,brett ,fishburne ,,the ,,game ,,of ,,logic ,by ,lewis ,carroll --------------------- #i #aj -----x------ #aa #ab ---y-----m------y'--- #ac #ad -----x'----- #ae #af --------------------- ,,colours ,,for ------------- ,,counters #e #f x ,see the ,sun is overhead1 --y-------y'- ,shining on us1 ,,full and ,,red6 x' #g #h ,now the ,sun is gone away1 ------------- ,and the ,,empty sky is ,,grey6 ,,the ,,game ,,of ,,logic ,by ,lewis ,carrol ,to my ,child-friend4 ,i charm in vain2 for never again1 ,all keenly as my glance ,i bend1 ,will ,memory1 goddess coy1 ,embody for my joy ,departed days1 nor let me gaze ,on thee1 my fairy friend6 ,yet could thy face1 in mystic grace1 ,a moment smile on me1 'twould send ,far-darting rays of light ,from ,heaven athwart the night1 ,by which to read in very deed ,thy spirit1 sweetest friend6 ,so may the stream of ,life's long dream ,flow gently onward to its end1 ,with many a floweret gay1 ,adown its willowy way3 ,may no sigh vex1 no care perplex1 ,my loving little friend6 ,,nota ,,bene4 ,with each copy of this ,book is given an ,envelope1 containing a ,diagram 7similar to the frontispiece7 on card1 and nine ,counters1 four red and five grey4 ,the ,envelope1 c4 can be had separately1 at #c;d4 each4 ,the ,author will be very grateful for suggestions1 especially from beginners in ,logic1 of any alterations1 or further explanations1 that may seem desirable4 ,letters should be addressed to him at #bi1 ,bedford ,street1 ,covent ,garden1 ,london4 ,,preface ,there foam'd rebellious ,logic1 gagg'd and bound4 ,this ,game requires nine ,counters--four of one colour and five of another3 say four red and five grey4 ,besides the nine ,counters1 it also requires one ,player1 ,,at ,,least4 ,i am not aware of any ,game that can be played with ,,less than this number3 while there are several that require ,,more3 take ,cricket1 for instance1 which requires twenty-two4 ,how much easier it is1 when you want to play a ,game1 to find ,,one ,player than twenty-two4 ,at the same time1 though one ,player is enough1 a good deal more amusement may be got by two working at it together1 and correcting each other's mistakes4 ,a second advantage1 possessed by this ,game1 is that1 besides being an endless source of amusement 7the number of arguments1 that may be worked by it1 being infinite71 it will give the ,players a little instruction as well4 ,but is there any great harm in ,,that1 so long as you get plenty of amusement8 ,,contents4 ,,chapter ,,page ,i4 ,,new ,,lamps ,,for ,,old4 #a4 ,propositions 4 4 4 4 4 4 4 #a #b4 ,syllogisms 4 4 4 4 4 4 4 4 #bj #c4 ,fallacies 4 4 4 4 4 4 4 4 #cb ,,ii4 ,,cross ,,questions4 #a4 ,elementary 4 4 4 4 4 4 4 4 #cg #b4 ,half of ,smaller ,diagram4 ,propositions to be represented 4 4 4 4 4 #dj #c4 ,do4 ,symbols to be interpreted4 4 #db #d4 ,smaller ,diagram4 ,propositions to be represented 4 4 4 4 4 4 4 #dd #e4 ,do4 ,symbols to be interpreted4 4 #df #f4 ,larger ,diagram4 ,propositions to be represented 4 4 4 4 4 4 4 #dh #g4 ,both ,diagrams to be employed 4 4 #ea ,,iii4 ,,crooked ,,answers4 #a4 ,elementary 4 4 4 4 4 4 4 4 #ee #b4 ,half of ,smaller ,diagram4 ,propositions represented 4 4 4 4 4 4 4 #ei #c4 ,do4 ,symbols interpreted 4 4 4 #fa #d4 ,smaller ,diagram4 ,propositions represented4 #fb #e4 ,do4 ,symbols interpreted 4 4 4 #fe #f4 ,larger ,diagram4 ,propositions represented4 #fg #g4 ,both ,diagrams employed 4 4 4 4 #gb ,,iv4 ,,hit ,,or ,,miss 4 4 4 4 4 4 4 4 4 #he ,,chapter ,i4 ,,new ,,lamps ,,for ,,old4 ,light come1 light go4 #a4 ,propositions4 ,some new ,cakes are nice4 ,no new ,cakes are nice4 ,all new cakes are nice4 ,there are three ',,propositions' for you--the only three kinds we are going to use in this ,game3 and the first thing to be done is to learn how to express them on the ,board4 ,let us begin with ,some new ,cakes are nice4 ,but before doing so1 a remark has to be made--one that is rather important1 and by no means easy to understand all in a moment3 so please to read this ,,very carefully4 ,the world contains many ,,things 7such as ,buns1 ,babies1 ,beetles4 ,battledores4 c472 and these ,things possess many ,,attributes 7such as baked1 beautiful1 black1 broken1 c43 in fact1 whatever can be attributed to1 that is said to belong to1 any ,thing1 is an ,attribute74 ,whenever we wish to mention a ,thing1 we use a ,,substantive3 when we wish to mention an ,attribute1 we use an ,,adjective4 ,people have asked the question ,can a ,thing exist without any ,attributes belonging to it8 ,it is a very puzzling question1 and ,i'm not going to try to answer it3 let us turn up our noses1 and treat it with contemptuous silence1 as if it really wasn't worth noticing4 ,but1 if they put it the other way1 and ask ,can an ,attribute exist without any ,thing for it to belong to81 we may say at once ,no3 no more than a ,baby could go a railway-journey with no one to take care of it6 ,you never saw beautiful floating about in the air1 or littered about on the floor1 without any ,thing to ,,be beautiful1 now did you8 ,and now what am ,i driving at1 in all this long rigmarole8 ,it is this4 ,you may put is or are between names of two ,,things 7for example1 some ,pigs are fat ,animals71 or between the names of two ,,attributes 7for example1 pink is light-red71 and in each case it will make good sense4 ,but1 if you put is or are between the name of a ,,thing and the name of an ,,attribute 7for example1 some ,pigs are pink71 you do ,,not make good sense 7for how can a ,thing ,,be an ,attribute87 unless you have an understanding with the person to whom you are speaking4 ,and the simplest understanding would1 ,i think1 be this--that the ,substantive shall be supposed to be repeated at the end of the sentence1 so that the sentence1 if written out in full1 would be some ,pigs are pink 7,pigs74 ,and now the word are makes quite good sense4 ,thus1 in order to make good sense of the ,proposition some new ,cakes are nice1 we must suppose it to be written out in full1 in the form some new ,cakes are nice 7,cakes74 ,now this contains two ',,terms'--new ,cakes being one of them1 and nice 7,cakes7 the other4 ,new ,cakes1 being the one we are talking about1 is called the ',,subject' of the ,proposition1 and nice 7,cakes7 the ',,predicate'4 ,also this ,proposition is said to be a ',,particular' one1 since it does not speak of the ,,whole of its ,subject1 but only of a ,,part of it4 ,the other two kinds are said to be ',,universal'1 because they speak of the ,,whole of their ,subjects--the one denying niceness1 and the other asserting it1 of the ,,whole class of new ,cakes4 ,lastly1 if you would like to have a definition of the word ',,proposition' itself1 you may take this3--a sentence stating that some1 or none1 or all1 of the ,things belonging to a certain class1 called its ',subject'1 are also ,things belonging to a certain other class1 called its ',predicate'4 ,you will find these seven words--,,proposition1 ,,attribute1 ,,term1 ,,subject1 ,,predicate1 ,,particular1 ,,universal--charmingly useful1 if any friend should happen to ask if you have ever studied ,logic4 ,mind you bring all seven words into your answer1 and you friend will go away deeply impressed--'a sadder and a wiser man'4 ,now please to look at the smaller ,diagram on the ,board1 and suppose it to be a cupboard1 intended for all the ,cakes in the world 7it would have to be a good large one1 of course74 ,and let us suppose all the new ones to be put into the upper half 7marked 'x'71 and all the rest 7that is1 the ,,not-new ones7 into the lower half 7marked 'x''74 ,thus the lower half would contain ,,elderly ,cakes1 ,,aged ,cakes1 ,,ante-,,diluvian ,cakes--if there are any3 ,i haven't seen many1 myself--and so on4 ,let us also suppose all the nice ,cakes to be put into the left-hand half 7marked 'y'71 and all the rest 7that is1 the not-nice ones7 into the right-hand half 7marked 'y''74 ,at present1 then1 we must understand x to mean new1 x' not-new1 y nice1 and y' not-nice4 ,and now what kind of ,cakes would you expect to find in compartment ,no4 #e8 ,it is part of the upper half1 you see2 so that1 if it has any ,cakes in it1 they must be ,,new3 and it is part of the left-hand half2 so that they must be ,,nice4 ,hence if there are any ,cakes in this compartment1 they must have the double ',,attribute' new and nice3 or1 if we use letters1 the must be x y4 ,observe that the letters x1 y are written on two of the edges of this compartment4 ,this you will find a very convenient rule for knowing what ,attributes belong to the ,things in any compartment4 ,take ,no4 #g1 for instance4 ,if there are any ,cakes there1 they must be x' y1 that is1 they must be not-new and nice4 ,now let us make another agreement--that a red counter in a compartment shall mean that it is ',,occupied'1 that is1 that there are ,,some ,cakes in it4 7,the word 'some1' in ,logic1 means 'one or more' so that a single ,cake in a compartment would be quite enough reason for saying there are ,,some ,cakes here74 ,also let us agree that a grey counter in a compartment shall mean that it is ',,empty'1 that is that there are ,,no ,cakes in it4 ,in the following ,diagrams1 ,i shall put '#a' 7meaning 'one or more'7 where you are to put a ,,red counter1 and '#j' 7meaning 'none'7 where you are to put a ,,grey one4 ,as the ,subject of our ,proposition is to be new ,cakes1 we are only concerned1 at present1 with the ,,upper half of the cupboard1 where all the ,cakes have the attribute x1 that is1 new4 ,now1 fixing our attention on this upper half1 suppose we found it marked like this1 ----------- #a ----------- that is1 with a red counter in ,no4 #e4 ,what would this tell us1 with regard to the class of new ,cakes8 ,would it not tell us that there are ,,some of them in the x y-compartment8 ,that is1 that some of them 7besides having the ,attribute x1 which belongs to both compartments7 have the ,attribute y 7that is1 nice74 ,this we might express by saying some x-,cakes are y-7,cakes71 or1 putting words instead of letters1 ,some new ,cakes are nice 7,cakes71 or1 in a shorter form1 ,some new ,cakes are nice4 ,at last we have found out how to represent the first ,proposition of this ,section4 ,if you have not ,,clearly understood all ,i have said1 go no further1 but read it over and over again1 till you ,,do understand it4 ,after that is once mastered1 you will find all the rest quite easy4 ,it will save a little trouble1 in doing the other ,propositions1 if we agree to leave out the word ,cakes altogether4 ,i find it convenient to call the whole class of ,things1 for which the cupboard is intended1 the ',,universe4' ,thus we might have begun this business by saying ,let us take a ,universe of ,cakes4 7,sounds nice1 doesn't it87 ,of course