is ,e4 
7#c7 ,all ,b is ,e4       ,all ,a is ,b4
       4'4 ,all ,a is ,e4   #hae4 ,here 
is a concrete example of the two kinds  
of sorites1 resolved each into its      
component syllogisms--  ,progressive    
,sorites4    ,all ,bideford men are     
,devonshire men4   ,all ,devonshire men 
are ,englishmen4   ,all ,englishmen are 
,teutons4   ,all ,teutons are ,aryans4  
4'4 ,all ,bideford men are ,aryans4     
7#a7 ,all ,devonshire men are           
,englishmen4       ,all ,bideford men   
are ,devonshire men4       4'4 ,all     
,bideford men are ,englishmen4    7#b7  
,all ,englishmen are ,teutons4          
,all ,bideford men are ,englishmen4     
4'4 ,all ,bideford men are ,teutons4    
7#c7 ,all ,teutons are ,aryans4         
,all ,bideford men are ,teutons4        
4'4 ,all ,bideford men are ,aryans4     

,regressive ,sorites4    ,all ,teutons  
are ,aryans4   ,all ,englishmen are     
,teutons4   ,all ,devonshiremen are     
,englishmen4   ,all ,bideford men are   
,devonshiremen4   4'4 ,all ,bideford men
 are ,aryans4    7#a7 ,all ,teutons are 
,aryans4       ,all ,englishmen are     
,teutons4       4'4 ,all ,englishmen are
 ,aryans4    7#b7 ,all ,englishmen are  
,aryans4       ,all ,devonshiremen are  
,englishmen4       4'4 ,all             
,devonshiremen are ,aryans4    7#c7 ,all
 ,devonshiremen are ,aryans4       ,all 
,bideford men are ,devonshiremen4       
4'4 ,all ,bideford men are ,aryans4     
#haf4 ,when expanded1 the sorites is    
found to contain as many syllogisms as  
there are propositions intermediate     
between the first and the last4 ,this is
 evident also on inspection by counting 
the number of middle terms4   #hag4 ,in 
expanding the progressive form we have  
to commence with the second proposition 
of the sorites as the major premiss of  
the first syllogism4 ,in the progressive

 form the subject of the conclusion is  
the same in all the syllogisms2 in the  
regressive form the predicate is the    
same4 ,in both the same series of means1
 or middle terms1 is employed1 the      
difference lying in the extremes that   
are compared with one another through   
them4  ,illustration   #hah4 ,it is     
apparent from the figure that in the    
progressive form we work from within    
outwards1 in the regressive form from   
without inwards4 ,in the former we first
 employ the term ',devonshiremen' as a  
mean to connect ',bideford men' with    
',englishmen'2 next we employ           
',englishmen' as a mean to connect the  
same subject ',bideford men' with the   
wider term ',teutons'2 and1 lastly1 we  
employ ',teutons' as a mean to connect  
the original subject ',bideford men'    
with the ultimate predicate ',ayrans4'  
#hai4 ,reversely1 in the regressive form
 we first use ',teutons' as a mean      
whereby to bring ',englishmen' under    
',aryans'2 next we use ',englishmen' as 

a mean whereby to bring ',devonshiremen'
 under the dame predicate ',aryans'2    
and1 lastly1 we use ',devonshiremen' as 
a mean whereby to bring the ultimate    
subject ',bideford men' under the       
original predicate ',aryans4'   #hbj4 ,a
 sorites may be either ,regular or      
,irregular4   #hba4 ,in the regular form
 the terms which connect each           
proposition in the series with its      
predecessor1 that is to say1 the middle 
terms1 maintain a fixed relative        
position2 so that1 if the middle term be
 subject in one1 it will always be      
predicate in the other1 and vice vers4  
,in the irregular form this symmetrical 
arrangement is violated4   #hbb4 ,the   
syllogisms which compose a regular      
sorites1 whether progressive or         
regressive1 will always be in the first 
figure4  ,in the irregular sorites the  
syllogisms may fall into different      
figures4   #hbc4 ,for the regular       
sorites the following rules may be laid 
down4    7#a7 ,only one premiss can be  

particular1 namely1 the first1 if the   
sorites be progressive1 the last1 if it 
be regressive4    7#b7 ,only one premiss
 can be negative1 namely1 the last1 if  
the   sorites be progressive1 the first1
 if it be regressive4   #hbd4 ,proof of 
the ,rules for the ,regular ,sorites4   
7#a7 ,in the progressive sorites the    
proposition which stands first is   the 
only one which appears as a minor       
premiss in the expanded   form4 ,each of
 the others is used in its turn as a    
major4  ,if any   proposition1          
therefore1 but the first were           
particular1 there would   be a          
particular major1 which involves        
undistributed middle1 if the   minor be 
affirmative1 as it must be in the first 
figure4    ,in the regressive sorites1  
if any proposition except the last were 
particular1 we should have a particular 
conclusion in the syllogism   in which  
it occurred as a premiss1 and so a      
particular major in the   next          
syllogism1 which again is inadmissible1 

as involving   undistributed middle4    
7#b7 ,in the progressive sorites1 if any
 premiss before the last were           
negative1 we should have a negative     
conclusion in the syllogism in   which  
it occurs4 ,this would necessitate a    
negative minor in the next   syllogism1 
which is inadmissible in the first      
figure1 as involving   illicit process  
of the major4    ,in the regressive     
sorites the proposition which stands    
first is the   only one which appears as
 a major premiss in the expanded form4  
,each of the others is used in its turn 
as a minor4 ,if any premiss1            
therefore1 but the first were negative1 
we should have a negative   minor in the
 first figure1 which involves illicit   
process of the   major4   #hbe4 ,the    
rules above given do not apply to the   
irregular sorites1 except so far as that
 only one premiss can be particular and 
only one negative1 which follows from   
the general rules of syllogism4 ,but    
there is nothing to prevent any one     

premiss from being particular or any one
 premiss from being negative1 as the    
subjoined examples will show4 ,both the 
instances chosen belong to the          
progressive order of sorites4    7#a7   
,barbara4   ,all ,b is ,a4   ,all ,c is 
,b4   ,all ,c is ,a4    ,all ,b is ,a4  
,all ,c is ,b4   ,some ,c is ,d4   ,all 
,d is ,e    4'4 ,some ,a is ,e          
,illustration    7#b7 ,disamis4   ,some 
,c is ,d4   ,all ,c is ,a4   ,some ,a is
 ,d4    7#c7 ,darii4   ,all ,d is ,e    
,some ,a is ,d4   ,some ,a is ,e4       
7#a7 ,barbara4   ,all ,b is ,c4   ,all  
,a is ,b4   ,all ,a is ,c4    ,all ,a is
 ,b4   ,all ,b is ,c4   ,no ,d is ,c4   
,all ,e is ,d4    4'4 ,no ,a is ,e4     
,illustration    7#b7 ,cesare4   ,no ,d 
is ,c4   ,all ,a is ,c4    4'4 ,no ,a is
 ,d4    7#c7 ,camestres4   ,all ,e is   
,d4   ,no ,a is ,d4    4'4 ,no ,a is ,e4
   #hbf4 ,a chain argument may be       
composed consisting of conjunctive      
instead of simple propositions4 ,this is
 subject to the same laws as the simple 

sorites1 to which it is immediately     
reducible4    ,progressive4             
,regressive4   ,if ,a is ,b1 ,c is ,d4  
,if ,e is ,f1 ,g is ,h4   ,if ,c is ,d1 
,e is ,f4                ,if ,c is ,d1  
,e is ,f4   ,if ,e is ,f1 ,g is ,h4     
,if ,a is ,b1 ,c is ,d4    4'4 ,if ,a is
 ,b1 ,g is ,h4            4'4 ,if ,a is 
,b1 ,g is ,h4     ,,chapter ,,xxx4  ,of 
,fallacies4    #hbg4 ,after examining   
the conditions on which correct thoughts
 depend1 it is expedient to classify    
some of the most familiar forms of      
error4 ,it is by the treatment of the   
,fallacies that logic chiefly vindicates
 its claim to be considered a practical 
rather than a speculative science4  ,to 
explain and give a name to fallacies is 
like setting up so many sign-posts on   
the various turns which it is possible  
to take off the road of truth4   #hbh4  
,by a fallacy is meant a piece of       
reasoning which appears to establish a  
conclusion without really doing so4     
,the term applies both to the legitimate

 deduction of a conclusion from false   
premisses and to the illegitimate       
deduction of a conclusion from any      
premisses4 ,there are errors incidental 
to conception and judgement1 which might
 well be brought under the name2 but the
 fallacies with which we shall concern  
ourselves are confined to errors        
connected with inference4   #hbi4 ,when 
any inference leads to a false          
conclusion1 the error may have arisen   
either in the thought itself or in the  
signs by which the thought is conveyed4 
,the main sources of fallacy then are   
confined to two--    7#a7 thought1      
7#b7 language4   #hcj4 ,this is the     
basis of ,aristotle's division of       
fallacies1 which has not yet been       
superseded4 ,fallacies1 according to    
him1 are either in the language or      
outside of it4 ,outside of language     
there is no source of error but thought4
 ,for things themselves do not deceive  
us1 but error arises owing to a         
misinterpretation of things by the mind4

 ,thought1 however1 may err either in   
its form or in its matter4 ,the former  
is the case where there is some         
violation of the laws of thought2 the   
latter whenever thought disagrees with  
its object4 ,hence we arrive at the     
important distinction between ,formal   
and ,material fallacies1 both of which1 
however1 fall under the same negative   
head of fallacies other than those of   
language4              ,in the language 
7in the signs of thought7               
,fallacy -                         --,in
 the ,form4            --,outside the   
language  -             7in the thought 
itself7                                 
--in the ,matter4   #hca4 ,there are    
then three heads to which fallacies may 
be referred-namely1 ,formal ,fallacies1 
,fallacies of ,language1 which are      
commonly known as ,fallacies of         
,ambiguity1 and1 lastly1 ,material      
,fallacies4   #hcb4 ,aristotle himself  
only goes so far as the first step in   
the division of fallacies1 being content

 to class them according as they are in 
the language or outside of it4  ,after  
that he proceeds at once to enumerate   
the infim species under each of the two 
main heads4 ,we shall presently imitate 
this procedure for reasons of           
expediency4  ,for the whole phraseology 
of the subject is derived from          
,aristotle's treatise on ,sophistical   
,refutations1 and we must either keep to
 his method or break away from tradition
 altogether4 ,sufficient confusion has  
already arisen from retaining           
,aristotle's language while neglecting  
his meaning4   #hcc4 ,modern writers on 
logic do not approach fallacies from the
 same point of view as ,aristotle4      
,their object is to discover the most   
fertile sources of error in solitary    
reasoning2 his was to enumerate the     
various tricks of refutation which could
 be employed by a sophist in            
controversy4 ,aristotle's classification
 is an appendix to the ,art of          
,dialectic4   #hcd4 ,another cause of   

confusion in this part of logic is the  
identification of ,aristotle's two-fold 
division of fallacies1 commonly known   
under the titles of ,in dictione and    
,extra diotionem1 with the division into
 ,logical and ,material1 which is based 
on quite a different principle4   #hce4 
,aristotle's division perhaps allows an 
undue importance to language1 in making 
that the principle of division1 and so  
throwing formal and material fallacies  
under a common head4 ,accordingly       
another classification has been adopted1
 which concentrates attention from the  
first upon the process of thought1 which
 ought certainly to be of primary       
importance in the eyes of the logician4 
,this classification is as follows4     
#hcf4 ,whenever in the course of our    
reasoning we are involved in error1     
either the conclusion follows from the  
premisses or it does not4 ,if it does   
not1 the fault must lie in the process  
of reasoning1 and we have then what is  
called a ,logical ,fallacy4 ,if1 on the 

other hand1 the conclusion does follow  
from the premisses1 the fault must lie  
in the premisses themselves1 and we then
 have what is called a ,material        
,fallacy4 ,sometimes1 however1 the      
conclusion will appear to follow from   
the premisses until the meaning of the  
terms is examined1 when it will be found
 that the appearance is deceptive owing 
to some ambiguity in the language4 ,such
 fallacies as these are1 strictly       
speaking1 non-logical1 since the meaning
 of words is extraneous to the science  
which deals with thought4 ,but they are 
called ,semi-logical4 ,thus we arrive by
 a different road at the same three     
heads as before1 namely1 7#a7 ,formal or
 ,purely ,logical ,fallacies1 7#b7      
,semi-logical ,fallacies or ,fallacies  
of ,ambiguity1 7#c7 ,material           
,fallacies4   #hcg4 ,for the sake of    
distinctness we will place the two      
divisions side by side1 before we       
proceed to enumerate the infimae        
species4            --,in the language  

