,,natural ,,philosophy ,,by ,,wilhelm ,,ostwald ,,translated ,,by ,,thomas ,,seltzer ,with the author's special revision for the ,american edition ,,new ,,york ,,henry ,,holt ,,and ,,company #aiaj ,,copyright1 #aiaj1 ,,by ,,henry ,,holt ,,and ,,company ,published ,november1 #aiaj ,,the ,,quinn ,,boden ,,co4 ,,press ,,rahway ,n4 ,j4 ,the original of this book was published as volume ,i in ,reclam's ,b,,cher ,,der ,,naturwissenschaft4 ,,preface ,the beginning of the twentieth century is marked by a sudden rise of interest in philosophy4 ,this is especially manifest in the vast growth of philosophic literature4 ,the present movement1 it is noteworthy1 is by no means a revival proceeding from the academic philosophy traditionally represented at the universities1 but has rather the original character of natural philosophy4 ,it owes its origin to the fact that after the specialization of the last half century1 the synthetic factors of science are again vigorously asserting themselves4 ,the need finally to consider all the numerous separate sciences from a general point of view and to find the connection between one's own activity and the work of mankind in its totality1 must be regarded as the most prolific source of the present philosophic movement1 just as it was the source of the natural philosophic endeavors a hundred years ago4 ,but while that old natural philosophy soon ended in a boundless sea of speculation1 the present movement gives promise of permanent results1 because it is built upon an extremely broad basis of experience4 ,the laws of energy in the inorganic world and the laws of evolution in the organic world furnish mental instruments for a conceptual elaboration of the material provided by science1 instruments capable not only of unifying present knowledge1 but also of evoking the knowledge of the future4 ,if it is not permissible to regard this unification as exhaustive and sufficient for all time1 yet there is still so much left for us to do in working over the material we have on hand from the general points of view just mentioned1 that the need for systematizing must be satisfied before we can turn our gaze upon things more remote4 ,the present work is meant to serve as the first aid and guide in the acquisition of these comprehensive notions of the external world and the inner life4 ,it is not meant to develop or uphold a system of philosophy4 ,through long experience as a teacher the writer has learned that those are the best pupils who soon go their own way4 ,however1 it is meant to uphold a certain method1 that is1 the scientific 7or1 if you will1 the natural scientific71 which takes its problems1 and endeavors to solve its problems1 from experience and for experience4 ,if1 as a result1 several points of view arise that differ from those of the present day1 and consequently demand a different attitude toward important matters in the immediate future1 this very fact affords proof that our present natural philosophy does not lead away from life1 but aims to form a part of our life1 and has a right to4 ,,contents ,,page ,,introduction #a ,,part ,i ,,general ,,theory ,,of ,,knowledge #aa #a4 ,the ,formation of ,concepts #aa #b4 ,science #ac #c4 ,the ,aim of ,science #ac #d4 ,concrete and ,abstract #af #e4 ,the ,subjective ,part #ag #f4 ,empirical ,concepts #ah #g4 ,simple and ,complex ,concepts #ai #h4 ,the ,conclusion #bd #i4 ,the ,natural ,laws #bh #aj4 ,the ,law of ,causation #ca #aa4 ,the ,purification of the ,causal ,relation #cd #ab4 ,induction #ch #ac4 ,deduction #dj #ad4 ,ideal ,cases #dd #ae4 ,the ,determinateness of ,things #dg #af4 ,the ,freedom of the ,will #ej #ag4 ,the ,classification of the ,sciences #ec #ah4 ,the ,applied ,sciences #eg ,,part ,,ii ,,logic1 ,,the ,,science ,,of ,,the ,,manifold1 ,,and ,,mathematics #fa #ai4 ,the ,most ,general ,concept #fa #bj4 ,association #fc #ba4 ,the ,group #fe #bb4 ,negation #fh #bc4 ,artificial and ,natural ,groups #fi #bd4 ,arrangement of the ,members #ge #be4 ,numbers #gh #bf4 ,arithmetic1 ,algebra1 and the ,theory of ,numbers #gi #bg4 ,co-ordination #hj #bh4 ,comparison #hb #bi4 ,numbers #he #cj4 ,signs and ,names #hf #ca4 ,the ,written ,language #hi #cb4 ,pasigraphy and ,sound ,writing #ib #cc4 ,sound ,writing #if #cd4 ,the ,science of ,language #ig #ce4 ,continuity #aja #cf4 ,measurement #ajg #cg4 ,the ,function #aji #ch4 ,the ,application of the ,functional ,relation #aab #ci4 ,the ,law of ,continuity #aac #dj4 ,time and ,space #aah #da4 ,recapitulation #abd ,,part ,,iii ,,the ,,physical ,,sciences #abg #db4 ,general #abg #dc4 ,mechanics #abh #dd4 ,kinetic ,energy #acb #de4 ,mass and ,matter #acf #df4 ,energetic ,mechanics #ach #dg4 ,the ,mechanistic ,theories #adj #dh4 ,complementary ,branches of ,mechanics #add #di4 ,the ,theory of ,heat #adg #ej4 ,the ,second ,fundamental ,principle #aej #ea4 ,electricity and ,magnetism #aed #eb4 ,light #aef #ec4 ,chemical ,energy #aei ,,part ,,iv ,,the ,,biologic ,,sciences #afc #ed4 ,life #afc #ee4 ,the ,storehouse of ,free ,energy #afh #ef4 ,the ,soul #aga #eg4 ,feeling1 ,thinking1 ,acting #agd #eh4 ,society #agi #ei4 ,language and ,intercourse #ahb #fj4 ,civilization #ahd ,,index #ahg ,,introduction ,natural science and natural philosophy are not two provinces mutually exclusive of each other4 ,they belong together4 ,they are like two roads leading to the same goal4 ,this goal is the domination of nature by man1 which the various natural sciences reach by collecting all the individual actual relations between the natural phenomena1 placing them in juxtaposition1 and seeking to discover their interdependence1 upon the basis of which one phenomenon may be foretold from another with more or less certainty4 ,natural philosophy accompanies these specialized labors and generalizations with similar labors and