any other ,things would have done just as well as ,cakes4 ,we might make ,propositions about a ,universe of ,lizards1 or even a ,universe of ,hornets4 7,wouldn't ,,that be a charming ,universe to live in87 ,so far1 then1 we have learned that ----------- #a ----------- means some x and y1 i4e4 some new are nice4 ,i think you will see without further explanation1 that ----------- #a ----------- means some x are y'1 i4e4 some new are not-nice4 ,now let us put a ,,grey counter into ,no4 #e1 and ask ourselves the meaning of ----------- #j ----------- ,this tells us that the x y-compartment is ,,empty1 which we may express by no x are y1 or1 no new ,cakes are nice4 ,this is the second of the three ,propositions at the head of this ,section4 ,in the same way1 ----------- #j ----------- would mean no x are y'1 or1 no new ,cakes are not-nice4 ,what would you make of this1 ,i wonder8 ----------- #a #a ----------- ,i hope you will not have much trouble in making out that this represents a ,,double ,proposition3 namely1 some x are y1 ,,and some are y'1 i4e4 some new are nice1 and some are not-nice4 ,the following is a little harder1 perhaps3 ----------- #j #j ----------- ,this means no x are y1 ,,and none are y'1 i4e4 no new are nice1 ,,and none are not-nice3 which leads to the rather curious result that no new exist1 i4e4 no ,cakes are new4 ,this is because nice and not-nice make what we call an ',,exhaustive' division of the class new ,cakes3 i4e4 between them1 they ,,exhaust the whole class1 so that all the new ,cakes1 that exist1 must be found in one or the other of them4 ,and now suppose you had to represent1 with counters the contradictory to no ,cakes are new1 which would be some ,cakes are new1 or1 putting letters for words1 some ,cakes are x1 how would you do it8 ,this will puzzle you a little1 ,i expect4 ,evidently you must put a red counter ,,somewhere in the x-half of the cupboard1 since you know there are ,,some new ,cakes4 ,but you must not put it into the ,,left-,,hand compartment1 since you do not know them to be ,,nice3 nor may you put it into the ,,right-,,hand one1 since you do not know them to be ,,not-,,nice4 ,what1 then1 are you to do8 ,i think the best way out of the difficulty is to place the red counter ,,on ,,the ,,division-,,line between the xy-compartment and the xy'-compartment4 ,this ,i shall represent 7as ,i always put '#a' where you are to put a red counter7 by the diagram ----------- -#a- ----------- ,our ingenious ,american cousins have invented a phrase to express the position of a man who wants to join one or the other of two parties--such as their two parties ',democrats' and ',republicans'--but can't make up his mind ,,which4 ,such a man is said to be sitting on the fence4 ,now that is exactly the position of the red counter you have just placed on the division-line4 ,he likes the look of ,no4 #e1 and he likes the look of ,no4 #f1 and he doesn't know ,,which to jump down into4 ,so there he sits astride1 silly fellow1 dangling his legs1 one on each side of the fence6 ,now ,i am going to give you a much harder one to make out4 ,what does this mean8 ----------- #a #j ----------- ,this is clearly a ,,double ,proposition4 ,it tells us not only that some x are y1 but also the no x are ,,not y4 ,hence the result is ,,all x are y1 i4e4 all new ,cakes are nice1 which is the last of the three ,propositions at the head of this ,section4 ,we see1 then1 that the ,universal ,proposition ,all new ,cakes are nice consists of ,,two ,propositions taken together1 namely1 ,some new ,cakes are nice1 and ,no new ,cakes are not-nice4 ,in the same way ----------- #j #a ----------- would mean all x are y' 1 that is1 ,all new ,cakes are not-nice4 ,now what would you make of such a ,proposition as ,the ,cake you have given me is nice8 ,is it ,particular or ,universal8 ,particular1 of course1 you readily reply4 ,one single ,cake is hardly worth calling 'some1' even4 ,no1 my dear impulsive ,reader1 it is ',universal'4 ,remember that1 few as they are 7and ,i grant you they couldn't well be fewer71 they are 7or rather 'it is'7 ,,all that you have given me6 ,thus1 if 7leaving 'red' out of the question7 ,i divide my ,universe of ,cakes into two classes--the ,cakes you have given me 7to which ,i assign the upper half of the cupboard71 and those you ,,haven',t given me 7which are to go below7--,i find the lower half fairly full1 and the upper one as nearly as possible empty4 ,and then1 when ,i am told to put an upright division into each half1 keeping the ,,nice ,cakes to the left1 and the ,,not-,,nice ones to the right1 ,i begin by carefully collecting ,,all the ,cakes you have given me 7saying to myself1 from time to time1 ,generous creature6 ,how shall ,i ever repay such kindness871 and piling them up in the left-hand compartment4 ,,and ,,it ,,doesn',t ,,take ,,long ,,to ,,do ,,it6 ,here is another ,universal ,proposition for you4 ,barzillai ,beckalegg is an honest man4 ,that means ,,all the ,barzillai ,beckaleggs1 that ,i am now considering1 are honest men4 7,you think ,i invented that name1 now don't you8 ,but ,i didn't4 ,it's on a carrier's cart1 somewhere down in ,cornwall47 ,this kind of ,universal ,proposition 7where the ,subject is a single ,thing7 is called an ',,individual' ,proposition4 ,now let us take ,,nice ,cakes as the ,subject of ,proposition3 that is1 let us fix our thoughts on the ,,left-,,hand half of the cupboard1 where all the ,cakes have attribute y1 that is1 nice4 ----- ,suppose we find it marked like this3-- #a ,what would that tell us8 ----- ----- ,i hope that it is not necessary1 after explaining the ,,horizontal oblong so fully1 to spend much time over the ,,upright one4 ,i hope you will see1 for yourself1 that this means some y are x1 that is1 ,some nice ,cakes are new4 ,but1 you will say1 we have had this case before4 ,you put a red counter into ,no4 #e1 and you told us it meant 'some new ,cakes are nice'2 and ,,now you tell us that it means 'some ,,nice ,cakes are ,,new'6 ,can it mean ,,both8 ,the question is a very thoughtful one1 and does you ,,great credit1 dear ,reader6 ,it ,,does mean both4 ,if you choose to take x 7that is1 new ,cakes7 as your ,subject1 and to regard ,no4 #e as part of a ,,horizontal oblong1 you may read it some x are y1 that is1 some new ,cakes are nice3 but1 if you choose to take y 7that is1 nice ,cake7 as your ,subject1 and to regard ,no4 #e as part of an ,,upright oblong1 ,,then you may read it some y are x1 that is1 some nice ,cakes are new4 ,they are merely two different ways of expressing the very same truth4 ,without more words1 ,i will simply set down the other ways in which this upright oblong might be marked1 adding the meaning in each case4 ,by comparing them with the various cases of the horizontal oblong1 you will1 ,i hope1 be able to understand them clearly4 ,you will find it a good plan to examine yourself on this table1 by covering up first one column and then the other1 and 'dodging about'1 as the children say4 ,also you will do well to write out for yourself two other tables--one for the ,,lower half of the cupboard1 and the other for its ,,right-,,hand half4 ,and now ,i think we have said all we need to say about the smaller ,diagram1 and may go on to the larger one4 ,symbols4 ,meanings4 ----- ,some y are x'2 i4e4 ,some nice are not-new4 ----- #a ----- ----- ,no y are x2 #j i4e4 ,no nice are new4 ----- ,observe that this is merely another way of expressing ,no new are nice4 ----- ----- ,no y are x'2 i4e4 ,no nice are not-new4 ----- #j ----- ----- #a ,some y are x1 and some are x'2 i4e4 ,some nice are new1 and some are ----- not-new4 #a ----- ----- #j ,no y are x1 and none are x'2 i4e4 ,no y exist2 ----- i4e4 ,no ,cakes are nice4 #j ----- ----- #a ,all y are x2 i4e4 ,all nice are new4 ----- #j ----- ----- #j ,all y are x'2 i4e4 ,all nice are not-new4 ----- #a ----- ,this may be taken to be a cupboard divided in the same way as the last1 but ,,also divided into two portions1 for the ,attribute m4 ,let us give to m the meaning wholesome3 and let us suppose that all ,,wholesome ,cakes are placed ,,inside the central ,square1 and all the ,,unwholesome ones ,,outside it1 that is1 in one or other of the four queer-shaped ,,outer compartments4 ,we see that1 just as1 in the smaller ,diagram1 the ,cakes in each compartment had ,,two ,attributes1 so1 here1 the ,cakes in each compartment have ,,three ,attributes3 and1 just as the letters1 representing the ,,two ,attributes1 were written on the ,,edges of the compartment1 so1 here1 they are written at the ,,corners4 7,observe that m' is supposed to be written at each of the four outer corners47 ,so that we can tell in a moment1 by looking at a compartment1 what three ,attributes belong to the ,things in it4 ,for instance1 take ,no4 #ab4 ,here we find x1 y'1 m1 at the corners3 so we know that the ,cakes in it1 if there are any1 have the triple ,attribute1 'xy'm'1 that is1 new1 not-nice1 and wholesome4 ,again1 take ,no4 #af4 ,here we find1 at the corners1 x'1 y'1 m'3 so the ,cakes in it are not-new1 not-nice1 and unwholesome4 7,remarkably untempting ,cakes67 ,it would take far too long to go through all the ,propositions1 containing x and y1 x and m1 and y and m which can be represented on this diagram 7there are ninety-six altogether1 so ,i am sure you will excuse me67 and ,i must content myself with doing two or three1 as specimens4 ,you will do well to work out a lot more for yourself4 ,taking the upper half by itself1 so that our ,subject is new ,cakes1 how are we to represent no new ,cakes are wholesome8 ,this is1 writing letters for words1 no x are m4 ,now this tells us that none of the ,cakes1 belonging to the upper half of the cupboard1 are to be found ,,inside the central ,square3 that is1 the two compartments1 ,no4 #aa and ,no4 #ab1 are ,,empty4 ,and this1 of course1 is represented by ------------------- #j #j ------------------- ,and now how are we to represent the contradictory ,proposition ,,some x are m8 ,this is a difficulty ,i have already considered4 ,i think the best way is to place a red counter ,,on ,,the ,,division-,,line between ,no4 #aa and ,no4 #ab1 and to understand this to mean that ,,one of the two compartments is 'occupied1' but that we do not at present know ,,which4 ,this ,i shall represent thus3-- ------------------- -#a- ------------------- ,now let us express all x are m4 ,this consists1 we know1 of ,,two ,propositions1 ,some x are m1 and ,no x are m'4 ,let us express the negative part first4 ,this tells us that none of the ,cakes1 belonging to the upper half of the cupboard1 are to be found ,,outside the central ,square3 that is1 the two compartments1 ,no4 #i and ,no4 #aj1 are ,,empty4 ,this1 of course1 is represented by ------------------- #j #j ------------------- ,but we have yet to represent ,some x are m4 ,this tells us that there are ,,some ,cakes in the oblong consisting of ,no4 #aa and ,no4 #ab3 so we place our red counter1 as in the previous example1 on the division-line between ,no4 #aa and ,no4 #ab1 and the result is ------------------- #j #j -#a- ------------------- ,now let us try one or two interpretations4 ,what are we to make of this1 with regard to x and y8 ------------------- #j #a #j ------------------- ,this tells us1 with regard to the xy'-,square1 that it is wholly 'empty'1 since ,,both compartments are so marked4 ,with regard to the xy-,square1 it tells us that it is 'occupied'4 ,true1 it is only ,,one compartment of it that is so marked2 but that is quite enough1 whether the other be 'occupied' or 'empty'1 to settle the fact that there is ,,something in the ,square4 ,if1 then1 we transfer our marks to the smaller ,diagram1 so as to get rid of the m-subdivisions1 we have a right to mark it ----------- #a #j ----------- which means1 you know1 all x are y4 ,the result would have been exactly the same1 if the given oblong had been marked thus3-- ------------------- #a #j #j ------------------- ,once more3 how shall we interpret this1 with regard to x and y8 ------------------- #j #a ------------------- ,this tells us1 as to the xy-,square1 that ,,one of its compartments is 'empty'4 ,but this information is quite useless1 as there is no mark in the ,,other compartment4 ,if the other compartment happened to be 'empty' too1 the ,square would be 'empty'3 and1 if it happened to be 'occupied'1 the ,square would be 'occupied'4 ,so1 as we do not know ,,which is the case1 we can say nothing about ,,this ,square4 ,the other ,square1 the xy'-,square1 we know 7as in the previous example7 to be 'occupied'4 ,if1 then1 we transfer our marks to the smaller ,diagram1 we get merely this3-- ----------- #a ----------- which means1 you know1 some x are y'4 ,these principles may be applied to all the other oblongs4 ,for instance1 to represent all y' are m' we should mark the ------- ,,right-,,hand ,,upright ,,oblong 7the one that has the attribute y'7 thus3-- --- #j ----#a- #j --- ------- and1 if we were told to interpret the lower half of the cupboard1 marked as follows1 with regard to x and y1 ------------------- #j ---------- #a #j ------------------- we should transfer it to the smaller ,diagram thus1 ----------- #a #j ----------- and read it all x' are y4 ,two more remarks about ,propositions need to be made4 ,one is that1 in every ,proposition beginning with some or all1 the ,,actual ,,existence of the ',subject' is asserted4 ,if1 for instance1 ,i say all misers are selfish1 ,i mean that misers ,,actually ,,exist4 ,if ,i wished to avoid making this assertion1 and merely to state the ,,law that miserliness necessarily involves selfishness1 ,i should say no misers are unselfish which does not assert that any misers exist at all1 but merely that1 if any ,,did exist1 they ,,would be selfish4 ,the other is that1 when a ,proposition begins with some or no1 and contains more that two ,attributes1 these ,attributes may be re-arranged1 and shifted from one ,term to the other1 ad libitum4 ,for example1 some abc are def may be re-arranged as some bf are acde1 each being equivalent to some ,things are abcdef4 ,again ,no wise old men are rash and reckless gamblers may be re-arranged as ,no rash old gamblers are wise and reckless1 each being equivalent to ,no men are wise old rash reckless gamblers4 #b4 ,syllogisms ,now suppose we divide our ,universe of ,things in three ways1 with regard to three different ,attributes4 ,out of these three ,attributes1 we may make up three different couples 7for instance1 if they were a1 b1 c1 we might make up the three couples ab1 ac1 bc74 ,also suppose we have two ,propositions given us1 containing two of these three couples1 and that from them we can prove a third ,proposition containing the third couple4 7,for example1 if we divide our ,universe for m1 x1 and y2 and if we have the two ,propositions given us1 no m are x' and all m' are y1 containing the two couples mx and my1 it might be possible to prove from them a third ,proposition1 containing x and y47 ,in such a case we call the given ,propositions ',,the ,,premisses'1 the third one ',,the ,,conclusion' and the whole set ',a ,,syllogism'4 ,evidently1 ,,one of the ,attributes must occur in both ,premisses2 or else one must occur in ,,one ,premiss1 and its ,,contradictory in the other4 ,in the first case 7when1 for example1 the ,premisses are some m are x and no m are y'7 the ,term1 which occurs twice1 is called ',,the ,,middle ,,term'1 because it serves as a sort of link between the other two ,terms4 ,in the second case 7when1 for example1 the ,premisses are no m are x' and all m' are y7 the two ,terms1 which contain these contradictory ,attributes1 may be called ',,the ,,middle ,,terms'4 ,thus1 in the first case1 the class of m-,things is the ,middle ,term2 and1 in the second case1 the two classes of m-,things and m'-,things are the ,middle ,terms4 ,the ,attribute1 which occurs in the ,middle ,term or ,terms1 disappears in the ,conclusion1 and is said to be eliminated1 which literally means turned out of doors4 ,now let us try to draw a ,conclusion from the two ,premisses-- ,some new ,cakes are unwholesome2 ,no nice ,cakes are unwholesome4 ,in order to express them with counters1 we need to divide ,cakes in ,,three different ways1 with regard to newness1 to niceness1 and to wholesomeness4 ,for this we must use the larger ,diagram1 making x mean new1 y nice1 and m wholesome4 7,everything ,,inside the central ,square is supposed to have the attribute m1 and everything ,,outside it the attribute m'1 i4e4 not-m47 ,you had better adopt the rule to make m mean the ,attribute which occurs in the ,,middle ,term or ,terms4 7,i have chosen m as the symbol1 because 'middle' begins with 'm'47 ,now1 in representing the two ,premisses1 ,i prefer to begin with the ,,negative one 7the one beginning with no71 because ,,grey counters can always be placed with ,,certainty1 and will then help to fix the position of the red counters1 which are sometimes a little uncertain where they will be most welcome4 ,let us express1 the no nice ,cakes are unwholesome 7,cakes71 i4e4 no y-,cakes are m'-7,cakes74 ,this tells us that none of the ,cakes belonging to the y-half of the cupboard are in its m'-compartments 7i4e4 the ones outside the central ,square74 ,hence the two compartments1 ,no4 #i and ,no4 #ae1 are both ',,empty'2 and we must place a grey counter in ,,each of them1 thus3-- ----------- #j ---- --------- ---- #j ----------- ,we have now to express the other ,premiss1 namely1 some new ,cakes are unwholesome 7,cakes71 i4e4 some x-,cakes are m'-7,cakes74 ,this tells us that some of the ,cakes in the x-half of the cupboard are in its m'-compartments4 ,hence ,,one of the two compartments1 ,no4 #i and ,no4 #aj1 is 'occupied'3 and1 as we are not told in ,,which of these two compartments to place the red counter1 the usual rule would be to lay it on the division-line between them3 but1 in this case1 the other ,premiss has settled the matter for us1 by declaring ,no4 #i to be ,,empty4 ,hence the red counter has no choice1 and ,,must go into ,no4 #aj1 thus3-- ----------- #j #a ---- --------- ---- #j ----------- ,and now what counters will this information enable us to place in the ,,smaller ,diagram1 so as to get some ,proposition involving x and y only1 leaving out m8 ,let us take its four compartments1 one by one4 ,first1 ,no4 #e4 ,all we know about ,,this is that its ,,outer portion is empty3 but we know nothing about its inner portion4 ,thus the ,square ,,may be empty1 or it ,,may have something in it4 ,who can tell8 ,so we dare not place ,,any counter in this ,square4 ,secondly1 what of ,no4 #f8 ,here we are a little better off4 ,we know that there is ,,something in it1 for there is a red counter in its outer portion4 ,it is true we do not know whether its inner portion is empty or occupied3 but what does ,,that matter8 ,one solitary ,cake1 in one corner of the ,square1 is quite sufficient excuse for saying ,,this ,,square ,,is ,,occupied1 and for marking it with a red counter4 ,as to ,no4 #g1 we are in the same condition as with ,no4 #e--we find it ,,partly 'empty'1 but we do not know whether the other part is empty or occupied3 so we dare not mark this ,square4 ,and as to ,no4 #h1 we have simply no information at all4 ,the result is ------- #a ------ ------- ,our ',conclusion'1 then1 must be got out of the rather meager piece of information that there is a red counter in the xy'-,square4 ,hence our ,conclusion is some x are y' 1 i4e4 some new ,cakes are not-nice 7,cakes73 or1 if you prefer to take y' as your ,subject1 some not-nice ,cakes are new 7,cakes72 but the other looks neatest4 ,we will now write out the whole ,syllogism1 putting the symbol there#d99 for therefore1 and omitting ,cakes1 for the sake of brevity1 at the end of each ,proposition4 99,,note from ,brett3 ,the use of there#d is a rather arbitrary selection4 ,there is no font available in general practice which renders the therefore symbol correction 7three dots in a triangular formation74 ,this can be done1 however1 in ,,html1 so if this document is read in a browser1 then the symbol will be properly recognized4 ,this is a poor man's excuse4 ,some new ,cakes are unwholesome2 ,no nice ,cakes are unwholesome there#d ,some new ,cakes are not-nice4 ,and you have now worked out1 successfully1 your first ',,syllogism'4 ,permit me to congratulate you1 and to express the hope that it is but the beginning of a long and glorious series of similar victories6 ,we will work out one other ,syllogism--a rather harder one than the last--and then1 ,i think1 you may be safely left to play the ,game by yourself1 or 7better7 with any friend whom you can find1 that is able and willing to take a share in the sport4 ,let us see what we can make of the two ,premisses-- ,all ,dragons are uncanny2 ,all ,scotchmen are canny4 ,remember1 ,i don't guarantee the ,premisses to be ,,facts4 ,in the first place1 ,i never even saw a ,dragon3 and1 in the second place1 it isn't of the slightest consequence to us1 as ,,logicians1 whether our ,premisses are true or false3 all ,,we have to do is to make out whether they ,,lead ,,logically ,,to ,,the ,,conclusion1 so that1 if ,,they were true1 ,,it would be true also4 ,you see1 we must give up the ,cakes now1 or our cupboard will be of no use to us4 ,we must take1 as our ',universe'1 some class of things which will include ,dragons and ,scotchmen3 shall we say ',animals'8 ,and1 as canny is evidently the ,attribute belonging to the ',middle ,terms'1 