7,fallacy of ,ambiguity7   ,fallacy-    
--,in the ,form4           --,outside   
the language -                          
--,in the ,matter4                      
--,formal or purely logical4            
--,logical -   ,fallacy-                
--,semi-logical                         
7,fallacy of ,ambiguity74               
--,material  #hch4 ,of one of these     
three heads1 namely1 formal fallacies1  
it is not necessary to say much1 as they
 have been amply treated of in the      
preceding pages4 ,a formal fallacy      
arises from the breach of any of the    
general rules of syllogism4             
,consequently it would be a formal      
fallacy to present as a syllogism       
anything which had more or less than two
 premisses4 ,under the latter variety   
comes what is called 'a woman's reason1'
 which asserts upon its own evidence    
something which requires to be proved4  
,schoolboys also have been known to     
resort to this form of                  
argument--',you're a fool4' ',why8'     

',because you are4' ,when the conclusion
 thus merely reasserts one of the       
premisses1 the other must be either     
absent or irrelevant4  ,if1 on the other
 hand1 there are more than two          
premisses1 either there is more than one
 syllogism or the superfluous premiss is
 no premiss at all1 but a proposition   
irrelevant to the conclusion4  #hci4    
,the remaining rules of the syllogism   
are more able to be broken than the     
first2 so that the following scheme     
presents the varieties of formal fallacy
 which are commonly enumerated--        
--,four ,terms4   ,formal               
,fallacy---,undistributed ,middle4      
--,illicit ,process4                    
--,negative ,premisses and ,conclusion4 
#hdj4 ,the ,fallacy of ,four ,terms is a
 violation of the second of the general 
rules of syllogism 7 #ehb74 ,here is a  
palpable instance of it--    ,all men   
who write books are authors4   ,all     
educated men could write books4   4'4   
,all educated men are authors4  ,here   

the middle term is altered in the minor 
premiss to the destruction of the       
argument4 ,the difference between the   
actual writing of books and the power to
 write them is precisely the difference 
between one who is an author and one who
 is not4   #hda4 ,since a syllogism     
consists of three terms1 each of which  
is used twice over1 it would be possible
 to have an apparent syllogism with as  
many as six terms in it4  ,the true name
 for the fallacy therefore is the       
,fallacy of ,more than ,three ,terms4   
,but it is rare to find an attempted    
syllogism which has more than four terms
 in it1 just as we are seldom tendered a
 line as an hexameter1 which has more   
than seven feet4   #hdb4 ,the ,fallacies
 of ,undistributed ,middle and ,illicit 
,process have been treated of under     
#ehe1 #ehf4  ,the heading ',negative    
,premisses and ,conclusion' covers      
violations of the three general rules of
 syllogism relating to negative         
premisses 7 #eij-eic74 ,here is an      

instance of the particular form of the  
fallacy which consists in the attempt to
 extract an affirmative conclusion out  
of two negative premisses--    ,all     
salmon are fish1 for neither salmon nor 
fish belong to the class   mammalia4    
,the accident of a conclusion being true
 often helps to conceal the fact that it
 is illegitimately arrived at4  ,the    
formal fallacies which have just been   
enumerated find no place in ,aristotle's
 division4 ,the reason is plain4  ,his  
object was to enumerate the various     
modes in which a sophist might snatch an
 apparent victory1 whereas by openly    
violating any of the laws of syllogism a
 disputant would be simply courting     
defeat4   #hdc4 ,we now revert to       
,aristotle's classification of          
fallacies1 or rather of ,modes of       
,refutation4 ,we will take the species  
he enumerates in their order1 and notice
 how modern usage has departed from the 
original meaning of the terms4 ,let it  
be borne in mind that1 when the         

deception was not in the language1      
,aristotle did not trouble himself to   
determine whether it lay in the matter  
or in the form of thought4   #hdd4 ,the 
following scheme presents the           
,aristotelian classification to the eye 
at a glance3--                          
--,equivocation4                        
--,amphiboly4               --,in the   
language ---,composition4               
--,division4                            
--,accent4                              
--,figure of ,speech4   ,modes of   -   
,refutation4                            
--,accident4                            
--,a dicto secundum quid4               
--,ignoratio ,elenchi4                  
--,outside the language ---,consequent4 
--,petitio ,principii4                  
--,non causa pro causa4                 
--,many ,questions4  ,footnote3 for ,in 
the language3 ,the ,greek is ,greek3    
para ten lexin1 the exact meaning of    
which is2 'due to the statement4'       
#hde4 ,the ,fallacy of ,equivocation    

,greek3 monuma consists in an ambiguous 
use of any of the three terms of a      
syllogism4 ,if1 for instance1 anyone    
were to argue thus--    ,no human being 
is made of paper1   ,all pages are human
 beings1   4'4 ,no pages are made of    
paper--  the conclusion would appear    
paradoxical1 if the minor term were     
there taken in a different sense from   
that which it bore in its proper        
premiss4 ,this therefore would be an    
instance of the fallacy of ,equivocal   
,minor4   #hdf4 ,for a glaring instance 
of the fallacy of ,equivocal ,major1 we 
may take the following--    ,no         
courageous creature flies1   ,the eagle 
is a courageous creature1   4'4 ,the    
eagle does not fly--  the conclusion    
here becomes unsound only by the major  
being taken ambiguously4   #hdg4 ,it is1
 however1 to the middle term that an    
ambiguity most frequently attaches4 ,in 
this case the fallacy of equivocation   
assumes the special name of the ,fallacy
 of ,ambiguous ,middle4 ,take as an     

instance the following--    ,faith is a 
moral virtue4   ,to believe in the ,book
 of ,mormon is faith4   4'4 ,to believe 
in the ,book of ,mormon is a moral      
virtue4  ,here the premisses singly     
might be granted2 but the conclusion    
would probably be felt to be            
unsatisfactory4  ,nor is the reason far 
to seek4 ,it is evident that belief in a
 book cannot be faith in any sense in   
which that quality can rightly be       
pronounced to be a moral virtue4   #hdh4
 ,the ,fallacy of ,amphiboly 7,greek3   
mphibola7 is an ambiguity attaching to  
the construction of a proposition rather
 than to the terms of which it is       
composed4 ,one of ,aristotle's examples 
is this--    ,greek3 t bolesthai laben  
me tos polemous  which may be           
interpreted to mean either 'the fact of 
my wishing to take the enemy1' or 'the  
fact of the enemies' wishing to take    
me4' ,the classical languages are       
especially liable to this fallacy owing 
to the oblique construction in which the

 accusative becomes subject to the verb4
  ,thus in ,latin we have the oracle    
given to ,pyrrhus 7though of course1 if 
delivered at all1 it must have been in  
,greek7--    ,aio te1 ,a,eacida1        
,romanos vincere posse4   ,pyrrhus the  
,romans shall1 ,i say1 subdue           
7,whately71   ,footnote3 ,cicero1 ,de   
,divinatione1 ii4  #aaf2 ,quintilian1   
,inst4 ,orat4 vii #i1  #f4  which       
,pyrrhus1 as the story runs1 interpreted
 to mean that he could conquer the      
,romans1 whereas the oracle subsequently
 explained to him that the real meaning 
was that the ,romans could conquer him4 
,similar to this1 as ,shakspeare makes  
the ,duke of ,york point out1 is the    
witch's prophecy in ,henry ,,vi 7,second
 ,part1 ,act i1 sc4 #d71    ,the duke   
yet lives that ,henry shall depose4  ,an
 instance of amphiboly may be read on   
the walls of ,windsor ,castle--,hoc     
fecit ,wykeham4 ,the king mas incensed  
with the bishop for daring to record    
that he made the tower1 but the latter  

adroitly replied that what he really    
meant to indicate was that the tower was
 the making of him4 ,to the same head   
may be referred the famous sentence--',i
 will wear no clothes to distinguish me 
from my ,christian brethren4'   #hdi4   
,the ,fallacy of ,composition ,greek3   
diaresis is likewise a case of ambiguous
 construction4 ,it consists1 as         
expounded by ,aristotle1 in taking words
 together which ought to be taken       
separately1 e4g4    ',is it possible for
 a man who is not writing to write8'    
',of course it is4'   ',then it is      
possible for a man to write without     
writing4'  ,and again--    ',can you    
carry this1 that1 and the other8'       
',yes4'   ',then you can carry this1    
that1 and the other1'--  a fallacy      
against which horses would protest1 if  
they could4   #hej4 ,it is doubtless    
this last example which has led to a    
convenient misuse of the term 'fallacy  
of composition' among modern writers1 by
 whom it is defined to consist in       

arguing from the distributive to the    
collective use of a term4   #hea4 ,the  
,fallacy of ,division 7,greek3          
diaresis71 on the other hand1 consists  
in taking words separately which ought  
to be taken together1 e4g4    ,greek3 g 
s' teka dolon nt' leteron ,footnote3    
,evidently the   original of the line in
 ,terence's ,andria1 #cg1--;feci ex     
servo   ut esses libertus mihi41  where 
the separation of ,greek3 dolon from    
,greek3 ntra would lead to an           
interpretation exactly contrary to what 
is intended4  ,and again--    ,greek3   
pentkont' ndrn katn lpe dos chilles1    
where the separation of ,greek3 ndrn    
from ,greek3 katn leads to a ludicrous  
error4  ,any reader whose youth may have
 been nourished on ',the ,fairchild     
,family' may possibly recollect a       
sentence which ran somewhat on this     
wise--',henry1' said ,mr4  ,fairchild1  
'is this true8 ,are you a thief and a   
liar too8'  ,but ,i am afraid he will   
miss the keen delight which can be      

extracted at a certain age from turning 
the tables upon ,mr4 ,fairchild         
thus--,henry said1 ',mr4 ,fairchild1 is 
this true8 ,are you a thief and a liar  
too8'   #heb4 ,the fallacy of division  
has been accommodated by modern writers 
to the meaning which they have assigned 
to the fallacy of composition4 ,so that 
by the 'fallacy of division' is now     
meant arguing from the collective to the
 distributive use of a term4 ,further1  
it is laid down that when the middle    
term is used distributively in the major
 premiss and collectively in the minor1 
we have the fallacy of composition2     
whereas1 when the middle term is used   
collectively in the major premiss and   
distributively in the minor1 we have the
 fallacy of division4 ,thus the first of
 the two examples appended would be     
composition and the second division4    
7#a7 ,two and three are odd and even4   
,five is two and three4       4'4 ,five 
is odd and even4    7#b7 ,the ,germans  
are an intellectual people4       ,hans 

and ,fritz are ,germans4       4'4 ,they
 are intellectual people4   #hec4 ,as   
the possibility of this sort of         
ambiguity is not confined to the middle 
term1 it seems desirable to add that    
when either the major or minor term is  
used distributively in the premiss and  
collectively in the conclusion1 we have 
the fallacy of composition1 and in the  
converse case the fallacy of division4  
,here is an instance of the latter kind 
in which the minor term is at fault--   
,anything over a hundredweight is too   
heavy to lift4   ,these sacks           
7collectively7 are over a hundredweight4
   4'4 ,these sacks 7distributively7 are
 too heavy to lift4   #hed4 ,the        
ambiguity of the word 'all1' which has  
been before commented upon 7 #aai71 is a
 great assistance in the ,english       
language to the pair of fallacies just  
spoken of4   #hce4 ,the ,fallacy of     
,accent 7,greek3 prosoda7 is neither    
more nor less than a mistake in ,greek  
accentuation4 ,as an instance ,aristotle