we will let m stand for canny1 x for ,dragons1 and y for ,scotchmen4 ,so that our two ,premisses are1 in full1 ,all ,dragon-,animals are uncanny 7,animals72 ,all ,scotchman-,animals are canny 7,animals74 ,and these may be expressed1 using letters for words1 thus3-- ,all x are m'2 ,all y are m4 ,the first ,premiss consists1 as you already know1 of two parts3-- ,some x are m'1 and ,no x are m4 ,and the second also consists of two parts3-- ,some y are m1 and ,no y are m'4 ,let us take the negative portions first4 ,we have1 then1 to mark1 on the larger ,diagram1 first1 no x are m1 and secondly1 no y are m'4 ,i think you will see1 without further explanation1 that the two results1 separately1 are ----------- ----------- #j ---- ---- #j #j -------- -------- ---- ---- #j ----------- ----------- and that these two1 when combined1 give us ----------- #j ---- #j #j -------- ---- #j ----------- ,we have now to mark the two positive portions1 some x are m' and some y are m4 ,the only two compartments1 available for ,things which are xm'1 are ,no4 #i and ,no4 #aj4 ,of these1 ,no4 #i is already marked as 'empty'2 so our red counter must go into ,no4 #aj4 ,similarly1 the only two1 available for ym1 are ,no4 #aa and ,no4 #ac4 ,of these1 ,no4 #aa is already marked as 'empty'2 so our red counter ,,must go into ,no4 #ac4 ,the final result is ----------- #j #a ---- #j #j -------- #a ---- #j ----------- ,and now how much of this information can usefully be transferred to the smaller ,diagram8 ,let us take its four compartments1 one by one4 ,as to ,no4 #e8 ,this1 we see1 is wholly 'empty'4 7,so mark it with a grey counter47 ,as to ,no4 #f8 ,this1 we see1 is 'occupied'4 7,so mark it with a red counter47 ,as to ,no4 #g8 ,ditto1 ditto4 ,as to ,no4 #h8 ,no information4 ,the smaller ,diagram is now pretty liberally marked3-- ------- #j #a ------ #a ------- ,and now what ,conclusion can we read off from this8 ,well1 it is impossible to pack such abundant information into ,,one ,proposition3 we shall have to indulge in ,,two1 this time4 ,first1 by taking x as ,subject1 we get all x are y'1 that is1 ,all ,dragons are not-,scotchmen3 secondly1 by taking y as ,subject1 we get all y are x'1 that is1 ,all ,scotchmen are not-,dragons4 ,let us now write out1 all together1 our two ,premisses and our brace of ,conclusions4 ,all ,dragons are uncanny2 ,all ,scotchmen are canny4 there#d ,all ,dragons are not-,scotchmen2 ,all ,scotchmen are not-,dragons4 ,let me mention1 in conclusion1 that you may perhaps meet with logical treatises in which it is not assumed that any ,thing ,,exists at all1 by some x are y is understood to mean the ,attributes x1 y are ,,compatible1 so that a ,thing can have both at once1 and no x are y to mean the ,attributes x1 y are ,,incompatible1 so that nothing can have both at once4 ,in such treatises1 ,propositions have quite different meanings from what they have in our ',game of ,logic'1 and it will be well to understand exactly what the difference is4 ,first take some x are y4 ,here ,,we understand are to mean are1 as an actual ,,fact--which of course implies that some x-,things ,,exist4 ,but ,,they 7the writers of these other treatises7 only understand are to mean ,,can be1 which does not at all imply that any ,,exist4 ,so they mean ,,less than we do3 our meaning includes theirs 7for of course some x ,,are y includes some x ,,can ,,be y71 but theirs does ,,not include ours4 ,for example1 some ,welsh hippopotami are heavy would be ,,true1 according to these writers 7since the ,attributes ,welsh and heavy are quite ,,compatible in a hippopotamus71 but it would be ,,false in our ,game 7since there are no ,welsh hippopotami to ,,be heavy74 ,secondly1 take no x are y4 ,here ,,we only understand are to mean are1 as an actual ,,fact--which does not at all imply that no x ,,can be y4 ,but ,,they understand the ,proposition to mean1 not only that none ,,are y1 but that none ,,can ,,possibly be y4 ,so they mean more than we do3 their meaning includes ours 7for of course no x ,,can be y includes no x ,,are y71 but ours does ,,not include theirs4 ,for example1 no ,policemen are eight feet high would be ,,true in our ,game 7since1 as an actual fact1 no such splendid specimens are ever found71 but it would be ,,false1 according to these writers 7since the ,attributes belonging to the ,police ,force and eight feet high are quite ,,compatible3 there is nothing to ,,prevent a ,policeman from growing to that height1 if sufficiently rubbed with ,rowland's ,macassar ,oil--which said to make ,,hair grow1 when rubbed on hair1 and so of course will make a ,,policeman grow1 when rubbed on a ,policeman74 ,thirdly1 take all x are y1 which consists of the two partial ,propositions some x are y and no x are y'4 ,here1 of course1 the treatises mean ,,less than we do in the ,,first part1 and more than we do in the ,,second4 ,but the two operations don't balance each other--any more than you can console a man1 for having knocked down one of his chimneys1 by giving him an extra door-step4 ,if you meet with ,syllogisms of this kind1 you may work them1 quite easily1 by the system ,i have given you3 you have only to make 'are' mean 'are ,,capable of being'1 and all will go smoothly4 ,for some x are y will become some x are capable of being y1 that is1 the ,attributes x1 y are ,,compatible4 ,and no x are y will become no x are capable of being y1 that is1 the ,attributes x1 y are ,,incompatible4 ,and1 of course1 all x are y will become some x are capable of being y1 and none are capable of being y'1 that is1 the ,attributes x1 y are ,,compatible1 and the ,attributes x1 y' are ,,incompatible4 ,in using the ,diagrams for this system1 you must understand a red counter to mean there may ,,possibly be something in this compartment1 and a grey one to mean there cannot ,,possibly be anything in this compartment4 #c4 ,fallacies4 ,and so you think1 do you1 that the chief use of ,logic1 in real life1 is to deduce ,conclusions from workable ,premisses1 and to satisfy yourself that the ,conclusions1 deduced by other people1 are correct8 ,i only wish it were6 ,society would be much less liable to panics and other delusions1 and ,,political life1 especially1 would be a totally different thing1 if even a majority of the arguments1 that scattered broadcast over the world1 were correct6 ,but it is all the other way1 ,i fear4 ,for ,,one workable ,pair of ,premisses 7,i mean a ,pair that lead to a logical ,conclusion7 that you meet with in reading your newspaper or magazine1 you will probably find ,,five that lead to no ,conclusion at all3 and1 even when the ,premisses ,,are workable1 for ,,one instance1 where the writer draws a correct ,conclusion1 there are probably ,,ten where he draws an incorrect one4 ,in the first case1 you may say the ,,premisses are fallacious3 in the second1 the ,,conclusion is fallacious4 ,the chief use you will find1 in such ,logical skill as this ,game may teach you1 will be in detecting ',,fallacies' of these two kinds4 ,the first kind of ,fallacy--',fallacious ,premisses'--you will detect when1 after marking them on the larger ,diagram1 you try to transfer the marks to the smaller4 ,you will take its four compartments1 one by one1 and ask1 for each in turn1 ,what mark can ,i place ,,here82 and in ,,every one the answer will be ,no information61 showing that there is ,,no ,,conclusion ,,at ,,all4 ,for instance1 ,all soldiers are brave2 ,some ,englishmen are brave4 there#d ,some ,englishmen are soldiers4 looks uncommonly ,,like a ,syllogism1 and might easily take in a less experienced ,logician4 ,but ,,you are not to be caught by such a trick6 ,you would simply set out the ,premisses1 and would then calmly remark ,fallacious ,,premisses63 you wouldn't condescend to ask what ,,conclusion the writer professed to draw--knowing that1 ,,whatever it is1 it ,,must be wrong4 ,you would be just as safe as that wise mother was1 who said ,mary1 just go up to the nursery1 and see what ,baby's doing1 ,,and ,,tell ,,him ,,not ,,to ,,do ,,it6 ,the other kind of ,fallacy--',fallacious ,conclusion'--you will not detect till you have marked ,,both ,diagrams1 and have read off the correct ,conclusion1 and have compared it with the ,conclusion which the writer has drawn4 ,but mind1 you mustn't say ,,fallacious ,conclusion1 simply because it is not ,,identical with the correct one3 it may be a ,,part of the correct ,conclusion1 and so be quite correct1 ,,as ,,far ,,as ,,it ,,goes4 ,in this case you would merely remark1 with a pitying smile1 ,,defective ,conclusion6 ,suppose1 of example1 you were to meet with this ,syllogism3-- ,all unselfish people are generous2 ,no misers are generous4 there#d ,no misers are unselfish4 the ,premisses of which might be thus expressed in letters3-- ,all x' are m2 ,no y are m4 ,here the correct ,conclusion would be ,all x' are y' 7that is1 ,all unselfish people are not misers71 while the ,conclusion1 drawn by the writer1 is ,no y are x'1 7which is the same as ,no x' are y1 and so is ,,part of ,all x' are y'47 ,here you would simply say ,,defective ,conclusion6 ,the same thing would happen1 if you were in a confectioner's shop1 and if a little boy were to come in1 put down twopence1 and march off triumphantly with a single penny-bun4 ,you would shake your head mournfully1 and would remark ,defective ,conclusion6 ,poor little chap6 ,and perhaps you would ask the young lady behind the counter whether she would let ,,you eat the bun1 which the little boy had paid for and left behind him3 and perhaps ,,she would reply ,sha'n't6 ,but if1 in the above example1 the writer had drawn the ,conclusion ,all misers are selfish 7that is1 ,all y are x71 this would be going ,,beyond his legitimate rights 7since it would assert the ,,existence of y1 which is not contained in the ,premisses71 and you would very properly say ,fallacious ,conclusion6 ,now1 when you read other treatises on ,logic1 you will meet with various kinds of 7so-called7 ',fallacies' which are by no means ,,always so4 ,for example1 if you were to put before one of these ,logicians the ,pair of ,premisses ,no honest men cheat2 ,no dishonest men are trustworthy4 and were to ask him what ,conclusion followed1 he would probably say ,none at all6 ,your ,premisses offend against ,,two distinct ,rules1 and are as fallacious as they can well be6 ,then suppose you were bold enough to say ,the ,conclusion is ',no men who cheat are trustworthy'1 ,i fear your ,logical friend would turn away hastily--perhaps angry1 perhaps only scornful3 in any case1 the result would be unpleasant4 ,i ,,advise ,,you ,,not ,,to ,,try ,,the ,,experiment6 ,but why is this8 you will say4 ,do you mean to tell us that all these ,logicians are wrong8 ,far from it1 