 gives ,iliad xxiii4 #cbh1 where the    
ancient copies of ,homer made nonsense  
of the words ,greek3 t mn o kataptetai  
mbro by writing ,greek3 o with the      
circumflex in place of ,greek3 o with   
the acute accent4 ,footnote3 ,this goes 
to show that the ancient ,greeks did not
 distinguish in pronunciation between   
the rough and smooth breathing any more 
than their modern representatives4      
,aristotle remarks that the fallacy is  
one which cannot easily occur in verbal 
argument1 but rather in writing and     
poetry4   #hef4 ,modern writers explain 
the fallacy of accent to be the mistake 
of laying the stress upon the wrong part
 of a sentence4 ,thus when the country  
parson reads out1 ',thou shall not bear 
false witness against thy neighbour1'   
with a strong emphasis upon the word    
'against1' his ignorant audience leap   
sic to the conclusion that it is not    
amiss to tell lies provided they be in  
favour of one's neighbour4   #heg4 ,the 
,fallacy of ,figure of ,speech ,greek3 t

 schma ts lxeos results from any        
confusion of grammatical forms1 as      
between the different genders of nouns  
or the different voices of verbs1 or    
their use as transitive or intransitive1
 e4g4 ,greek3 gianein has the same      
grammatical form as ,greek3 tmnein or   
,greek3 okodomen1 but the former is     
intransitive1 while the latter are      
transitive4 ,a sophism of this kind is  
put into the mouth of ,socrates by      
,aristophanes in the ,clouds 7#fgj-hj74 
,the philosopher is there represented as
 arguing that ,greek3 kpdopos must be   
masculine because ,greek3 ,klenumos is4 
,on the surface this is connected with  
language1 but it is essentially a       
fallacy of false analogy4   #heh4 ,to   
this head may be referred what is known 
as the ,fallacy of ,paronymous ,terms4  
,this is a species of equivocation which
 consists in slipping from the use of   
one part of speech to that of another1  
which is derived from the same source1  
but has a different meaning4 ,thus this 

fallacy would be committed if1 starting 
from the fact that there is a certain   
probability that a hand at whist will   
consist of thirteen trumps1 one were to 
proceed to argue that it was probable1  
or that he had proved it4   #hei4 ,we   
turn now to the tricks of refutation    
which lie outside the language1 whether 
the deception be due to the assumption  
of a false premiss or to some           
unsoundness in the reasoning4   #hfj4   
,the first on the list is the ,fallacy  
of ,accident 7,greek3 t sumbebeks74     
,this fallacy consists in confounding an
 essential with an accidental           
difference1 which is not allowable1     
since many things are the same in       
essence1 while they differ in accidents4
 ,here is the sort of example that      
,aristotle gives--    ',is ,plato       
different from ,socrates 8' ',yes4' ',is
 ,socrates a man 8'   ',yes4' ',then    
,plato is different from man4'  ,to this
 we answer--,no3 the difference of      
accidents between ,plato and ,socrates  

does not go so deep as to affect the    
underlying essence4 ,to put the thing   
more plainly1 the fallacy lies in       
assuming that whatever is different from
 a given subject must be different from 
it in all respects1 so that it is       
impossible for them to have a common    
predicate4 ,here ,socrates and ,plato1  
though different from one another1 are  
not so different but that they have the 
common predicate 'man4' ,the attempt to 
prove that they have not involves an    
illicit process of the major4   #hfa4   
,the next fallacy suffers from the want 
of a convenient name4 ,it is called by  
,aristotle ,greek3 t plos tde  p lgestai
 ka m kupos or1 more briefly1 ,greek3 t 
pls  m1 or ,greek3 t p ka pls1 and by   
the ,latin writers ',fallacia a dicto   
secundum quid ad dictum simpliciter4'   
,it consists in taking what is said in a
 particular respect as though it held   
true without any restriction1 e4g41 that
 because the nonexistent 7,greek3 t m n7
 is a matter of opinion1 that therefore 

the non-existent is1 or again that      
because the existent 7,greek3 t n7 is   
not a man1 that therefore the existent  
is not4 ,or again1 if an ,indian1 who as
 a whole is black1 has white teeth1 we  
should be committing this species of    
fallacy in declaring him to be both     
white and not-white4 ,for he is only    
white in a certain respect 7,greek3 p71 
but not absolutely 7,greek3 pls74 ,more 
difficulty1 says ,aristotle1 may arise  
when opposite qualities exist in a thing
 in about an equal degree4 ,when1 for   
instance1 a thing is half white and half
 black1 are we to say that it is white  
or black8 ,this question the philosopher
 propounds1 but does not answer4 ,the   
force of it lies in the implied attack  
on the ,law of ,contradiction4 ,it would
 seem in such a case that a thing may be
 both white and not-white at the same   
time4 ,the fact is--so subtle are the   
ambiguities of language--that even such 
a question as ',is a thing white or     
not-white8' straightforward1 as it      

seems1 is not really a fair one4 ,we are
 entitled sometimes to take the bull by 
the horns1 and answer with the          
adventurous interlocutor in one of      
,plato's dialogues--',both and neither4'
 ,it may be both in a certain respect1  
and yet neither absolutely4   #hfb4 ,the
 same sort of difficulties attach to the
 ,law of ,excluded ,middle1 and may be  
met in the same way4  ,it might1 for    
instance1 be urged that it could not be 
said with truth of the statue seen by   
,nebuchadnezzar in his dream either that
 it was made of gold or that it was not 
made of gold3 but the apparent          
plausibility of the objection would be  
due merely to the ambiguity of language4
  ,it is not true1 on the one hand1 that
 it was made of gold 7in the sense of   
being composed entirely of that metal72 
and it is not true1 on the other1 that  
it was not made of gold 7in the sense of
 no gold at all entering into its       
composition74 ,but let the ambiguous    
proposition be split up into its two    

meanings1 and the stringency of the ,law
 of ,excluded ,middle will at once      
appear--    7#a7 ,it must either have   
been composed entirely of gold or not4  
7#b7 ,either gold must have entered into
 its composition or not4   #hfc4 ,by    
some writers this fallacy is treated as 
the converse of the last1 the fallacy of
 accident being assimilated to it under 
the title of the ',fallacia a dicto     
simpliciter ad dictum secundum quid4'   
,in this sense the two fallacies may be 
defined thus4  ,the ,fallacy of         
,accident consists in assuming that what
 holds true as a general rule will hold 
true under some special circumstances   
which may entirely alter the case4  ,the
 ,converse ,fallacy of ,accident        
consists in assuming that what holds    
true under some special circumstances   
must hold true as a general rule4  ,the 
man who1 acting on the assumption that  
alcohol is a poison1 refuses to take it 
when he is ordered to do so by the      
doctor1 is guilty of the fallacy of     

accident2 the man who1 having had it    
prescribed for him when he was ill1     
continues to take it morning1 noon1 and 
night1 commits the converse fallacy4    
#hfd4 ,there ought to be added a third  
head to cover the fallacy of arguing    
from one special case to another4       
#hfe4 ,the next fallacy is ,ignoratio   
,elenchi ,greek3 lgchou gnoia4 ,this    
fallacy arises when by reasoning valid  
in itself one establishes a conclusion  
other than what is required to upset the
 adversary's assertion4 ,it is due to an
 inadequate conception of the true      
nature of refutation4  ,aristotle       
therefore is at the pains to define     
refutation at full length1 thus--  ',a  
refutation ,greek3 legchos is the denial
 of one and the same--not name1 but     
thing1 and by means1 not of a synonymous
 term1 but of the same term1 as a       
necessary consequence from the data1    
without assumption of the point         
originally at issue1 in the same        
respect1 and in the same relation1 and  

in the same way1 and at the same time4' 
,the ,,elenchus then is the exact       
contradictory of the opponent's         
assertion under the terms of the law of 
contradiction4 ,to establish by a       
syllogism1 or series of syllogisms1 any 
other proposition1 however slightly     
different1 is to commit this fallacy4   
,even if the substance of the           
contradiction be established1 it is not 
enough unless the identical words of the
 opponent are employed in the           
contradictory4 ,thus if his thesis      
asserts or denies something about       
,greek3 lpion1 it is not enough for you 
to prove the contradictory with regard  
to ,greek3 mtion4 ,there will be need of
 a further question and answer to       
identify the two1 though they are       
admittedly synonymous4 ,such was the    
rigour with which the rules of the game 
of dialectic were enforced among the    
,greeks6   #hff4 ,under the head of     
,ignoratio ,elenchi it has become usual 
to speak of various forme of argument   

which have been labelled by the ,latin  
writers under such names as 'argumentum 
ad hominem1' 'ad populum1' 'ad          
verecundiam1' 'ad ignorantiam1' 'ad     
baculum'--all of them opposed to the    
'argumentum ad rem' or 'ad judicium4'   
#hfg4 ,by the 'argumentum ad hominem'   
was perhaps meant a piece of reasoning  
which availed to silence a particular   
person1 without touching the truth of   
the question4  ,thus a quotation from   
,scripture is sufficient to stop the    
mouth of a believer in the inspiration  
of the ,bible4  ,hume's ,essay on       
,miracles is a noteworthy instance of   
the 'argumentum ad hominem' in this     
sense of the term4 ,he insists strongly 
on the evidence for certain miracles    
which he knew that the prejudices of his
 hearers would prevent their ever       
accepting1 and then asks triumphantly if
 these miracles1 which are declared to  
have taken place in an enlightened age  
in the full glare of publicity1 are     
palpably imposture1 what credence can be

 attached to accounts of extraordinary  
occurrences of remote antiquity1 and    
connected with an obscure corner of the 
globe8 ,the 'argumentum ad judicium'    
would take miracles as a whole1 and     
endeavour to sift the amount of truth   
which may lie in the accounts we have of
 them in every age4 ,footnote3 ,on this 
subject see the author's ,attempts at   
,truth 7,trubner  ,co471 pp4 #df-ei4    
#hfh4 ,in ordinary discourse at the     
present day the term 'argumentum ad     
hominem' is used for the form of        
irrelevancy which consists in attacking 
the character of the opponent instead of
 combating his arguments1 as illustrated
 in the well-known instructions to a    
barrister--',no case3 abuse the         
plaintiff's attorney4'   #hfi4 ,the     
'argumentum ad populum' consists in an  
appeal to the passions of one's         
audience4 ,an appeal to passion1 or to  
give it a less question-begging name1 to
 feeling1 is not necessarily amiss4 ,the
 heart of man is the instrument upon    

which the rhetorician plays1 and he has 
to answer for the harmony or the discord
 that comes of his performance4   #hgj4 
,the 'argumentum ad verecundiam' is an  
appeal to the feeling of reverence or   
shame4 ,it is an argument much used by  
the old to the young and by             
,conservatives to ,radicals4   #hga4    
,the 'argumentum ad ignorantiam'        
consists simply in trading on the       
ignorance of the person addressed1 so   
that it covers any kind of fallacy that 
is likely to prove effective with the   
hearer4   #hgb4 ,the 'argumentum ad     
baculum' is unquestionably a form of    
irrelevancy4 ,to knock a man down when  
he differs from you in opinion may prove
 your strength1 but hardly your logic4  
,a sub-variety of this form of          
irrelevancy was exhibited lately at a   
socialist lecture in ,oxford1 at which  
an undergraduate1 unable or unwilling to
 meet the arguments of the speaker1     
uncorked a bottle1 which had the effect 
of instantaneously dispersing the       