dear ,reader6 ,from ,,their point of view1 they are perfectly right4 ,but they do not include1 in their system1 anything like ,,all the possible forms of ,syllogisms4 ,they have a sort of nervous dread of ,attributes beginning with a negative particle4 ,for example1 such ,propositions as ,all not-x are y1 ,no x are not-y1 are quite outside their system4 ,and thus1 having 7from sheer nervousness7 excluded a quantity of very useful forms1 they have made rules which1 though quite applicable to the few forms which they allow of1 are no use at all when you consider all possible forms4 ,let us not quarrel with them1 dear ,reader6 ,there is room enough in the world for both of us4 ,let us quietly take our broader system3 and1 if they choose to shut their eyes to all these useful forms1 and to say ,they are not ,syllogisms at all6 we can but stand aside1 and let them ,rush upon their ,fate6 ,there is scarcely anything of yours1 upon which it is so dangerous to ,rush1 as your ,fate4 ,you may ,rush upon your ,potato-beds1 or your ,strawberry-beds1 without doing much harm3 you may even ,rush upon your ,balcony 7unless it is a new house1 built by contract1 and with no clerk of the works7 and may survive the foolhardy enterprise3 but if you once ,rush upon your ,,fate--why1 you must take the consequences6 ,,chapter ,,ii4 ,,cross ,,questions4 ,the ,man in the ,wilderness asked of me ',how many strawberries grow in the sea8' #a4 ,elementary4 #a4 ,what is an ',attribute'8 ,give examples4 #b4 ,when is it good sense to put is or are between two names8 ,give examples4 #c4 ,when is it ,,not good sense8 ,give examples4 #d4 ,when it is ,,not good sense1 what is the simplest agreement to make1 in order to make good sense8 #e4 ,explain ',proposition'1 ',term'1 ',subject'1 and ',predicate'4 ,give examples4 #f4 ,what are ',particular' and ',universal' ,propositions8 ,give examples4 #g4 ,give a rule for knowing1 when we look at the smaller ,diagram1 what ,attributes belong to the things in each compartment4 #h4 ,what does some mean in ,logic8 ,see pp4 #ee1 #f #i4 ,in what sense do we use the word ',universe' in this ,game8 #aj4 ,what is a ',double' ,proposition8 ,give examples4 #aa4 ,when is a class of ,things said to be 'exhaustively' divided8 ,give examples4 #ab4 ,explain the phrase sitting on the fence4 #ac4 ,what two partial ,propositions make up1 when taken together1 all x are y8 #ad4 ,what are ',individual' ,propositions8 ,give examples4 #ae4 ,what kinds of ,propositions imply1 in this ,game1 the ,,existence of their ,subjects8 #af4 ,when a ,proposition contains more than two ,attributes1 these ,attributes may in some cases be re-arranged1 and shifted from one ,term to the other4 ,in what cases may this be done8 ,give examples4 ,break up each of the following into two partial ,propositions3 #ag4 ,all tigers are fierce4 #ah4 ,all hard-boiled eggs are unwholesome4 #ai4 ,i am happy4 #bj4 ,john is not at home4 ,see pp4 #ef1 #g #ba4 ,give a rule for knowing1 when we look at the larger ,diagram1 what ,attributes belong to the ,things contained in each compartment4 #bb4 ,explain ',premisses'1 ',conclusion'1 and ',syllogism'4 ,give examples4 #bc4 ,explain the phrases ',middle ,term' and ',middle ,terms'4 #bd4 ,in marking a pair of ,premisses on the larger ,diagram1 why is it best to mark ,,negative ,propositions before ,,affirmative ones8 #be4 ,why is it of no consequence to us1 as ,logicians1 whether the ,premisses are true or false8 #bf4 ,how can we work ,syllogisms in which we are told that some x are y is to be understood to mean the ,attribute x1 y are ,,compatible1 and no x are y to mean the ,attributes x1 y are ,,incompatible8 #bg4 ,what are the two kinds of ',fallacies'8 #bh4 ,how may we detect ',fallacious ,premisses'8 #bi4 ,how may we detect a ',fallacious ,conclusion'8 #cj4 ,sometimes the ,conclusion1 offered to us1 is not identical with the correct ,conclusion1 and yet cannot be fairly called ',fallacious'4 ,when does this happen8 ,and what name may we give to such a ,conclusion8 ,see pp4 #eg-ei #b4 ,half of ,smaller ,diagram4 ,propositions to be represented4 ----------- x --y-----y'- #a4 ,some x are not-y4 #b4 ,all x are not-y4 #c4 ,some x are y1 and some are not-y4 #d4 ,no x exist4 #e4 ,some x exist4 #f4 ,no x are not-y4 #g4 ,some x are not-y1 and some x exist4 ,taking xjudges2 yjust2 #h4 ,no judges are just4 #i4 ,some judges are unjust4 #aj4 ,all judges are just4 ,taking xplums2 ywholesome2 #aa4 ,some plums are wholesome4 #ab4 ,there are no wholesome plums4 #ac4 ,plums are some of them wholesome1 and some not4 #ad4 ,all plums are unwholesome4 ,see pp4 #ei1 #fj ----- x --y-- x' ----- ,taking ydiligent students2 xsuccessful2 #ae4 ,no diligent students are unsuccessful4 #af4 ,all diligent students are successful4 #ag4 ,no students are diligent4 #ah4 ,there are some diligent1 but unsuccessful1 students4 #ai4 ,some students are diligent4 ,see pp4 #fj1 #a #c4 ,half of ,smaller ,diagram4 ,symbols to be interpreted4 ----------- x --y-----y'- ------- ------- #a4 #j #b4 #j #j ------- ------- ------- ------- #c4 - #d4 #j #a ------- ------- ,taking xgood riddles2 yhard2 ------- ------- #e4 #a #f4 #a #j ------- ------- ------- ------- #g4 #j #j #h4 #j ------- ------- ,see pp4 #fa1 #b ,taking xlobster2 yselfish2 ------- ------- #i4 #a #aj4 #j ------- ------- ------- ------- #aa4 #j #a #ab4 #a #a ------- ------- ----- x --y'- x' ----- ,taking yhealthy people2 xhappy2 --- --- --- --- #j #a #j #ac4 --- #ad4 -#a- #ae4 --- #af4 --- #a #a --- --- --- --- ,see p4 #fb #d4 ,smaller ,diagram4 ,propositions to be represented4 ----------- x --y----y'- x' ----------- #a4 ,all y are x4 #b4 ,some y are not-x4 #c4 ,no not-x are not-y4 #d4 ,some x are not-y4 #e4 ,some not-y are x4 #f4 ,no not-x are y4 #g4 ,some not-x are not-y4 #h4 ,all not-x are not-y4 #i4 ,some not-y exist4 #aj4 ,no not-x exist4 #aa4 ,some y are x1 and some are not-x4 #ab4 ,all x are y1 and all not-y are not-x4 ,see pp4 #fb1 #c ,taking nations as ,universe2 xcivilised2 ywarlike2 #ac4 ,no uncivilised nation is warlike4 #ad4 ,all unwarlike nations are uncivilised4 #ae4 ,some nations are unwarlike4 #af4 ,all warlike nations are civilised1 and all civilised nations are warlike4 #ag4 ,no nation is uncivilised4 ,taking crocodiles as ,universe2 xhungry2 and yamiable2 #ah4 ,all hungry crocodiles are unamiable4 #ai4 ,no crocodiles are amiable when hungry4 #bj4 ,some crocodiles1 when not hungry1 are amiable2 but some are not4 #ba4 ,no crocodiles are amiable1 and some are hungry4 #bb4 ,all crocodiles1 when not hungry1 are amiable2 and all unamiable crocodiles are hungry4 #bc4 ,some hungry crocodiles are amiable1 and some that are not hungry are unamiable4 ,see pp4 #fc1 #d #e4 ,smaller ,diagram4 ,symbols to be interpreted4 ----------- x --y----y'- x' ----------- ------- ------- #a4 ------ #b4 ------ #a #j ------- ------- ------- ------- #a #c4 ------ #d4 ------ #j #j #j ------- ------- ,taking houses as ,universe2 xbuilt of brick2 and ytwo-storied2 interpret ------- ------- #j #e4 ------ #f4 ------ #j - ------- ------ ------- ------- #j #g4 ------ #h4 ------ #j #a ------- ------- ,see p4 #fe ,taking boys as ,universe2 xfat2 and yactive2 interpret ------- ------- #a #a #j #i4 ------ #aj4 ------ #a ------- ------- ------- ------- #j #a #a #aa4 ------ #ab4 ------ #j #j #a ------- ------- ,taking cats as ,universe2 xgreen-eyed2 and ygood-tempered2 interpret ------- ------- #j #j #a #ac4 ------ #ad4 ------ #j #a ------- ------- ------- ------- #a #j #a #ae4 ------ #af4 ------ #j #a #j ------- ------- ,see pp4 #fe1 #f #f4 ,larger ,diagram4 ,propositions to be represented4 ----------- --x-- --y--m--y'- --x'- ----------- #a4 ,no x are m4 #b4 ,some y are m'4 #c4 ,all m are x'4 #d4 ,no m' are y'4 #e4 ,no m are x2 ,all y are m4 #f4 ,some x are m2 ,no y are m4 #g4 ,all m are x'2 ,no m are y4 #h4 ,no x' are m2 ,no y' are m'4 ,see pp4 #fg1h ,taking rabbits as ,universe2 mgreedy2 xold2 and yblack2 represent #i4 ,no old rabbits are greedy4 #aj4 ,some not-greedy rabbits are black4 #aa4 ,all white rabbits are free from greediness4 #ab4 ,all greedy rabbits are young4 #ac4 ,no old rabbits are greedy2 ,all black rabbits are greedy4 #ad4 ,all rabbits1 that are not greedy1 are black2 ,no old rabbits are free from greediness4 ,taking birds as ,universe2 mthat sing loud2 xwell-fed2 and yhappy2 represent #ae4 ,all well-fed birds sing loud2 ,no birds1 that sing loud1 are unhappy4 #af4 ,all birds1 that do not sing loud1 are unhappy2 ,no well-fed birds fail to sing loud4 ,taking persons as ,universe2 min the house2 x,john2 and yhaving a tooth-ache2 represent #ag4 ,john is in the house2 ,everybody in the house is suffering from tooth-ache4 #ah4 ,there is no one in the house but ,john2 ,nobody1 out of the house1 has a tooth-ache4 ,see pp4 #fh-gj ,taking persons as ,universe2 m,i2 xthat has taken a walk2 ythat feels better2 represent #ai4 ,i have been out for a walk2 ,i feel much better4 ,choosing your own ',universe' c41 represent #bj4 ,i sent him to bring me a kitten2 ,he brought me a kettle by mistake4 ,see pp4 #gj1 #a #g4 ,both ,diagrams to be employed4 ----------- ----------- --x-- x --y--m--y'- --y----y'- x' --x'- ----------- ----------- ,n4,b4 ,in each ,question1 a small ,diagram should be drawn1 for x and y only1 and marked in accordance with the given large ,diagram3 and then as many ,propositions as possible1 for x and y1 should be read off from this small ,diagram4 ----------- ----------- #j ---- ---- #j #j #j #a #a4 -------- #b4 -------- #a #j ---- ---- #j ----------- ----------- ,see p4 #gb ----------- ----------- #j ---- ---- #j #j #c4 -------- #d4 -------- #a #j #j ---- ---- #j ----------- ----------- ,mark1 in a large ,diagram1 the following pairs of ,propositions from the preceding ,section3 then mark a small ,diagram in accordance with it1 c4 #e4 ,no4 #ac4 see p4 #di #i4 ,no4 #ag4 #f4 ,no4 #ad4 #aj4 ,no4 #ah4 #g4 ,no4 #ae4 #aa4 ,no4 #ai4 see p4 #ej #h4 ,no4 #af4 #ab4 ,no4 #bj4 ,mark1 on a large ,diagram1 the following ,pairs of ,propositions3 then mark a small ,diagram1 c4 ,these are1 in fact1 ,pairs of ,,premisses for ,syllogisms3 and the results1 read off from the small ,diagram1 are the ,,conclusions4 #ac4 ,no exciting books suit feverish patients2 ,unexciting books make one drowsy4 #ad4 ,some1 who deserve the fair1 get their deserts2 ,none but the brave deserve the fair4 #ae4 ,no children are patient2 ,no impatient person can sit still4 ,see pp4 #gb-e #af4 ,all pigs are fat2 ,no skeletons are fat4 #ag4 ,no monkeys are soldiers2 ,all monkeys are mischievous4 #ah4 ,none of my cousins are just2 ,no judges are unjust4 #ai4 ,some days are rainy2 ,rainy days are tiresome4 #bj4 ,all medicine is nasty2 ,senna is a medicine4 #ba4 ,some ,jews are rich2 ,all ,patagonians are ,gentiles4 #bb4 ,all teetotalers like sugar2 ,no nightingale drinks wine4 #bc4 ,no muffins are wholesome2 ,all buns are unwholesome4 #bd4 ,no fat creatures run well2 ,some greyhounds run well4 #be4 ,all soldiers march2 ,some youths are not soldiers4 #bf4 ,sugar is sweet2 ,salt is not sweet4 #bg4 ,some eggs are hard-boiled2 ,no eggs are uncrackable4 #bh4 ,there are no ,jews in the house2 ,there are no ,gentiles in the garden4 ,see pp4 #ge-hb #bi4 ,all battles are noisy2 ,what makes no noise may escape notice4 #cj4 ,no ,jews are mad2 ,all ,rabbis are ,jews4 #ca4 ,there are no fish that cannot swim2 ,some skates are fish4 #cb4 ,all passionate people are unreasonable2 ,some orators are passionate4 ,see pp4 #hb-hd ,,chapter ,,iii4 ,,crooked ,,answers4 ,i answered him1 as ,i thought good1 ',as many as red-herrings grow in the wood'4 #a4 ,elementary4 #a4 ,whatever can be attributed to1 that is said to belong to1 a ,thing1 is called an ',attribute'4 ,for example1 baked1 which can 7frequently7 be attributed to ,buns1 and beautiful1 which can 7seldom7 be attributed to ,babies4 #b4 ,when they are the ,names of two ,things 7for example1 these ,pigs are fat ,animals71 or of two ,attributes 7for example1 pink is light red74 #c4 ,when one is the ,name of a ,thing1 and the other the ,name of an ,attribute 7for example1 these ,pigs are pink71 since a ,thing cannot actually ,,be an ,attribute4 #d4 ,that the ,substantive shall be supposed to be repeated at the end of the sentence 7for example1 these ,pigs are pink 7,pigs774 #e4 ,a ',proposition' is a sentence stating that some1 or none1 or all1 of the ,things belonging to a certain class1 called the ',subject'1 are also ,things belonging to a certain other class1 called the ',predicate'4 ,for example1 some new ,cakes are not nice1 that is 7written in full7 some new ,cakes are not nice ,cakes2 where the class new ,cakes is the ,subject1 and the class not-nice ,cakes is the ,predicate4 #f4 ,a ,proposition1 stating that ,,some of the ,things belonging to its ,subject are so-and-so1 is called ',particular'4 ,for example1 some new ,cakes are nice1 some new ,cakes are not nice4 ,a ,proposition1 stating that ,,none of the ,things belonging to its ,subject1 or that ,,all of them1 are so-and-so1 is called ',universal'4 ,for example1 no new ,cakes are nice1 all new ,cakes are not nice4 #g4 ,the ,things in each compartment possess ,,two ,attributes1 whose symbols will be found written on two of the ,,edges of that compartment4 #h4 ,one or more4 #i4 ,as a name of the class of ,things to which the whole ,diagram is assigned4 #aj4 ,a ,proposition containing two statements4 ,for example1 some new ,cakes are nice and some are not-nice4 #aa4 ,when the whole class1 thus divided1 is exhausted among the sets into which it is divided1 there being no member of it which does not belong to some one of them4 ,for example1 the class new ,cakes is exhaustively divided into nice and not-nice since ,,every new ,cake must be one or the other4 #ab4 ,when a man cannot make up his mind which of two parties he will join1 he is said to be sitting on the fence--not being able to decide on which side he will jump down4 #ac4 ,some x are y and no x are y'4 #ad4 ,a ,proposition1 whose ,subject is a single ,thing1 is called ',individual'4 ,for example1 ,i am happy1 ,john is not at home4 ,these are ,universal ,propositions1 being the same as all the ,i's that exist are happy1 ,,all the ,johns1 that ,i am now considering1 are not at home4 #ae4 ,propositions beginning with some or all4 #af4 ,when they begin with some or no4 ,for example1 some abc are def may be re-arranged as some bf are acde1 each being equivalent to some abcdef exist4 #ag4 ,some tigers are fierce1 ,no tigers are not-fierce4 #ah4 ,some hard-boiled eggs are unwholesome1 ,no hard-boiled eggs are wholesome4 #ai4 ,some ,i's are happy1 ,no ,i's are unhappy4 #bj4 ,some ,johns are not at home1 ,no ,johns are at home4 #ba4 ,the ,things1 in each compartment of the larger ,diagram1 possess ,,three ,attributes1 whose symbols will be found written at three of the ,,corners of the compartment 7except in the case of m'1 which is not actually inserted in the ,diagram1 but is ,,supposed to stand at each of its four outer corners74 #bb4 ,if the ,universe of ,things be divided with regard to three different ,attributes2 and if two ,propositions be given1 containing two different couples of these ,attributes2 and if from these we can prove a third ,proposition1 containing the two ,attributes that have not yet occurred together2 the given ,propositions are called 'the ,premisses'1 the third one 'the ,conclusion'1 and the whole set 'a ,syllogism'4 ,for example1 the ,premisses might be no m are x' and all m' are y2 and it might be possible to prove from them a ,conclusion containing x and y4 #bc4 ,if an ,attribute occurs in both ,premisses1 the ,term containing it is called 'the ,middle ,term'4 ,for example1 if the ,premisses are some m are x and no m are y'1 the class of m-,things is 'the ,middle ,term4' ,if an ,attribute occurs in one ,premiss1 and its contradictory in the other1 the ,terms containing them may be called 'the ,middle ,terms'4 ,for example1 if the ,premisses are no m are x' and all m' are y1 the two classes of m-,things and m'-,things may be called 'the ,middle ,terms'4 #bd4 ,because they can be marked with ,,certainty3 whereas ,,affirmative ,propositions 7that is1 those that begin with some or all7 sometimes require us to place a red counter 'sitting on a fence'4 #be4 ,because the only question we are concerned with is whether the ,conclusion ,,follows ,,logically from the ,premisses1 so that1 if ,,they were true1 ,,it also would be true4 #bf4 ,by understanding a red counter to mean this compartment ,,can be occupied1 and a grey one to mean this compartment ,,cannot be occupied or this compartment ,,must be empty4 #bg4 ',fallacious ,premisses' and ',fallacious ,conclusion'4 #bh4 ,by finding1 when we try to transfer marks from the larger ,diagram to the smaller1 that there is 'no information' for any of its four compartments4 #bi4 ,by finding the correct ,conclusion1 and then observing that the ,conclusion1 offered to us1 is neither identical with it nor a part of it4 #cj4 ,when the offered ,conclusion is ,,part of the correct ,conclusion4 ,in this case1 we may call it a ',defective ,conclusion'4 #b4 ,half of ,smaller ,diagram4 ,propositions represented4 ------- ------- #a4 #a #b4 #j #a ------- ------- ------- ------- #c4 #a #a #d4 #j #j ------- ------- ------- ------- #e4 #a #f4 #j ------- ------- ------- #g4 #a #a ,it might be thought that the proper ------- ------- ,diagram would be #a #a 1 in order to express some ------- x exist3 but this is really contained in some x are y'4 ,to put a red counter on the division-line would only tell us ,,one ,,of ,,the compartments is occupied1 which we know already1 in knowing that ,,one is occupied4 ------- #h4 ,no x are y4 i4e4 #j ------- ------- #i4 ,some x are y'4 i4e4 #a ------- ------- #aj4 ,all x are y4 i4e4 #a #j ------- ------- #aa4 ,some x are y4 i4e4 #a ------- ------- #ab4 ,no x are y4 i4e4 #j ------- ------- #ac4 ,some x are y1 and some are y'4 i4e4 #a #a ------- ------- #ad4 ,all x are y'4 i4e4 #j #a ------- --- #ae4 ,no y are x'4 i4e4 --- #j --- --- #a #af4 ,all y are x4 i4e4 --- #j --- --- #j #ag4 ,no y exist4 i4e4 --- #j --- --- #ah4 ,some y are x'4 i4e4 --- #a --- --- #ae4 ,some y exist4 i4e4 -#a- --- #c4 ,half of ,smaller ,diagram4 ,symbols interpreted4 #a4 ,no x are y'4 #b4 ,no x exist4 #c4 ,some x exist4 #d4 ,all x are y'4 #e4 ,some x are y4 i4e4 ,some good riddles are hard4 #f4 ,all x are y4 i4e4 ,all good riddles are hard4 #g4 ,no x exist4 i4e4 ,no riddles are good4 #h4 ,no x are y4 i4e4 ,no good riddles are hard4 #i4 ,some x are y'4 i4e4 ,some lobsters are unselfish4 #aj4 ,no x are y4 i4e4 ,no lobsters are selfish4 #aa4 ,all x are y'4 i4e4 ,all lobsters are unselfish4 #ab4 ,some x are y1 and some are y'4 i4e4 ,some lobsters are selfish1 and some are unselfish4 #ac4 ,all y' are x'4 i4e4 ,all invalids are unhappy4 #ad4 ,some y' exist4 i4e4 ,some people are unhealthy4 #ae4 ,some y' are x1 and some are x'4 i4e4 ,some invalids are happy1 and some are unhappy4 #af4 ,no y' exist4 i4e4 ,nobody is unhealthy4 #d4 ,smaller ,diagram4 ,propositions represented4 ------- ------- #a #a4 ------ #b4 ------ #j #a ------- ------- ------- ------- #a #c4 ------ #d4 ------ #j ------- ------- ------- ------- #a #e4 ------ #f4 ------ #j ------- ------- ------- ------- #g4 ------ #h4 ------ #a #j #a ------- ------- ------- ------- #i4 ----#a- #aj4 ------ #j #j ------- ------- ------- ------- #a #a #j #aa4 ------ #ab4 ------ #a #a ------- ------- ------- #ac4 ,no x' are y4 i4e4 ------ #j ------- ------- #j #ad4 ,all y' are x'4 i4e4 ------ #a ------- ------- #ae4 ,some y' exist4 i4e4 ----#a- ------- ------- #a #j #af4 ,all y are x1 and all x are y4 i4e4 ------ #j ------- ------- #ag4 ,no x' exist4 i4e4 ------ #j #j ------- ------- #j #a #ah4 ,all x are y'4 i4e4 ------ ------- ------- #j #ai4 ,no x are y4 i4e4 ------ ------- ------- #bj4 ,some x' are y1 and some are y'4 i4e4 ------ #a #a ------- ------- #j #a #ba4 ,no y exist1 and some x exist4 i4e4 ------ #j ------- ------- #a #bb4 ,all x' are y1 and all y' are x4 i4e4 ------ #a #j ------- ------- #a #ag4 ,some x are y1 and some x' are y'4 i4e4 ------ #a ------- #e4 ,smaller ,diagram4 ,symbols interpreted4 #a4 ,some y are not-x1 or1 ,some not-x are y4 #b4 ,no not-x are not-y1 or1 ,no not-y are not-x4 #c4 ,no not-y are x4 #d4 ,no not-x exist4 i4e4 ,no ,things are not-x4 #e4 ,no y exist4 i4e4 ,no houses are two-storied4 #f4 ,some x' exist4 i4e4 ,some houses are not built of brick4 #g4 ,no x are y'4 ,or1 no y' are x4 i4e4 ,no houses1 built of brick1 are other than two-storied4 ,or1 no houses1 that are not two-storied1 are built of brick4 #h4 ,all x' are y'4 i4e4 ,all houses1 that are not built of brick1 are not two-storied4 #i4 ,some x are y1 and some are y'4 i4e4 ,some fat boys are active1 and some are not4 #aj4 ,all y' are x'4 i4e4 ,all lazy boys are thin4 #aa4 ,all x are y'1 and all y' are x4 i4e4 ,all fat boys are lazy1 and all lazy ones are fat4 #ab4 ,all y are x1 and all x' are y4 i4e4 ,all active boys are fat1 and all thin ones are lazy4 #ac4 ,no x exist1 and no y' exist4 i4e4 ,no cats have green eyes1 and none have bad tempers4 #ad4 ,some x are y'1 and some x' are y4 ,or some y are x'1 and some y' are x4 i4e4 ,some green-eyed cats are bad-tempered1 and some1 that have not green eyes1 are good-tempered4 ,or1 some good-tempered cats have not green eyes1 and some bad-tempered ones have green eyes4 #ae4 ,some x are y1 and no x' are y'4 ,or1 some y are x1 and no y' are x'4 i4e4 ,some green-eyed cats are good-tempered1 