audience4 ,this might be set down as the
 'argumentum ad nasum4'   #hgc4 ,we now 
come to the ,fallacy of the ,consequent1
 a term which has been more hopelessly  
abused than any4  ,what ,aristotle meant
 by it was simply the assertion of the  
consequent in a conjunctive proposition1
 which amounts to the same thing as the 
simple conversion of ,a 7 #dhi71 and is 
a fallacy of distribution4 ,aristotle's 
example is this--    ,if it has rained1 
the ground is wet4   4'4 ,if the ground 
is wet1 it has rained4  ,this fallacy1  
he tells us1 is often employed in       
rhetoric in dealing with presumptive    
evidence4 ,thus a speaker1 wanting to   
prove that a man is an adulterer1 will  
argue that he is a showy dresser1 and   
has been seen about at nights4 ,both    
these things however may be the case1   
and yet the charge not be true4   #hgd4 
,the ,fallacy of ,petitio or ,assumptio 
,principii ,greek3 t n rch atestai or   
lambnein to which we now come1 consists 
in an unfair assumption of the point at 

issue4  ,the word ,greek3 atestai1 in   
,aristotle's name for it points to the  
,greek method of dialectic by means of  
question and answer4 ,this fact is      
rather disguised by the mysterious      
phrase 'begging the question4' ,the     
fallacy would be committed when you     
asked your opponent to grant1 overtly or
 covertly1 the very proposition         
originally propounded for discussion4   
#hge4 ,as the question of the precise   
nature of this fallacy is of some       
importance we will take the words of    
,aristotle himself 7,top4 viii4 #ac4    
#b1 #c74 ',people seem to beg the       
question in five ways4 ,first and most  
glaringly1 when one takes for granted   
the very thing that has to be proved4   
,this by itself does not readily escape 
detection1 but in the case of synonyms1 
that is1 where the name and the         
definition have the same meaning1 it    
does so more easily4 ,footnote3 ,some   
light is thrown upon this obscure       
passage by a comparison with ,cat4 ,i4  

#c1 where 'synonym' is defined4 ,to take
 the word here in its later and modern  
sense affords an easy interpretation1   
which is countenanced by ,alexander     
,aphrodisiensis1 but it is flat against 
the usage of ,aristotle1 who elsewhere  
gives the name 'synonym1' not to two    
names for the same thing1 but to two    
things going under the same name4 ,see  
,trendelenberg on the passage4          
,secondly1 when one assumes universally 
that which has to be proved in          
particular1 as1 if a man undertaking to 
prove that there is one science of      
contraries1 were to assume that there is
 one science of opposites generally4    
,for he seems to be taking for granted  
along with several other things what he 
ought to have proved by itself4         
,thirdly1 when one assumes the          
particulars where the universal has to  
be proved2 for in so doing a man is     
taking for granted separately what he   
was bound to prove along with several   
other things4  ,again1 when one assumes 

the question at issue by splitting it   
up1 for instance1 if1 when the point to 
be proved is that the art of medicine   
deals with health and disease1 one were 
to take each by itself for granted4     
,lastly1 if one were to take for granted
 one of a pair of necessary             
consequences1 as that the side is       
incommensurable with the diagonal1 when 
it is required to prove that the        
diagonal is incommensurable with the    
side4'   #hgf4 ,to sum up briefly1 we   
may beg the question in five ways--     
7#a7 ,by simply asking the opponent to  
grant the point which requires   to be  
proved2    7#b7 by asking him to grant  
some more general truth which involves  
it2    7#c7 by asking him to grant the  
particular truths which it involves2    
7#d7 by asking him to grant the         
component parts of it in detail2    7#e7
 by asking him to grant a necessary     
consequence of it4   #hgg4 ,the first of
 these five ways1 namely1 that of       
begging the question straight off1 lands

 us in the formal fallacy already spoken
 of 7 #hch71 which violates the first of
 the general rules of syllogism1        
inasmuch as a conclusion is derived from
 a single premiss1 to wit1 itself4      
#hgh4 ,the second1 strange to say1 gives
 us a sound syllogism in ,barbara1 a    
fact which countenances the blasphemers 
of the syllogism in the charge they     
bring against it of containing in itself
 a petitio principii4 ,certainly        
,aristotle's expression might have been 
more guarded4 ,but it is clear that his 
quarrel is with the matter1 not with the
 form in such an argument4 ,the fallacy 
consists in assuming a proposition which
 the opponent would be entitled to deny4
 ,elsewhere ,aristotle tells us that the
 fallacy arises when a truth not evident
 by its own light is taken to be so4    
,footnote3 ,greek3 tan t m d ato gnostn 
d ato tis picheira deiknnai1 tt' atetai 
t x rchs44 ,anal4 ,pr4 ,,ii4 #af4  ,i ad
 fin4   #hgi4 ,the third gives us an    
inductio per enumerationem simplicem1 a 

mode of argument which would of course  
be unfair as against an opponent who was
 denying the universal4   #hhj4 ,the    
fourth is a more prolix form of the     
first4   #hha4 ,the fifth rests on      
,immediate ,inference by ,relation 7    
#ecd74   #hhb4 ,under the head of       
petitio principii comes the fallacy of  
,arguing in a ,circle1 which is         
incidental to a train of reasoning4 ,in 
its most compressed form it may be      
represented thus--    7#a7 ,b is ,a4    
,c is ,b4       4'4 ,c is ,a4    7#b7 ,c
 is ,a4       ,b is ,c4       4'4 ,b is 
,a4   #hhc4 ,the ,fallacy of ,non causa 
pro causa 7,greek3 t m ation or ,greek3 
atoin7 is another1 the name of which has
 led to a complete misinterpretation4   
,it consists in importing a             
contradiction into the discussion1 and  
then fathering it on the position       
controverted4 ,such arguments1 says     
,aristotle1 often impose upon the users 
of them themselves4  ,the instance he   
gives is too recondite to be of general 

interest4   #hhd4 ,lastly1 the ,fallacy 
of ,many ,questions 7,greek3 t t do     
rotmata n poien7 is a deceptive form of 
interrogation1 when a single answer is  
demanded to what is not really a single 
question4 ,in dialectical discussions   
the respondent was limited to a simple  
'yes' or 'no'2 and in this fallacy the  
question is so framed as that either    
answer would seem to imply the          
acceptance of a proposition which would 
be repudiated4 ,the old stock instance  
will do as well as another--',come now1 
sir1 answer yes or no4 ,have you left   
off beating your mother yet8'  ,either  
answer leads to an apparent admission of
 impiety4  ,a late ,senior ,proctor once
 enraged a man at a fair with this form 
of fallacy4 ,the man was exhibiting a   
blue horse2 and the distinguished       
stranger asked him--',with what did you 
paint your horse8'     ,,exercises4     
,these exercises should be supplemented 
by direct questions upon the text1 which
 it is easy for the student or the      

teacher to supply for himself4   ,,part 
,i4   ,,chapter ,i4  ,classify the      
following words according as they are   
categorematic1 syncategorematic or      
acategorematic2--    come               
peradventure    why   through           
inordinately    pshaw   therefore       
circumspect     puss   grand            
inasmuch        stop   touch            
sameness        back   cage             
disconsolate    candle4   ,,chapter     
,,ii4  ,classify the following things   
according as they are substances1       
qualities or relations2--    ,god       
likeness       weight   blueness        
grass          imposition   ocean       
introduction   thinness   man           
air            spirit   ,socrates       
raillery       heat   mortality   plum  
fire4   ,,chapter ,,iii4  #a4 ,give six 
instances each of-attribute1 abstract1  
singular1 privative1 equivocal and      
relative terms4  #b4 ,select from the   
following list of words such as are     
terms1 and state whether they are 7#a7  

abstract or concrete1 7#b7 singular or  
common1 7#c7 univocal or equivocal3--   
van        table        however   enter 
decidedly    tiresome   very       butt 
,solomon   infection  bluff        ,czar
   short      although     ,caesarism   
distance   elderly      ,nihilist4  #c4 
,which of the following words are       
abstract terms8--    quadruped          
event           through   hate          
desirability    thorough   fact         
expressly       thoroughness   faction  
wish            light   inconvenient    
will            garden   inconvenience  
volition        grind4  #d4 ,refer the  
following terms to their proper place   
under each of the divisions in the      
scheme3--    horse          husband     
,london   free           lump           
empty   liberty        rational         
capital   impotent       reason         
,capitol   impetuosity    irrationality 
grave   impulsive      double           
calf4  #e4 ,give six instances each of  
proper names and designations4  #f4     

,give six instances each of connotative 
and non-connotative terms4  #g4 ,give   
the extension and intension of--        
sermon          animal      sky   clock 
square      gold   sport           fish 
element   bird            student       
fluid   art             river       line
   gas             servant     language 
,,chapter ,,iv4  ,arrange the following 
terms in order of                       
extension--carnivorous1 thing1 matter1  
mammal1 organism1 vertebrate1 cat1      
substance1 animal4         99       99  
99       99       99   ,,part ,,ii4     
,,chapter ,i4  ,give a name to each of  
the following sentences3--    7#a7 ,oh1 
that ,i had wings like a dove6    7#b7  
,the more1 the merrier4    7#c7 ,come   
rest in this bosom1 my own stricken     
deer4    7#d7 ,is there balm in ,gilead8
    7#e7 ,hearts may be trumps4         
,,chapter ,,ii4  ,analyse the following 
propositions into subject1 copula and   
predicate3--    7#a7 ,he being dead yet 
speaketh4    7#b7 ,there are foolish    

politicians4    7#c7 ,little does he    
care4    7#d7 ,there is a land of pure  
delight4    7#e7 ,all's well that ends  
well4    7#f7 ,sweet is the breath of   
morn4    7#g7 ,now it came to pass that 
the beggar died4    7#h7 ,who runs may  
read4    7#i7 ,great is ,diana of the   
,ephesians4    7#aj7 ,such things are4  
7#aa7 ,not more than others ,i deserve4 
7#ab7 ,the day will come when ,ilium's  
towers shall perish4   ,,chapter ,,iii4 
#a4 ,express in logical form1 affixing  
the proper symbol3--    7#a7 ,some swans
 are not white4    7#b7 ,all things are 
possible to them that believe4    7#c7  
,no politicians are unprincipled4       
7#d7 ,some stones float on water4       
7#e7 ,the snow has melted4    7#f7 ,eggs
 are edible4    7#g7 ,all kings are not 
wise4    7#h7 ,moths are not            
butterflies4    7#i7 ,some men are born 
great4    7#aj7 ,not all who are called 
are chosen4    7#aa7 ,it is not good for
 man to be alone4    7#ab7 ,men of      
talents have been known to fail in life4

    7#ac7 ',tis none but a madman would 
throw about fire4    7#ad7 ,every bullet
 does not kill4    7#ae7 ,amongst       
,unionists are ,whigs4    7#af7 ,not all
 truths are to be told4    7#ag7 ,not   
all your efforts can save him4    7#ah7 
,the whale is a mammal4    7#ai7 ,cotton
 is grown in ,cyprus4    7#bj7 ,an      
honest man's the noblest work of ,god4  
7#ba7 ,no news is good news4    7#bb7   
,no friends are like old friends4       
7#bc7 ,only the ignorant affect to      
despise knowledge4    7#bd7 ,all that   
trust in ,him shall not be ashamed4     
7#be7 ,all is not gold that glitters4   
7#bf7 ,the sun shines upon the evil and 
upon the good4    7#bg7 ,not to go on is
 to go back4    7#bh7 ,the king1        
minister1 and general are a pretty trio4
    7#bi7 ,amongst dogs are hounds4     
7#cj7 ,a fool is not always wrong4      
7#ca7 ,alexander was magnanimous4       
7#cb7 ,food is necessary to life4       
7#cc7 ,there are three things to be     
considered1    7#cd7 ,by penitence the  

,eternal's wrath's appeased4    7#ce7   
,money is the miser's end4    7#cf7 ,few
 men succeed in life4    7#cg7 ,all is  
lost1 save honour4    7#ch7 ,it is mean 
to hit a man when he is down4    7#ci7  
,nothing but coolness could have saved  
him4    7#dj7 ,books are generally      
useful4    7#da7 ,he envies others'     
virtue who has none himself4    7#db7   
,thankless are all such offices4        
7#dc7 ,only doctors understand this     
subject4    7#dd7 ,all her guesses but  
two were correct4    7#de7 ,all the men 
were twelve4    7#df7 ,gossip is seldom 
charitable4  #b4 ,give six examples of  
indefinite propositions1 and then       
quantify them according to their matter4
  #c4 ,compose three propositions of    
each of the following kinds3--    7#a7  
with common terms for subjects2    7#b7 
with abstract terms for subjects2       
7#c7 with singular terms for predicates2
    7#d7 with collective terms for      
predicates2    7#e7 with attributives in
 their subjects2    7#f7 with abstract  

terms for predicates4   ,,chapter ,,iv4 
#a4 ,point out what terms are           
distributed or undistributed in the     
following propositions3--    7#a7 ,the  
,chinese are industrious4    7#b7 ,the  
angle in a semi-circle is a right angle4
    7#c7 ,not one of the crew survived4 
7#d7 ,the weather is sometimes not      
propitious4  ,the same exercise may be  
performed upon any of the propositions  
in the preceding list4  #b4 ,prove that 
in a negative proposition the predicate 
must be distributed4   ,,chapter ,v4    
,affix its proper symbol to each of the 
following propositions3--    7#a7 ,no   
lover he who is not always fond4    7#b7
 ,there are ,irishmen and ,irishmen4    
7#c7 ,men only disagree1       ,of      
creatures rational4    7#d7 ,some wise  
men are poor4    7#e7 ,no ,popes are    
some fallible beings4    7#f7 ,some     
step-mothers are not unjust4    7#g7    
,the most original of the ,roman poets  
was ,lucretius4    7#h7 ,some of the    
immediate inferences are all the forms  

of   conversion4   ,,chapter ,,vi4  #a4 
,give six examples of terms standing one
 to another as genus to species4  #b4   
,to which of the heads of predicables   
would you refer the following           
statements8 ,and why8    7#a7 ,a circle 
is the largest space that can be        
contained by one line4    7#b7 ,all the 
angles of a square are right angles4    
7#c7 ,man alone among animals possesses 
the faculty of laughter4    7#d7 ,some  
fungi are poisonous4    7#e7 ,most      
natives of ,africa are negroes4    7#f7 
,all democracies are governments4       
7#g7 ,queen ,anne is dead4   ,,chapter  
,,vii4  #a4 ,define the following       
terms--    ,sun          inn-keeper     
tea-pot   hope         anger            
virtue   bread        diplomacy    milk 
carpet       man          death         
sincerity    telescope    mountain      
poverty      ,senate       novel4  #b4  
,define the following terms as used in  
,political ,economy--    ,commodity     
barter     value   wealth       land    

price   money        labour     rent    
interest     capital    wages   credit  
demand     profits4  #c4 ,criticise the 
following as definitions--    7#a7 ,noon
 is the time when the shadows of bodies 
are shortest4    7#b7 ,grammar is the   
science of language4    7#c7 ,grammar is
 a branch of philology4    7#d7 ,grammar
 is the art of speaking and writing a   
language with   propriety4    7#e7      
,virtue is acting virtuously4    7#f7   
,virtue is that line of conduct which   
tends to produce happiness4    7#g7 ,a  
dog is an animal of the canine species4 
7#h7 ,logic is the art of reasoning4    
7#i7 ,logic is the science of the       
investigation of truth by means of      
evidence4    7#aj7 ,music is an         
expensive noise4    7#aa7 ,the sun is   
the centre of the solar system4    7#ab7
 ,the sun is the brightest of those     
heavenly bodies that move   round the   
earth4    7#ac7 ,rust is the red        
desquamation of old iron4    7#ad7      
,caviare is a kind of food4    7#ae7    

,life is the opposite of death4    7#af7
 ,man is a featherless biped4    7#ag7  
,man is a rational biped4    7#ah7 ,a   
gentleman is a person who has no visible
 means of   subsistence4    7#ai7 ,fame 
is a fancied life in others' breath4    
7#bj7 ,a fault is a quality productive  
of evil or inconvenience4    7#ba7 ,an  
oligarchy is the supremacy of the rich  
in a state4    7#bb7 ,a citizen is one  
who is qualified to exercise            
deliberative and   judicial functions4  
7#bc7 ,length is that dimension of a    
solid which would be measured by   the  
longest line4    7#bd7 ,an eccentricity 
is a peculiar idiosyncrasy4    7#be7    
,deliberation is that species of        
investigation which is   concerned with 
matters of action4    7#bf7 ,memory is  
that which helps us to forget4    7#bg7 
,politeness is the oil that lubricates  
the wheels of society4    7#bh7 ,an     
acute-angled triangle is one which has  
an acute angle4    7#bi7 ,a cause is    
that without which something would not  

be4    7#cj7 ,a cause is the invariable 
antecedent of a phenomenon4    7#ca7    
,necessity is the mother of invention4  
7#cb7 ,peace is the absence of war4     
7#cc7 ,a net is a collection of holes   
strung together4    7#cd7 ,prudence is  
the ballast of the moral vessel4        
7#ce7 ,a circle is a plane figure       
contained by one line4    7#cf7         
,superstition is a tendency to look for 
constancy where   constancy is not to be
 expected4    7#cg7 ,bread is the staff 
of life4    7#ch7 ,an attributive is a  
term which cannot stand as a subject4   
7#ci7 ,life is bottled sunshine4        
7#dj7 ,eloquence is the power of        
influencing the feelings by speech or   
writing4    7#da7 ,a tombstone is a     
monument erected over a grave in memory 
of the   dead4    7#db7 ,whiteness is   
the property or power of exciting the   
sensation of   white4    7#dc7 ,figure  
is the limit of a solid4    7#dd7 ,an   
archdeacon is one who exercises         
archidiaconal functions4    7#de7       

,humour is thinking in jest while       
feeling in earnest4   ,,chapter ,,viii4 
#a4 ,divide the following terms--       
,soldier    end           book   church 
good          oration   apple      cause
         school   ship       government 
letter   vehicle    science       verse4
  #b4 ,divide the following terms as    
used in ,political ,economy--           
,requisites of production1 labour1      
consumption1 stock1 wealth1   capital4  
#c4 ,criticise the following as         
divisions--    7#a7 ,great ,britain into
 ,england1 ,scotland1 ,wales1 and       
,ireland4    7#b7 ,pictures into sacred1
 historical1 landscape1 and             
mythological4    7#c7 ,vertebrate       
animals into quadrupeds1 birds1 fishes1 
and reptiles4    7#d7 ,plant into stem1 
root1 and branches4    7#e7 ,ship into  
frigate1 brig1 schooner1 and            
merchant-man4    7#f7 ,books into       
octavo1 quarto1 green1 and blue4    7#g7
 ,figure into curvilinear and           
rectilinear4    7#h7 ,ends into those   

which are ends only1 means and ends1 and
 means   only4    7#i7 ,church into     
,gothic1 episcopal1 high1 and low4      
7#aj7 ,sciences into physical1 moral1   
metaphysical1 and medical4    7#aa7     
,library into public and private4       
7#ab7 ,horses into race-horses1 hunters1
 hacks1 thoroughbreds1 ponies1   and    
mules4  #d4 ,define and divide--        
,meat1 money1 virtue1 triangle2  and    
give1 as far as possible1 a property and
 accident of each4   ,,part ,,iii4      
,,chapters ,i-,,iii4  #a4 ,what kind of 
influence have we here8    ,the author  
of the ,iliad was unacquainted with     
writing4   ,homer was the author of the 
,iliad4   4'4 ,homer was unacquainted   
with writing4  #b4 ,give the logical    
opposites of the following              
propositions--    7#a7 ,knowledge is    
never useless4    7#b7 ,all ,europeans  
are civilised4    7#c7 ,some monks are  
not illiterate4    7#d7 ,happy is the   
man that findeth wisdom4    7#e7 ,no    
material substances are devoid of       

weight4    7#f7 ,every mistake is not   
culpable4    7#g7 ,some ,irishmen are   
phlegmatic4  #c4 ,granting the truth of 
the following propositions1 what other  
propositions can be inferred by         
opposition to be true or false8     7#a7
 ,men of science are often mistaken4    
7#b7 ,he can't be wrong1 whose life is  
in the right4    7#c7 ,sir ,walter      
,scott was the author of ,waverley4     
7#d7 ,the soul that sinneth it shall    
die4    7#e7 ,all women are not vain4   
#d4 ,granting the falsity of the        
following propositions1 what other      
propositions can be inferred by         
opposition to be true or false8--       
7#a7 ,some men are not mortal4    7#b7  
,air has no weight4    7#c7 ,all actors 
are improper characters4    7#d7 ,none  
but dead languages are worth studying4  
7#e7 ,some elements are compound4       
,,chapter ,,iv4  #a4 ,give1 as far as   
possible1 the logical converse of each  
of the following propositions--    7#a7 
,energy commands success4    7#b7       

,mortals cannot be happy4    7#c7 ,there
 are mistakes which are criminal4       
7#d7 ,all's well that ends well4    7#e7
 ,envious men are disliked4    7#f7 ,a  
term is a kind of word or collection of 
words4    7#g7 ,some ,frenchmen are not 
vivacious4    7#h7 ,all things in heaven
 and earth were hateful to him4    7#i7 
,the square of three is nine4    7#aj7  
,all cannot receive this saying4        
7#aa7 ,p struck ,q4    7#ab7 ,amas4  #b4
 ',more things may be contained in my   
philosophy than exist in heaven or      
earth3 but the converse proposition is  
by no means true4' ,is the term converse
 here used in its logical meaning8      
,,chapter ,v4  ,permute the following   
propositions--    7#a7 ,all just acts   
are expedient4    7#b7 ,no display of   
passion is politic4    7#c7 ,some clever
 people are not prudent4    7#d7 ,some  
philosophers have been slaves4  ,the    
same exercise may be performed upon any 
of the propositions in the preceding    
lists4   ,,chapter ,,vi4  #a4 ,give the 

converse by negation of--    7#a7 ,all  
women are lovely4    7#b7 ,some         
statesmen are not practical4    7#c7    
,all lawyers are honest4    7#d7 ,all   
doctors are skilful4    7#e7 ,some men  
are not rational4  #b4 ,give the        
contrapositive of--    7#a7 ,all solid  
substances are material4    7#b7 ,all   
the men who do not row play cricket4    
7#c7 ,all impeccable beings are other   
than human1    7#d7 ,some prejudiced    
persons are not dishonest4  #c4 ,prove  
indirectly the truth of the             
contrapositive of ',all ,a is ,b4'  #d4 
,criticise the following as immediate   
inferences--    7#a7 ,all wise men are  
modest4       4'4 ,no immodest men are  
wise4    7#b7 ,some ,german students are
 not industrious4       4'4 ,some       
industrious students are not ,germans4  
7#c7 ,absolute difference excludes all  
likeness4       4'4 ,any likeness is a  
proof of sameness4    7#d7 ,none but the
 brave deserve the fair4       4'4 ,all 
brave men deserve the fair4    7#e7 ,all

 discontented men are unhappy4       4'4
 ,no contented men are unhappy4    7#f7 
,books being a source of instruction1   
our knowledge must come   from our      
libraries4    7#g7 ,all ,jews are       
,semitic4       4'4 ,some non-,semitic  
people are not ,jews4  #e4 ,show by what
 kind of inference each of the subjoined
 propositions follows from    ,all      
discontented men are unhappy4    7#a7   
,all happy men are contented4    7#b7   
,some discontented men are unhappy4     
7#c7 ,some contented men are happy4     
7#d7 ,some unhappy men are not          
contented4    7#e7 ,no discontented men 
are happy4    7#f7 ,some happy men are  
contented4    7#g7 ,some contented men  
are not unhappy4    7#h7 ,some unhappy  
men are discontented4    7#i7 ,no happy 
men are discontented4    7#aj7 ,some    
discontented men are not happy4    7#aa7
 ,some happy men are not discontented4  
7#ab7 ,none but unhappy men are         
discontented4  ,from how many of these  
propositions can the original one be    