and none1 that are not green-eyed1 are bad-tempered4 ,or1 some good-tempered cats have green eyes1 and none1 that are bad-tempered1 have not green eyes4 #af4 ,all x are y'1 and all x' are y4 ,or1 all y are x'1 and all y' are x4 i4e4 ,all green-eyed cats are bad-tempered and all1 that have not green eyes1 are good-tempered4 ,or1 all good-tempered ones have eyes that are not green1 and all bad-tempered ones have green eyes4 #f4 ,larger ,diagram4 ,propositions represented4 --------------- --------------- ------ ------ #j #j #a4 ------------ #b4 -#a---------- ------ ------ --------------- --------------- --------------- --------------- #j ------ ------ #j #j #c4 ------------ #d4 ------------ - ------ ------ #j --------------- --------------- --------------- --------------- #j ------ ------ #j #j #j #a #e4 ------------ #f4 ------------ #a #j ------ ------ #j --------------- --------------- --------------- --------------- #j ------ ------ #j #j #g4 ------------ #h4 ------------ #j #a #j #j ------ ------ #j --------------- --------------- --------------- ------ #j #j #i4 ,no x are m4 i4e4 ------------ #j ------ --------------- --------------- ------ #aj4 ,some m' are y4 i4e4 -#a---------- ------ --------------- --------------- ------ #j #aa4 ,all y' are m'4 i4e4 ----------#a- #j ------ --------------- --------------- ------ #j #j #ab4 ,all m are x'4 i4e4 ------------ #a ------ --------------- --------------- #j ------ #j #j #ac4 ,no x are m2 i4e4 ------------ ,all y are m4 #a ------ #j --------------- --------------- #j #j ------ #ad4 ,all m' are y2 i4e4 ------------ ,no x are m'4 ------ #a #j --------------- --------------- #j #j ------ #a #j #ae4 ,all x are m2 i4e4 ------------ ,no m are y'4 #j ------ --------------- --------------- #j #j ------ #af4 ,all m' are y'2 i4e4 ------------ ,no x are m'4 ------ #j #a --------------- --------------- #j #j ------ #a #j #ag4 ,all x are m2 i4e4 ------------ ,all m are y4 #j ------ ,see remarks on ,no4 #g1 p4 #fj4 --------------- --------------- #j ------ #ah4 ,no x' are m2 i4e4 ------------ ,no m' are y4 #j #j ------ #j --------------- --------------- ------ #a #j #ai4 ,all m are x2 i4e4 ------------ ,all m are y4 #j #j ------ --------------- #bj4 ,we had better take persons as ,universe4 ,we may choose myself as ',middle ,term'1 in which case the ,premisses will take the form ,i am a-person-who-sent-him-to-bring-a-kitten2 ,i am a-person-to-whom-he-brought-a-kettle-by- mistake4 ,or we may choose he as ',middle ,term'1 in which case the ,premisses will take the form ,he is a-person-whom-,i-sent-to-bring-me-a-kitt en2 ,he is a-person-who-brought-me-a-kettle-by-mist ake4 ,the latter form seems best1 as the interest of the anecdote clearly depends on ,,his stupidity--not on what happened to ,,me4 ,let us then make m he2 x persons whom ,i sent1 c42 and y persons who brought1 c4 ,hence1 ,all m are x2 ,all m are y4 and the required ,diagram is --------------- ------ #a #j ------------ #j #j ------ --------------- #g4 ,both ,diagrams employed4 ------- #j #a4 ------ i4e4 ,all y are x'4 #a ------- ------- #a #b4 ------ i4e4 ,some x are y'2 or1 ,some y' are x4 ------- ------- #c4 ------ i4e4 ,some y are x'2 or1 ,some x' are y4 #a ------- ------- #d4 ------ i4e4 ,no x' are y'2 or1 ,no y' are x'4 #j ------- ------- #j #e4 ------ i4e4 ,all y are x'4 i4e4 ,all black rabbits #a are young4 ------- ------- #f4 ------ i4e4 ,some y are x'4 i4e4 ,some black #a rabbits are young4 ------- ------- #a #j #g4 ------ i4e4 ,all x are y4 i4e4 ,all well-fed birds are happy4 ------- ------- i4e4 ,some x' are y'4 i4e4 ,some birds1 #h4 ------ that are not well-fed1 are unhappy2 #a or1 ,some unhappy birds are not ------- well-fed4 ------- #a #j #i4 ------ i4e4 ,all x are y4 i4e4 ,john has got a tooth-ache4 ------- ------- #aj4 ------ i4e4 ,no x' are y4 i4e4 ,no one1 but ,john1 #j has got a tooth-ache4 ------- ------- #a #aa4 ------ i4e4 ,some x are y4 i4e4 ,some one1 who has taken a walk1 feels better4 ------- ------- #a i4e4 ,some x are y4 i4e4 ,some one1 #ab4 ------ whom ,i sent to bring me a kitten1 brought me a kettle by mistake4 ------- --------------- #j ------ #j #j #ac4 -#a---------- ------- #j ------ ------ #j --------------- ------- ,let books be ,universe2 mexciting1 xthat suit feverish patients2 ythat make one drowsy4 ,no m are x2 there#d ,no y' are x4 ,all m' are y4 i4e4 ,no books suit feverish patients1 except such as make one drowsy4 --------------- ------ #a #j #ad4 ------------ ------- #j #a ------ ------ --------------- ------- ,let persons be ,universe2 mthat deserve the fair2 xthat get their deserts2 ybrave4 ,some m are x2 there#d ,some y are x4 ,no y' are m4 i4e4 ,some brave persons get their deserts4 --------------- #j ------ #j #j #ae4 ------------ ------- #j ------ ------ #j --------------- ------- ,let persons be ,universe2 mpatient2 xchildren2 ythat can sit still4 ,no x are m2 there#d ,no x are y4 ,no m' are y4 i4e4 ,no children can sit still4 --------------- #j #j ------ #j #a #af4 ------------ ------- #j #j #a ------ ------ --------------- ------- ,let things be ,universe2 mfat2 xpigs2 yskeletons4 ,all x are m2 there#d ,all x are y'4 ,no y are m4 i4e4 ,all pigs are not-skeletons4 --------------- ------ #j #j #ag4 ------------ ------- #a #j ------ ------ #a --------------- ------- ,let creatures be ,universe2 mmonkeys2 xsoldiers2 ymischievous4 ,no m are x2 there#d ,some y are x'4 ,all m are y4 i4e4 ,some mischievous creatures are not soldiers4 --------------- #j ------ #j #j #ah4 ------------ ------- #j ------ ------ #j --------------- ------- ,let persons be ,universe2 mjust2 xmy cousins2 yjudges4 ,no x are m2 there#d ,no x are y4 ,no y are m'4 i4e4 ,none of my cousins are judges4 --------------- ------ #a #j #ai4 ------------ ------- #a ------ ------ --------------- ------- ,let periods be ,universe2 mdays2 xrainy2 ytiresome4 ,some m are x2 there#d ,some x are y4 ,all xm are y4 i4e4 ,some rainy periods are tiresome4 ,n4,b4 ,these are not legitimate ,premisses1 since the ,conclusion is really part of the second ,premiss1 so that the first ,premiss is superfluous4 ,this may be shown1 in letters1 thus3-- ,all xm are y contains ,some xm are y1 which contains ,some x are y4 ,or1 in words1 ,all rainy days are tiresome contains ,some rainy days are tiresome1 which contains ,some rainy periods are tiresome4 ,moreover1 the first ,premiss1 besides being superfluous1 is actually contained in the second2 since it is equivalent to ,some rainy days exist1 which1 as we know1 is implied in the ,proposition ,all rainy days are tiresome4 ,altogether1 a most unsatisfactory ,pair of ,premisses6 --------------- #j ------ #a #bj4 ------------ ------- #j #j #a ------ ------ #j #j --------------- ------- ,let things be ,universe2 mmedicine2 xnasty2 ysenna4 ,all m are x2 there#d ,all y are x4 ,all y are m4 i4e4 ,senna is nasty4 ,see remarks on ,no4 #g1 p #fj4 --------------- ------ #j #a #ba4 -#a---------- ------- #j #a ------ ------ --------------- ------- ,let persons be ,universe2 m,jews2 xrich2 y,patagonians4 ,some m are x2 there#d ,some x are y'4 ,all y are m'4 i4e4 ,some rich persons are not ,patagonians4 --------------- #j ------ - #bb4 ------------ ------- #j #j ------ ------ #j #j --------------- ------- ,let creatures be ,universe2 mteetotalers2 xthat like sugar2 ynightingales4 ,all m are x2 there#d ,no y are x'4 ,no y are m'4 i4e4 ,no nightingales dislike sugar4 --------------- ------ #j #j #bc4 -#a---------- ------- #j ------ ------ --------------- ------- ,let food be ,universe2 mwholesome2 xmuffins2 ybuns4 ,no x are m2 ,all y are m4 ,there is 'no information' for the smaller ,diagram2 so no ,conclusion can be drawn4 --------------- ------ #j #j #bd4 ------------ ------- #a ------ ------ #a --------------- ------- ,let creatures be ,universe2 mthat run well2 xfat2 ygreyhounds4 ,no x are m2 there#d ,some y are x'4 ,some y are m4 i4e4 ,some greyhounds are not fat4 --------------- ------ - #be4 -#a---------- ------- #j #j ------ ------ --------------- ------- ,let persons be ,universe2 msoldiers2 xthat march2 yyouths4 ,all m are x2 ,some y are m'4 ,there is 'no information' for the smaller ,diagram2 so no ,conclusion can be drawn4 --------------- #j #j ------ #j #a #bf4 ------------ ------- #j #j #a ------ ------ #a #a --------------- ------- ,let food be ,universe2 msweet2 xsugar2 ysalt4 ,all x are m2 there#d ,all x are y'4 ,all y are m'4 ,all y are x'4 i4e4 ,sugar is not salt4 ,salt is not sugar4 --------------- ------ #a #j #bg4 ------------ ------- #j #a ------ ------ --------------- ------- ,let ,things be ,universe2 meggs2 xhard-boiled2 ycrackable4 ,some m are x2 there#d ,some x are y4 ,no m are y'4 i4e4 ,some hard-boiled things can be cracked4 --------------- #j ------ #j #j #bh4 ------------ ------- #j ------ ------ #j --------------- ------- ,let persons be ,universe2 m,jews2 xthat are in the house2 ythat are in the garden4 ,no m are x2 there#d ,no x are y4 ,no m' are y4 i4e4 ,no persons1 that are in the house1 are also in the garden4 --------------- #j #j ------ - #bi4 ------------ ------- ------ ------ #a #j #a --------------- ------- ,let ,things be ,universe2 mnoisy2 xbattles2 ythat may escape notice4 ,all x are m2 there#d ,some x' are y4 ,all m' are y4 i4e4 ,some things1 that are not battles1 may escape notice4 --------------- #j ------ #j #j #cj4 ------------ ------- #a #j ------ ------ #j #a --------------- ------- ,let persons be ,universe2 m,jews2 xmad2 y,rabbis4 ,no m are x2 there#d ,all y are x'4 ,all y are m4 i4e4 ,all ,rabbis are sane4 --------------- ------ #a #ca4 ------------ ------- #j #j #a ------ ------ --------------- ------- ,let ,things be ,universe2 mfish2 xthat can swim2 yskates4 ,no m are x'2 there#d ,some y are x4 ,some y are m4 i4e4 ,some skates can swim4 --------------- ------ #j #j #cb4 ------------ ------- #a ------ ------ #a --------------- ------- ,let people be ,universe2 mpassionate2 xreasonable2 yorators4 ,all m are x'2 there#d ,some y are x'4 ,some y are m4 i4e4 ,some orators are unreasonable4 ,see remarks on ,no4 #g1 p4 #fj4 ,,chapter ,,iv4 ,,hit ,,or ,,miss4 ,thou canst not hit it1 hit it1 hit it1 ,thou canst not hit it1 my good man4 #a4 ,pain is wearisome2 ,no pain is eagerly wished for4 #b4 ,no bald person needs a hair-brush2 ,no lizards have hair4 #c4 ,all thoughtless people do mischief2 ,no thoughtful person forgets a promise4 #d4 ,i do not like ,john2 ,some of my friends like ,john4 #e4 ,no potatoes are pine-apples2 ,all pine-apples are nice4 #f4 ,no pins are ambitious2 ,no needles are pins4 #g4 ,all my friends have colds2 ,no one can sing who has a cold4 #h4 ,all these dishes are well-cooked2 ,some dishes are unwholesome if not well-cooked4 #i4 ,no medicine is nice2 ,senna is a medicine4 #aj4 ,some oysters are silent2 ,no silent creatures are amusing4 #aa4 ,all wise men walk on their feet2 ,all unwise men walk on their hands4 #ab4 ,mind your own business2 ,this quarrel is no business of yours4 #ac4 ,no bridges are made of sugar2 ,some bridges are picturesque4 #ad4 ,no riddles interest me that can be solved2 ,all these riddles are insoluble4 #ae4 ,john is industrious2 ,all industrious people are happy4 #af4 ,no frogs write books2 ,some people use ink in writing books4 #ag4 ,no pokers are soft2 ,all pillows are soft4 #ah4 ,no antelope is ungraceful2 ,graceful animals delight the eye4 #ai4 ,some uncles are ungenerous2 ,all merchants are generous4 #bj4 ,no unhappy people chuckle2 ,no happy people groan4 #ba4 ,audible music causes vibration in the air2 ,inaudible music is not worth paying for4 #bb4 ,he gave me five pounds2 ,i was delighted4 #bc4 ,no old ,jews are fat millers2 ,all my friends are old millers4 #bd4 ,flour is good for food2 ,oatmeal is a kind of flour4 #be4 ,some dreams are terrible2 ,no lambs are terrible4 #bf4 ,no rich man begs in the street2 ,all who are not rich should keep accounts4 #bg4 ,no thieves are honest2 ,some dishonest people are found out4 #bh4 ,all wasps are unfriendly2 ,all puppies are friendly4 #bi4 ,all improbable stories are doubted2 ,none of these stories are probable4 #cj4 ,he told me you had gone away4 ,he never says one word of truth4 #ca4 ,his songs never last an hour2 ,a song1 that lasts an hour1 is tedious4 #cb4 ,no bride-cakes are wholesome2 ,unwholesome food should be avoided4 #cc4 ,no old misers are cheerful2 ,some old misers are thin4 #cd4 ,all ducks waddle2 ,nothing that waddles is graceful4 #ce4 ,no ,professors are ignorant2 ,some ignorant people are conceited4 #cf4 ,toothache is never pleasant2 ,warmth is never unpleasant4 #cg4 ,bores are terrible2 ,you are a bore4 #ch4 ,some mountains are insurmountable2 ,all stiles can be surmounted4 #ci4 ,no ,frenchmen like plumpudding2 ,all ,englishmen like plumpudding4 #dj4 ,no idlers win fame2 ,some painters are not idle4 #da4 ,no lobsters are unreasonable2 ,no reasonable creatures expect impossibilities4 #db4 ,no kind deed is unlawful2 ,what is lawful may be done without fear4 #dc4 ,no fossils can be crossed in love2 ,any oyster may be crossed in love4 #dd4 ,this is beyond endurance6 ,well1 nothing beyond endurance has ever happened to me4 #de4 ,all uneducated men are shallow2 ,all these students are educated4 #df4 ,all my cousins are unjust2 ,no judges are unjust4 #dg4 ,no country1 that has been explored1 is infested by dragons2 ,unexplored countries are fascinating4 #dh4 ,no misers are generous2 ,some old men are not generous4 #di4 ,a prudent man shuns hyaenas2 ,no banker is imprudent4 #ej4 ,some poetry is original2 ,no original work is producible at will4 #ea4 ,no misers are unselfish2 ,none but misers save egg-shells4 #eb4 ,all pale people are phlegmatic2 ,no one1 who is not pale1 looks poetical4 #ec4 ,all spiders spin webs2 ,some creatures1 that do not spin webs1 are savage4 #ed4 ,none of my cousins are just2 ,all judges are just4 #ee4 ,john is industrious2 ,no industrious people are unhappy4 #ef4 ,umbrellas are useful on a journey2 ,what is useless on a journey should be left behind4 #eg4 ,some pillows are soft2 ,no pokers are soft4 #eh4 ,i am old and lame2 ,no old merchant is a lame gambler4 #ei4 ,no eventful journey is ever forgotten2 ,uneventful journeys are not worth writing a book about4 #fj4 ,sugar is sweet2 ,some sweet things are liked by children4 #fa4 ,richard is out of temper2 ,no one but ,richard can ride that horse4 #fb4 ,all jokes are meant to amuse2 ,no ,act of ,parliament is a joke4 #fc4 ,i saw it in a newspaper4 ,all newspapers tell lies4 #fd4 ,no nightmare is pleasant2 ,unpleasant experiences are not anxiously desired4 #fe4 ,prudent travellers carry plenty of small change2 ,imprudent travellers lose their luggage4 #ff4 ,all wasps are unfriendly2 ,no puppies are unfriendly4 #fg4 ,he called here yesterday2 ,he is no friend of mine4 #fh4 ,no quadrupeds can whistle2 ,some cats are quadrupeds4 #fi4 ,no cooked meat is sold by butchers2 ,no uncooked meat is served at dinner4 #gj4 ,gold is heavy2 ,nothing but gold will silence him4 #ga4 ,some pigs are wild2 ,there are no pigs that are not fat4 #gb4 ,no emperors are dentists2 ,all dentists are dreaded by children4 #gc4 ,all1 who are not old1 like walking2 ,neither you nor ,i are old4 #gd4 ,all blades are sharp2 ,some grasses are blades4 #ge4 ,no dictatorial person is popular2 ,she is dictatorial4 #gf4 ,some sweet things are unwholesome2 ,no muffins are sweet4 #gg4 ,no military men write poetry2 ,no generals are civilians4 #gh4 ,bores are dreaded2 ,a bore is never begged to prolong his visit4 #gi4 ,all owls are satisfactory2 ,some excuses are unsatisfactory4 #hj4 ,all my cousins are unjust2 ,all judges are just4 #ha4 ,some buns are rich2 ,all buns are nice4 #hb4 ,no medicine is nice2 ,no pills are unmedicinal4 #hc4 ,some lessons are difficult2 ,what is difficult needs attention4 #hd4 ,no unexpected pleasure annoys me2 ,your visit is an unexpected pleasure4 #he4 ,caterpillars are not eloquent2 ,jones is eloquent4 #hf4 ,some bald people wear wigs2 ,all your children have hair4 #hg4 ,all wasps are unfriendly2 ,unfriendly creatures are always unwelcome4 #hh4 ,no bankrupts are rich2 ,some merchants are not bankrupts4 #hi4 ,weasels sometimes sleep2 ,all animals sometimes sleep4 #ij4 ,ill-managed concerns are unprofitable2 ,railways are never ill-managed4 #ia4 ,everybody has seen a pig2 ,nobody admires a pig4 ,extract a ,pair of ,premisses out of each of the following3 and deduce the ,conclusion1 if there is one3-- #ib4 ,the ,lion1 as any one can tell you who has been chased by them as often as ,i have1 is a very savage animal3 and there are certain individuals among them1 though ,i will not guarantee it as a general law1 who do not drink coffee4 #ic4 ,it was most absurd of you to offer it6 ,you might have known1 if you had had any sense1 that no old sailors ever like gruel6 ,but ,i thought1 as he was an uncle of yours-- ,an uncle of mine1 indeed6 ,stuff6 ,you may call it stuff1 if you like4 ,all ,i know is1 ,,my uncles are all old men3 and they like gruel like anything6 ,well1 then ,,your uncles are-- #id4 ,do come away6 ,i can't stand this squeezing any more4 ,no crowded shops are comfortable1 you know very well4 ,well1 who expects to be comfortable1 out shopping8 ,why1 ,i do1 of course6 ,and ,i'm sure there are some shops1 further down the street1 that are not crowded4 ,so-- #ie4 ,they say no doctors are metaphysical organists3 and that lets me into a little fact about ,,you1 you know4 ,why1 how do you make ,,that out8 ,you never heard me play the organ4 ,no1 doctor1 but ,i've heard you talk about ,browning's poetry3 and that showed me that you're ,,metaphysical1 at any rate4 ,so-- ,extract a ,syllogism out of each of the following3 and test its correctness3-- #if4 ,don't talk to me6 ,i've known more rich merchants than you have3 and ,i can tell you not ,,one of them was ever an old miser since the world began6 ,and what has that got to do with old ,mr4 ,brown8 ,why1 isn't he very rich8 ,yes1 of course he is4 ,and what then8 ,why1 don't you see that it's absurd to call him a miserly merchant8 ,either he's not a merchant1 or he's not a miser6 #ig4 ,it ,,is so kind of you to enquire6 ,i'm really feeling a great deal better to-day4 ,and is it ,nature1 or ,art1 that is to have the credit of this happy change8 ,art1 ,i think4 ,the ,doctor has given me some of that patent medicine of his4 ,well1 ,i'll never call him a humbug again4 ,there's ,,somebody1 at any rate1 that feels better after taking his medicine6 #ih4 ,no1 ,i don't like you one bit4 ,and ,i'll go and play with my doll4 ,,dolls are never unkind4 ,so you like a doll better than a cousin8 ,oh you little silly6 ,of course ,i do6 ,,cousins are never kind--at least no cousins ,i've ever seen4 ,well1 and what does ,,that prove1 ,i'd like to know6 ,if you mean that cousins aren't dolls1 who ever said they were8 #ii4 ,what are you talking about geraniums for8 ,you can't tell one flower from another1 at this distance6 ,i grant you they're all ,,red flowers3 it doesn't need a telescope to know ,,that4 ,well1 some geraniums are red1 aren't they8 ,i don't deny it4 ,and what then8 ,i suppose you'll be telling me some of those flowers are geraniums6 ,of course that's what ,i should tell you1 if you'd the sense to follow an argument6 ,but what's the good of proving anything to ,,you1 ,i should like to know8 #ajj4 ,boys1 you've passed a fairly good examination1 all things considered4 ,now let me give you a word of advice before ,i go4 ,remember that all1 who are really anxious to learn1 work ,,hard4 ,i thank you1 ,sir1 in the name of my scholars6 ,and proud am ,i to think there are ,,some of them1 at least1 that are really ,,anxious to learn4 ,very glad to hear it3 and how do you make it out to be so8 ,why1 ,sir1 ,i know how hard they work--some of them1 that is4 ,who should know better8 ,extract from the following speech a series of ,syllogisms1 or arguments having the form of ,syllogisms3 and test their correctness4 ,it is supposed to be spoken by a fond mother1 in answer to a friend's cautious suggestion that she is perhaps a ,,little overdoing it1 in the way of lessons1 with her children4 #aja4 ,well1 they've got their own way to make in the world4 ,,we can't leave them a fortune apiece4 ,and money's not to be had1 as ,,you know1 without money's worth3 they must ,,work if they want to live4 ,and how are they to work1 if they don't know anything8 ,take my word for it1 there's no place for ignorance in ,,these times6 ,and all authorities agree that the time to learn is when you're young4 ,one's got no memory afterwards1 worth speaking of4 ,a child will learn more in an hour than a grown man in five4 ,so those1 that have to learn1 must learn when they're young1 if ever they're to learn at all4 ,of course that doesn't do unless children are ,,healthy3 ,i quite allow ,,that4 ,well1 the doctor tells me no children are healthy unless they've got a good colour in their cheeks4 ,and only just look at my darlings6 ,why1 their cheeks bloom like peonies6 ,well1 now1 they tell me that1 to keep children in health1 you should never give them more than six hours altogether at lessons in the day1 and at least two half-holidays in the week4 ,and that's ,,exactly our plan ,i can assure you6 ,we never go beyond six hours1 and every ,wednesday and ,saturday1 as ever is1 not one syllable of lessons do they do after their one o'clock dinner6 ,so how you can imagine ,i'm running any risk in the education of my precious pets is more than ,i can understand1 ,i promise you6 ,,the ,,end4