derived8 ,and why not from all8         
,,chapter ,,vii4  ,what kind of         
inference have we here8--    7#a7 ,none 
but the ignorant despise knowledge4     
4'4 ,no wise man despises knowledge4    
7#b7 ,a is superior to ,b4       4'4 ,b 
is inferior to ,a4   ,,chapter ,,viii4  
,fill up the following enthymemes1      
mentioning to which order they belong1  
and state which of them are expressed in
 problematic form--    7#a7 ,i am fond  
of music3 for ,i always like a comic    
song4    7#b7 ,all men are born to      
suffering1 and therefore you must expect
   your share4    7#c7 ,job must have   
committed some secret sins3 for he fell 
into   dreadful misfortunes4    7#d7    
,latin was the language of the ,vestals1
 and therefore no lady   need be ashamed
 of speaking it4    7#e7 ,none but      
physicians came to the meeting4 ,there  
were therefore no   nurses there4       
7#f7 ,the human soul extends through the
 whole body1 for it is found   in every 
member4    7#g7 ,no traitor can be      

trusted1 and you are a traitor4    7#h7 
,whatever has no parts does not perish  
by the dissolution of its   parts4      
,therefore the soul of man is           
imperishable4  ,is the suppressed       
premiss in any case disputable on       
material grounds8   ,,chapters          
,,ix-,,xviii4  ,refer the following     
arguments to their proper mood and      
figure1 or show what rules of syllogism 
they violate4    7#a7 ,no miser is a    
true friend1 for he does not assist his 
friend   with his purse4    7#b7        
,governments are good which promote     
prosperity4       ,the government of    
,burmah does not promote prosperity4    
4'4 ,it is not a good government4       
7#c7 ,land is not property4       ,land 
produces barley4       4'4 ,beer is     
intoxicating4    7#d7 ,nothing is       
property but that which is the product  
of man's hand4       ,the horse is not  
the product of man's hand4       4'4    
,the horse is not property4    7#e7     
,some ,europeans at least are not       

,aryans1 because the ,finns are   not4  
7#f7 ,saturn is visible from the earth1 
and the moon is visible from   the      
earth4 ,therefore the moon is visible   
from ,saturn4    7#g7 ,some men of      
self-command are poor1 and therefore    
some noble   characters are poor4       
7#h7 ,sparing the rod spoils the child3 
so ,john will turn out very   good1 for 
his mother beats him every day4    7#i7 
,some effects of labour are not painful1
 since every virtue is an   effect of   
labour4   7#aj7 ,the courageous are     
confident and the experienced are       
confident4 ,therefore the experienced   
are courageous4   7#aa7 ,no tale-bearer 
is to be trusted1 and therefore no great
 talker  is to be trusted1 for all      
tale-bearers are great talkers4   7#ab7 
,socrates was wise1 and wise men alone  
are happy3 therefore  ,socrates was     
happy4   ,,ii4  #a4 ,from the major ',no
 matter thinks' draw1 by supplying the  
minor1 the following conclusions--      
7#a7 ,some part of man does not think4  

7#b7 ,the soul of man is not matter4    
7#c7 ,some part of man is not matter4   
7#d7 ,some substance does not think4    
,name the figured mood into which each  
syllogism falls4  #b4 ,construct        
syllogisms in the following moods and   
figures1 stating whether they are valid 
or invalid1 and giving your reasons in  
each case--    ,,aee in the first       
figure2 ,,eao in the second2 ,,iai in   
the third2 ,,aii in   the fourth4  #c4  
,prove that ',brass is not a metal1'    
using as your middle term 'compound     
body4'  #d4 ,construct syllogisms to    
prove or disprove--    7#a7 ,some taxes 
are necessary4    7#b7 ,no men are free4
    7#c7 ,laws are salutary4  #e4 ,prove
 by a syllogism in ,bokardo that ',some 
,socialists are not unselfish1' and     
reduce your syllogism directly and      
indirectly4  #f4 ,prove the following   
propositions in the second figure1 and  
reduce the syllogisms you use to the    
first--    7#a7 ,all negroes are not    
averse to education4    7#b7 ,only      

murderers should be hanged4  #g4 ,prove 
in ,baroko and also in ,ferio that      
',some ,irishmen are not ,celts4'  #h4  
,construct in words the same syllogism  
in all the four figures4  #i4 ,invent   
instances to show that false premisses  
may give true conclusions4   ,,iii4  #a4
 ,what moods are peculiar to the first1 
second1 and third figures respectively8 
#b4 ,what moods are common to all the   
figures8  #c4 ,why can there be no      
subaltern moods in the third figure8    
#d4 ,what is the only kind of conclusion
 that can be drawn in all the figures8  
#e4 ,show that ,,ieo violates the       
special rules of all the figures4  #f4  
,in what figures is ,,aee valid8  #g4   
,show that ,,aeo is superfluous in any  
figure4  #h4 ,prove that ,o cannot be a 
premiss in the first figure1 nor a minor
 premiss anywhere but in the second4    
#i4 ,show that in the first figure the  
conclusion must have the quality of the 
major premiss and the quantity of the   
minor4  #aj4 ,why do the premisses ,,ea 

yield a universal conclusion in the     
first two figures and only a particular 
one in the last two8  #aa4 ,show that   
,,aai is the only mood in the fourth    
figure in which it is possible for the  
major term to be distributed in the     
premiss and undistributed in the        
conclusion4  #ab4 ,why are the premisses
 of ,fesapo and ,fresison not transposed
 in reduction like those of the other   
moods of the fourth figure8   ,,iv4  #a4
 ,why is it sufficient to distribute the
 middle term once only8  #b4 ,prove that
 from two affirmative premisses you     
cannot get a negative conclusion4  #c4  
,prove that there must be at least one  
more term distributed in the premisses  
than in the conclusion4  #d4 ,prove that
 the number of distributed terms in the 
premisses cannot exceed those in the    
conclusion by more than two4  #e4 ,prove
 that the number of undistributed terms 
in the premisses cannot exceed those in 
the conclusion by more than one4  #f4   
,prove that wherever the minor premiss  

is negative1 the major must be          
universal4  #g4 ,prove that wherever the
 minor term is distributed1 the major   
premiss must be universal4  #h4 ,if the 
middle term be twice distributed1 what  
mood and figure are possible8  #i4 ,if  
the major term of a syllogism be the    
predicate of the major premiss1 what do 
we know about the minor premiss8  #aj4  
,when the middle term is distributed in 
both premisses1 what must be the        
quantity of the conclusion8  #aa4 ,prove
 that if the conclusion be universal1   
the middle term can only be distributed 
once in the premisses4  #ab4 ,show how  
it is sometimes possible to draw three  
different conclusions from the same     
premisses4   ,,chapter ,,xix4  #a4      
,convert the following propositions--   
7#a7 ,if a man is wise1 he is humble4   
7#b7 ,where there is sincerity there is 
no affectation4    7#c7 ,when night-dogs
 run1 all sorts of deer are chased4     
7#d7 ,the nearer the ,church1 the       
further from ,god4    7#e7 ,if there    

were no void1 all would be solid4       
7#f7 ,not to go on is sometimes to go   
back4  #b4 ,express in a single         
proposition--    ,if he was divine1 he  
was not covetous2 and if he was         
covetous1 he   was not divine4  #c4     
,exhibit the exact logical relation to  
one another of the following pairs of   
propositions--    7#a7 ,if the          
conclusion be false1 the premisses are  
false4  ,if the   conclusion be true1   
the premisses are not necessarily true4 
7#b7 ,if one premiss be negative1 the   
conclusion must be negative4    ,if the 
conclusion be negative1 one of the      
premisses must be   negative4    7#c7   
,the truth of the universal involves the
 truth of the particular4    ,the       
falsity of the particular involves the  
falsity of the universal4    7#d7 ,from 
the truth of the particular no          
conclusion follows as to the            
universal4    ,from the falsity of the  
universal no conclusion follows as to   
the   particular4    7#e7 ,if the       

conclusion in the fourth figure be      
negative1 the major   premiss must be   
universal4    ,if the major premiss in  
the fourth figure be particular1 the    
conclusion must be affirmative4    7#f7 
,if both premisses be affirmative1 the  
conclusion must be   affirmative4    ,if
 the conclusion be negative1 one of the 
premisses must be   negative4  #d4 ',the
 ,method of ,agreement stands on the    
ground that whatever circumstance can be
 eliminated is not connected with the   
phenomenon by any law2 the ,method of   
,difference stands on the ground that   
whatever circumstance cannot be         
eliminated is connected with the        
phenomenon by a law4' ,do these two     
principles imply one another8           
,,chapters ,,xx-,,xxviii4  #a4 ,fill up 
the following enthymemes1 and state the 
exact nature of the resulting           
syllogism--    7#a7 ,if ,livy is a      
faultless historian1 we must believe all
 that he   tells us2 but that it is     
impossible to do4    7#b7 ,if they stay 

abroad1 the wife will die2 while the    
husband's   lungs will not stand the    
,english climate4 ,it is to be feared   
therefore that one must fall a victim4  
7#c7 ,he is either very good1 very bad1 
or commonplace4  ,but he is not   very  
good4    7#d7 ,either a slave is capable
 of virtue or he is not4   4'4 ,either  
he ought not to be a slave or he is not 
a man4    7#e7 ,does not his feebleness 
of character indicate either a bad      
training or a natural imbecility8       
7#f7 ,those who ask shan't have2 those  
who don't ask don't want4    7#g7 ,if a 
man be mad1 he deviates from the common 
standard of   intellect4   4'4 ,if all  
men be alike mad1 no one is mad4    7#h7
 ',i cannot dig2 to beg ,i am ashamed4' 
#b4 ',the infinite divisibility of space
 implies that of time4  ,if the latter  
therefore be impossible1 the former must
 be equally so4' ,formulate this        
argument as an immediate inference4  #c4
 ,examine the following arguments--     
7#a7 ,if we have a dusty spring1 there  

is always a good wheat   harvest4 ,we   
shall therefore have a poor harvest this
 year1 for the   spring has not been    
dusty4    7#b7 ,virtues are either      
feelings1 capacities1 or states2 and as 
they   are neither feelings nor         
capacities1 they must be states4    7#c7
 ,everything must be either just or     
unjust4       ,justice is a thing1 and  
is not unjust4       4'4 ,justice is    
just4        ,similarly justice is holy4
       ,but the virtues of knowledge1   
justice1 courage1 temperance1 and       
holiness were declared to be different  
from one another4       4'4 ,justice is 
unholy and holiness unjust4   ,,chapter 
,,xxix4  ,formulate the following trains
 of reasoning1 resolve them into their  
component parts1 and point out any      
violations of the rules of syllogism    
which they may contain--    7#a7 ,no    
,church ,institutions are useful2 for   
they teach religious   matters1 not     
business matters1 which latter are      
useful1 being   profitable4    7#b7 ,mr4

 ,darwin long ago taught us that the    
clover crop is dependent   on the number
 of maiden ladies in the district4 ,for 
the ladies keep   cats1 and the cats    
destroy the field-mice1 which prey on   
the bees1   which1 in their turn1 are   
all-important agents in the             
fertilisation   of the clover flowers4  
7#c7 ,athletic games are duties2 for    
whatever is necessary to health   is a  
duty1 and exercise is necessary to      
health1 and these games are   exercise4 
7#d7 ,the iron-trade leads to the       
improvement of a new country2 for       
furnaces require to be fed with fuel1   
which causes land to be   cleared4      
7#e7 ',is stone a body8' ',yes4' ',well1
 is not an animal a body8'   ',yes1'    
',and are you an animal8' ',it seems    
so4' ',then you are a   stone1 being an 
animal4'    7#f7 ,if ,a is ,b1 ,c is ,d4
   ,if ,e is ,f1 ,g is ,h4   ,but if ,a 
is ,b1 ,e is ,f4   4'4 ,if ,c is ,d1 ,g 
is sometimes ,h4    7#g7 ,the soul is   
not matter4   ,my arm is not myself4    

7#h7 ,honesty deserves reward and a     
negro is a   fellow-creature4 ,therefore
 an honest negro is a fellow-creature   
deserving of reward4   ,,chapter ,,xxx4 
#a4 ,point out any ambiguities which    
underlie the following propositions--   
7#a7 ,every one who has read the book in
 ,french will recommend those   who have
 not to read it in ,english4    7#b7 ,i 
will not do this because he did it4     
7#c7 ,these are all my books4    7#d7   
,by an old statute of the date of       
,edward ,,iii it was accorded   'that   
,parliament should be holden every year 
once or more often if   need be4'       
7#e7 ,they found ,mary and ,joseph and  
the babe lying in a manger4    7#f7 ,the
 king and his minister are feeble and   
unscrupulous4    7#g7 ,heres meus uxori 
meae triginta pondo vasorum argenteorum 
dato1   quae volet4  #b4 ,examine the   
following arguments1 formulating them   
when sound1 and referring them1 when    
unsound1 to the proper head of fallacy--
    7#a7 ,we know that thou art a       

teacher come from ,god2 for no man can  
do   these signs that thou doest1 except
 ,god be with him4 ,s4 ,john iii4 #b4   
7#b7 ',sir ,walter ,scott's novels have 
ceased to be popular4' ',well1   that's 
only because nobody reads them4'    7#c7
 ,what we produce is property4          
,the sheriff produces a prisoner4       
4'4 ,a prisoner is property4    7#d7 ,as
 all metals are not necessarily solid1  
we may expect some   metals to be       
liquid4    7#e7 ,moses was the son of   
,pharaoh's daughter4       4'4 ,moses   
was the daughter of ,pharaoh's son4     
7#f7 ,if ,aeschines took part in the    
public rejoicings over the success   of 
my policy1 he is inconsistent in        
condemning it now2 if he did   not1 he  
was a traitor then4    7#g7 ,it is wrong
 to stick knives into people4       4'4 
,surgeons ought to be punished4    7#h7 
,if a thing admits of being taught1     
there must be both teachers       and   
learners of it4       4'4 ,if there are 
neither teachers nor learners of a      

thing1 that       thing does not admit  
of being taught4    7#i7 ,it is         
unnecessary to lend books1 if they are  
common1 and wrong   to lend them1 if    
they are rare4  ,therefore books should 
not be lent   from public libraries4    
7#aj7 ,seeing is believing4        4'4  
,what is not seen cannot be believed4   
7#aa7 ,st4 ,paul was not of ,jewish     
blood1 for he was a ,roman citizen4     
7#ab7 ,to call you an animal is to speak
 the truth4        ,to call you an ass  
is to call you an animal4        4'4 ,to
 call you an ass is to speak the truth4 
7#ac7 ,pain chastens folly4 ,a life of  
ease must therefore be one of   folly   
incurable4    7#ad7 ,we cannot be happy 
in this world2 for we must either       
indulge   our passions or combat them4  
7#ae7 ,it must be clear to the most     
unlettered mind that1 as all   things   
were originally created by the ,deity1  
including the hair on   our heads and   
the beards on our faces1 there can be no
 such thing as   property4    7#af7 ,the

 crime was committed by the criminal4   
,the criminal was committed by the      
magistrate4        4'4 ,the crime was   
committed by the magistrate4    7#ag7   
,general councils are as likely to err  
as the fallible men of   whom they      
consist4    7#ah7 ,dead dogs are heavier
 than living ones1 because vitality is  
buoyant4    7#ai7 ,deliberation is      
concerned with actions4        ,actions 
are means4        4'4 ,deliberation is  
concerned with means4    7#bj7 ',no     
beast so fierce but has a touch of pity2
 ,but ,i have none3   therefore ,i am no
 beast4'    7#ba7 ,practical pursuits   
are better than theoretical4        4'4 
,mathematics are better than logic4     
7#bb7 ,death must be a good4 ,for either
 the soul1 ceasing to be1   ceases ta   
suffer1 or1 continuing to be1 lives in a
 better state4    7#bc7 ,what is right  
should be enforced by law4        4'4   
,charity should be so enforced4    7#bd7
 ,all animals were in the ,ark4         
4'4 ,no animals perished in the ,flood4 

7#be7 ,if he robs1 he is not honourable4
        ,if he pays all his dues1 he    
does not rob4        4'4 ,if he pays all
 his dues1 he is honourable4    7#bf7 ,a
 dove can fly a mile in a minute4       
,a swallow can fly faster than a dove4  
4'4 ,a swallow can fly more than a mile 
in a minute4    7#bg7 ',i must soap     
myself1 because it's ,sunday4'          
',then do you only soap yourself on     
,sunday4'    7#bh7 ,if the charge is    
false1 the author of it is either       
ignorant or   malicious4 ,but the charge
 is true4  ,therefore he is neither4    
7#bi7 ,all the angles of a triangle are 
equal to two right angles4        ,the  
angle at the vertex is an angle of a    
triangle4        4'4 ,it is equal to two
 right angles4    7#cj7 ,si gravis sit  
dolor1 brevis est2 si longus1 levis4    
,ergo   fortiter ferendus4    7#ca7 ,you
 are not what ,i am4        ,i am a man4
        4'4 ,you are not a man4    7#cb7
 ,the extension of the franchise is     
necessary1 for it is   imperative that  

the right of voting should be granted to
 classes who   have hitherto not        
possessed this privilege4    7#cc7 ,if  
,hannibal is really victorious1 he does 
not need supplies2   while1 if he is    
deluding us1 we ought certainly not to  
encourage him   by sending them4  ,livy1
 xxiii4 #ac4  #e4    7#cd7 ,laws must   
punish1 and punishment hurts4   ,all    
laws therefore are hurtful4    7#ce7    
,the sun is an insensible thing4        
,the ,persians worship the sun4         
4'4 ,the ,persians worship an insensible
 thing4    7#cf7 ,some ores are not     
metals2 for they are not fluids1   and  
some metals are not fluids4    7#cg7    
,all the ,grecian soldiers put the      
,persians to flight4        4'4 ,every  
,grecian soldier could rout the         
,persians4    7#ch7 ,the resurrection of
 ,jesus ,christ is either an isolated   
fact or   else admits of parallel4 ,but 
if it be an isolated fact1 it cannot be 
rendered probable to one who denies the 
authority of ,christianity2   and1 if it

 admit of parallel1 it no longer proves 
what is   required4 ,therefore it is    
either incapable of being substantiated 
or   else makes nothing for the truth of
 ,christianity4    7#ci7 ,the           
resurrection of ,christ in the flesh and
 his ascension into   heaven were events
 either intrinsically incredible in     
their nature   or not4 ,if the former1  
the prevalent belief in them can only be
   accounted for by miracles2 if the    
latter1 they ought to be believed   even
 without miracles4 ,st4  ,aug4 ,de ,civ4
 ,dei1 xxii4 #h4    7#dj7 ,only         
contented people are wise4 ,therefore   
the tramp contented   in his rags is    
necessarily a wise man4    7#da7        
,four-legged things are brutes4         
,tables are four-legged things4         
4'4 ,tables are brutes4    7#db7 ,the   
apparent volcanoes in the moon are not  
volcanoes2 for   eruptions are produced 
by gases only1 and there are no gases in
 the   moon4    7#dc7 ,to read the      
,scriptures is our duty4 ,therefore the 

,captain was   wrong in punishing the   
helmsman for reading the ,bible at the  
time   when the ship struck4    7#dd7   
,the divine law orders that kings should
 be honoured4        ,louis ,quatorze is
 a king4        4'4 ,the divine law     
orders that ,louis ,quatorze should be  
honoured4    7#de7 ,those who desire the
 same object are unanimous4             
,caesar and ,pompey both desire the same
 object1 namely1 supreme        power4  
4'4 ,they are unanimous4    7#df7       
,either the ministers left at home will 
be ciphers or they will   not be        
ciphers4 ,if they are ciphers1 cabinet  
government1 which is   equivalent to    
constitutional government1 will receive 
a rude blow4   ,if they are not ciphers1
 the cabinet will be considering matters
 of   the utmost importance in the      
absence1 and the gratuitous absence1 of 
two of its most important members4 ',the
 ,standard1' ,wed4 ,june #e1   #ahgh4   
7#dg7 ,one patent stove saves half the  
ordinary amount of   fuel4 ,therefore   

two would save it all4    7#dh7 ,one    
number must win in the lottery4         
,my ticket is one number4        4'4 ,it
 must win4    7#di7 ,all good shepherds 
are prepared to lay down their lives for
 the        sheep4        ,few in this  
age are so prepared4        4'4 ,few in 
this age are good shepherds4    7#ej7   
,you cannot define the sun2 for a       
definition must be clearer   than the   
thing defined1 and nothing can be       
clearer than the source   of all light4 
7#ea7 ,to give the monopoly of the home 
market to the produce of   domestic     
industry 444 must in almost all cases be
 either a useless   or a hurtful        
regulation4 ,if the produce of domestic 
can be brought   there as cheap as that 
of foreign industry1 the regulation is  
evidently useless2 if it cannot1 it is  
generally hurtful4 ,adam   ,smith1      
,wealth of ,nations1 ,bk4 iv4 ch4 #b4   
7#eb7 ,verberare est actio4        ,ergo
 et vapulare4    7#ec7 ,the ages of all 
the members of this family are over     

#aej4        ,the baby is a member of   
this family4        4'4 ,its age is over
 #aej4    7#ed7 ,romulus must be an     
historical person2 because it is not at 
all   likely that the ,romans1 whose    
memory was only burdened with seven     
kings1 should have forgotten the most   
famous of them1 namely1 the   first4    
7#ee7 ,all scientific treatises that are
 clear and true deserve                 
attention4        ,few scientific       
treatises are clear and true4        4'4
 ,few scientific treatises deserve      
attention4    7#ef7 ,the ,conservative  
,government is an expensive one2 for1 on
 their   going out of ,office1 there was
 a deficit4    7#eg7 ,a man is forbidden
 to marry his brother's wife1 or1 in    
other   words1 a woman is forbidden to  
marry her husband's brother1 that is1   
a woman is directly forbidden to marry  
two brothers4 ,therefore a man   may not
 marry two sisters1 so that a man may   
not marry his wife's   sister4          
,,index4   ,the references refer to the 

sections4  ,abstraction1 #ig4           
,acategorematic words1 #ga4  ,accent1   
,fallacy of1 #hee4  ,accident1 #cah4    
,accident1 ,fallacy of1 #hfj4  ,a dicto 
secundum quid1 ,fallacy of1 #hfa4       
,amphiboly1 ,fallacy of1 #hdh4          
,antecedent   of a complex proposition1 
#bab4   of an inference1 #dbh4  ,a      
posteriori ,truth1 #bcb4  ,a priori     
,truth1 #bca4  ',a' ,propositions1 #bfj4
   conversion of1 #dhi4  ,arguing in a  
circle1 #hhb4  ,argumentum ad hominem1  
etc41 #hfg4  ,art1 #bj4  ,attribute1 #ha
 sqq4   ,essential and non-essential1   
#cbj4  ,attributives1 #hh sqq4   ,basis 
of ,division1 #cia4   ,categorematic    
words1 #ga4  ,circulus in definiendo1   
#chb4  ,common ,terms1 #aje4   how      
formed1 #ii4   nature of1 #dh4  ,complex
 ,proposition1 #bji4   conversion of1   
#gji4   conversion by contraposition of1
 #gbh4   conversion by negation of1     
#gba4   divided into conjunctive and    
disjunctive1 #bad4   permutation of1    
#gah4  ,complex ,syllogism1 #gca4       

mixed form of1 #ggh4  ,composition1     
,fallacy of1 #hdi4  ,concept1 #cf1 #dj  
sqq4  ,conception1 #cc4                 
,conceptualists1 #ea4  ,conclusion1     
#edj4   predicate of1 #edb4   subject   
of1 #edb4  ,conjunctive ,syllogisms1    
#gcc4   canon of1 #gdb4   reduction of  
partly1 #gdd4   partly conjunctive      
syllogisms as an immediate inference1   
#gec4  ,connotation of ,terms1 #adh4    
,consequent of a complex proposition1   
#bac4   of an inference1 #dbh4          
,consequent1 ,fallacy of1 #hgc4         
,contingent1 #ag4  ,contradiction1 ,law 
of1 #be sqq4  ,contradictory            
,propositions1 #deh4   ,terms1 #abi4    
,contrary ,propositions1 #deh4   ,terms1
 #acj4  ,converse1 #dhj4  ,conversion1  
#dgi4   of complex propositions1 #gji4  
by contraposition1 #eaf4   illative1    
#dha4   by negation1 #ejd4   per        
accidens1 #dhg4   simple1 #dhf4   rules 
of1 #dhb4  ,convertend1 #dhj4  ,copula1 
#eh1 #fd1 #ahf sqq4   modality of1 #aif4
  ,correlatives1 #adb4   ,deduction and 

,induction1 difference of1 #dca sqq4    
,deductive ,inference1 #ddb4  ,deductive
 ,logic1 definition of1 #d4  ,definition
 of ,terms1 #cdg sqq4   of ,aristotle   
7,greek3 risms71 #ccf4   final1 #cgd4   
nominal1 #cge4   provisional1 #cgd4     
real1 #cge4   rules of1 #cgh4           
,denotation of ,terms1 #aeb4            
,description1 #cfj4  ,designations1     
#aab4  ,determination1 #afg4  ,dictum de
 omni et nullo1 #efi4   de diverso1     
#fda4   de exemplo et excepto1 #fdb4    
,difference1 #cah1 #ceh4   generic1     
#daj4   specific1 #dji4  ,dilemma1 #gcb1
 #ggi4   rebutted1 #gib4   reduction of1
 #gif4   regarded as an immediate       
inference1 #gih4  ,disjunctive          
,syllogism1 #gfj4   canon of1 #gfe4     
reduction of1 #gff4   regarded as an    
immediate inference1 #ggj4              
,distinction1 #dbd4  ,distribution of   
,terms1 #bgd4   four rules for1 #bic4   
,divided whole1 #cic4  ,dividing        
members1 #cid4  ,division1 #che sqq4    
by dichotomy1 #dab4   rules of1 #cie4   

,division1 ,fallacy of1 #hea4  ,division
 of ,propositions1 #bjf4   of terms1    
#hf4   of things1 #gg4   ,enthymeme1    
incorrectly so-called1 #eeg4            
,enumeration1 #chg1 #dbb4  ,epicheirema1
 #hjc4  ,episyllogism1 #hjb4  ',e'      
,propositions1 #bfj4   conversion of1   
#dij4  ,equivocation1 ,fallacy of1 #hde4
  ,excluded ,middle1 ,law of1 #be sqq41 
#ejb4  ,extension of ,terms1 #adi sqq41 
#aff sqq4   ,fallacy1 #hbg sqq4   of    
ambiguity1 #hca4   definition of1 #hbh4 
formal1 #hch4   logical1 #hcf4          
material1 #hca1 #hcf4   of undisturbed  
middle1 #ehe4  ,figure of ,speech1      
,fallacy of1 #heg4  ,figures1 of a      
,syllogism1 #eeh4   special canons of1  
#fcc4   special rules of1 #fjf4         
special uses of1 #fdh4  ,formal ,logic1 
#af4  ,four ,terms1 ,fallacy of1 #hdj4  
,fundamentum ,divisionis1 #cia4         
,generalisation1 #afh4  ,genus1 #cah4   
as used by ,aristotle1 #ccf4   cognate1 
#djh4   proximate1 #dbj4   subaltern1   
#djf4   summum1 #afg1 #djd4   ,heads of 

,predicables1 #cac4   as given by       
,aristotle1 #ccf4   ',ideas' of ,plato1 
#eb4  ,identity1 ,law of1 #be sqq4      
,ignoratio ,elenchi1 ,fallacy of1 #hfe4 
,ignotum per ignotius1 #chc4  ,illicit  
,process1 ,fallacy of1 #ehf4  ,immediate
 ,inference1 #ddb sqq4   by added       
determinants1 #ece4   by complex        
conception1 #ecg4   applied to complex  
propositions1 #gja4  ,immediate         
,inference1 compound forms of1 #ejc4    
partly conjunctive syllogisms regarded  
as1 #gec4   by conversion1 #dgi4        
disjunctive syllogisms regarded as1     
#ggj4   by opposition1 #dfb4   by       
permutation1 #dif4  ,induction1         
differing from ,deduction1 #dcj sqq4    
,inductive ,logic1 #b1 #bjd4            
,inferences in general1 #dbf4           
classification of1 #dda4   deductive1   
#ddb4   inductive1 #dcj4  ,intimae      
species1 #dje4  ,intension of ,terms1   
#aej1 #aff4  ,intuition1 #bcb4  ,inverse
 ,variation1 ,law of1 #aff4  ',i'       
,propositions1 #bfj4   conversion of1   

#dij4   ',judgement1' various meanings  
of1 #cb1 #cf4   ',law1' ambiguities of  
the word1 #g sqq4   ,major ,premiss1    
#edd4  ,major ,term1 #edb4  ,many       
,questions1 ,fallacy of1 #hhd4  ,mediate
 ,inferences or ,syllogisms1 #ddd1 #edj 
sqq4   axioms of1 #egf4  ,membra        
,dividentia1 #cid4  ,middle ,term1 #eda4
   position of1 in a syllogism1 #efc4   
,minor ,premiss1 #ede4  ,minor ,term1   
#edb4  ,modality1 ,question of1 #aif4   
,mode1 the1 #aif4  ,moods of a          
,syllogism1 #eeh4   determination of the
 legitimate1 #eii4   subaltern1 #fbh4   
valid in the ,four ,figures1 #fba4      
mnemonics of1 valid in ,four ,figures1  
#fbi4   ,name1 definition of1 #fa4      
,negative ,premisses and ,conclusion1   
,fallacy of1 #hdb4  ,nominalists1 #ej1  
#ed4  ,non causa pro causa1 ,fallacy of1
 #hhc4  ,nouns1 #fb4   ,opposition1 #ddi
 sqq4   contradictory1 #deg4   contrary1
 #ded4   laws of1 #dfd4   subaltern1    
#def4   sub-contrary1 #dee4  ',o'       
,propositions1 #bfj4   conversion of1   

#dia4   ,partition1 #dbc4  ,permutation1
 #dif sqq4   of ,complex ,propositions1 
#gah4  ,petitio ,principii1 ,fallacy of1
 #hgd4  ,predicable1 #cad4  ,predicate  
of a ,proposition1 #eh1 #ahd4   read in 
extension1 #cjg4   quantification of1   
#bie sqq4   quantity of1 #bha1 #did4    
,predication1 #aid4   in quid or in     
quale1 #ccb4  ,premisses1 #edj4   major1
 #edd4   minor1 #ede4  ,primary         
,existences1 #ee4  ,problema1 the1 #eef4
  ,proper ,names1 #aac4  ,property1     
#cah4   generic1 #daa4   specific1 #daa4
  ,proposition1 #agb sqq4   accidental1 
#bch4   affirmative1 #beh4   complex or 
conditional1 #bji4   conjunctive or     
hypothetical1 #bad1 #gjd4   conversion  
of1 #dgi4   definition of1 #agh4        
disjunctive1 #bad4   divisions of1 #bjf4
   essential1 #bch4   exceptive1 #bgj4  
exclusive1 #bff4   extensive1 #bfd4     
general1 #bea4   indefinite1 #bdd4      
intensive1 #bfd4   modal1 #bje4         
negative1 #beh4   particular1 #bdj4     
pure1 #bje4   quality of1 #beh4         

quantity of1 #bdf4   real or            
synthetical1 #bbg4   simple or          
categorical1 #bjg4   singular1 #bej4    
tautologous or identical1 #bgc4         
universal1 #bci4   verbal or analytical1
 #bbd4  ,proprium1 #ccf4                
,pro-syllogism1 #hjb4   ,quaestio1 the1 
#eef4  ,quality1 a1 #hb4  ,quality of   
the matter1 #bjd4   of propositions1    
#beh4  ,quantification of the           
,predicate1 #bie sqq41 #dic4  ,quantity 
of propositions1 #beh4   of terms1 #adh4
   ,realists1 #di4  ,real ,kinds1 #cga4 
,reasoning or ,inference1 #ce4   the    
canon of1 #efj4   trains of1 #hjj4      
,reduction of propositions1 #ffg4   of  
the dilemma1 #gif4   of disjunctive     
syllogisms1 #gff4   indirect1 #fia4     
mnemonics for1 #fig4   ostensive or     
direct1 #fgc4   of partly conjunctive   
syllogisms1 #gdd4  ,relation1 a1 #hc1   
#add4  ,relation1 immediate inference   
by1 #dfb4   compatible and incompatible1
 #dfb4   ,science1 #bj4  ,secondary     
,existences1 #ee4  ,simple              

,apprehension1 #cc4  ,sorites1 the1 #hjg
 sqq4  ,specialisation1 #afg4  ,species1
 #cah4   cognate1 #djg4   infimae1 #dje4
   subaltern1 #djf4  ,subalternant1     
#deh4  ,subalternate1 #deh4             
,subalternation1 #deh4  ,subalterns1    
#deh4  ,sub-contraries1 #deh4           
,sub-division1 #dja4  ,subject1 #eh1    
#ahc4   how used1 #bfd4   quantity of1  
#bgi4  ,substance1 #hj1 #hd4  ,summum   
,genus1 #afg1 #djd4  ,suppositio        
,materialis1 #gf4  ,syllogism1 #edf sqq4
   complex1 #gca4   in common discourse1
 #eeg4   conjunctive1 #gcc4   definition
 of1 #eeb4   disjunctive1 #gfj4         
general rules of1 #ehb4   figures of1   
#efj1 #efc4   with three figures1 #fef4 
legitimate moods of1 #eii sqq4          
mnemonics for1 #eih4   moods of1 #eei1  
#efb4  ,syncntegorematic words1 #gj4    
,synonym1 #cde4   ,term1 #eg sqq4       
absolute1 #adj4   abstract1 #ie4        
analogous1 #aci4   attributive1 #hh4    
collective1 #aah4   common1 #aje4       
concrete1 #if4   connotative1 #adg4     

contradictory1 #abi4   contrary1 #acj4  
definition of1 #cdg4  ,terms1           
distribution of1 #bge4   distributive   
and collective use of1 #aai4   division 
of1 #hf4   equivocal1 #acg4             
incompatible1 #ace4   individual1 #aba4 
major1 middle1 and minor1 #edb4         
negative1 #abf4   non-connotative1 #adg4
   positive1 #abf4   privative1 #abf4   
quantity of1 #adh4  ,terms1 relative1   
#ada4   repugnant1 #ace4   singular1    
#dc1 #ajd4   subject1 #hg4              
undistributed1 #bgg4   univocal1 #acg4  
,universals1 nature of1 #dh1 #ee4  ',u' 
,propositions1 #big4   ,verb1 #fd4      
,words1 their relation to terms1 #fe    
sqq1    ,,the ,,end4