generalizations1 only of a more universal nature4 ,for instance1 while the science of electricity1 as a branch of physics1 deals with the relation of electrical phenomena to one another and to phenomena in other branches of physics1 natural philosophy is not only concerned with the question of the mutual connection of all physical relations1 but also endeavors to include in the sphere of its study chemical1 biological1 astronomical1 in short1 all the known phenomena4 ,in other words1 natural philosophy is the most general branch of natural science4 ,here two questions are usually asked4 ,first1 how can we define the boundary line between natural philosophy and the special sciences1 since1 obviously1 sharp lines of demarcation are out of the question8 ,secondly1 how can we investigate and teach natural philosophy1 when it is impossible for any one person to master all the sciences completely1 and so obtain a bird's-eye view of the general relations between all the branches of knowledge8 ,to the beginner especially1 who must first learn the various sciences1 it seems quite hopeless to devote himself to a study that presupposes a command of them4 ,since a discussion of the two questions will afford an excellent preliminary survey of the work in hand1 it will be well to consider them in detail4 ,in the first place1 the lack of complete and precise boundary lines is a general characteristic of all natural things1 and science is a natural thing4 ,if1 for instance1 we try to differentiate sharply between physics and chemistry1 we are met with the same difficulty4 ,so also in biology if we try to settle beyond the shadow of a doubt the line of separation between the animal and the vegetable kingdoms4 ,if1 despite this well-known impossibility1 we consider the division of natural things into classes and orders as by no means useless and do not discard it1 but regard it as an important scientific work1 this is practical proof that such classification preserves its essential usefulness1 even if it does not attain ideal definiteness4 ,for1 this imperfection notwithstanding1 classification reaches its end1 which is a comprehensive view1 and thus a mastery1 of the manifoldness of phenomena4 ,for example1 with the overwhelming majority of organic beings there is no doubt whether they are animals or plants4 ,similarly1 most phenomena of inorganic nature can readily be designated as physical or chemical4 ,for all such cases1 therefore1 the existing classification is good and useful4 ,the few cases presenting difficulty may very well be considered by themselves wherever they occur1 and we need merely take cognizance of them here4 ,it follows from this1 to be sure1 that classification will be all the better fitted to its purpose the less frequently such doubtful cases arise1 and that we have an interest in repeatedly testing existing classifications with a view to finding out if they cannot be supplanted by more suitable ones4 ,in these matters it is much the same as when we look upon the waves on the surface of a large body of water4 ,our first glance tells us that a number of waves are rolling there2 and from a point giving us a sufficiently wide outlook1 we can count them and gauge their width4 ,but where is the line of division between one wave and the next8 ,we undoubtedly see one wave following another1 yet it is impossible for us to indicate precisely the end of one and the beginning of the next4 ,are we then to deduce that it is superfluous or unfeasible to designate the waves as different8 ,by no means4 ,on the contrary1 in strictly scientific work we will endeavor to find some suitable definition of the boundary line between two consecutive waves4 ,it may then be called an arbitrary line1 and in a degree arbitrary it will certainly be4 ,but to the investigator this does not matter4 ,what concerns him is1 if1 with the help of this definition1 wave lengths can be unequivocally determined1 and if this is possible1 he will use the definition as suitable to the purposes of science1 without dismissing from his mind the idea that possibly some other definition may provide an even easier or sharper determination4 ,such an one he would instantly prefer to the old one4 ,thus we see that these questions of classification are not questions of the so-called essence of the thing1 but pertain merely to purely practical arrangements for an easier and more successful mastery of scientific problems4 ,this is an extremely important point of view1 much more far-reaching than is apparent here at its first application4 ,as to the second objection1 ,i will admit its validity4 ,but here1 too1 we have a phenomenon appearing in all branches and forms of science4 ,therefore we must familiarize ourselves with it in advance4 ,science was created by man for man's purposes1 and1 consequently1 like all human achievements1 possesses the indestructible quality of imperfection4 ,but the mere fact that a successful working science exists1 with the help of which human life has been fundamentally modified1 signifies that the quality of incompleteness in human learning is no hindrance to its efficiency4 ,for what science has once worked out always contains a portion of truth1 hence a portion of efficiency4 ,the old corpuscular theory of light1 which now seems so childishly incomplete to us1 was adequate1 none the less1 for satisfactorily explaining the phenomena of reflection and refraction1 and the finest telescopes have been built with its help4 ,this is due to the true elements in it1 which taught us correctly to calculate the direction of rays of light in reflection and refraction4 ,the rest was merely an arbitrary accessory which had to fall when new1 contradictory facts were discovered4 ,these facts could not have been taken into consideration when the theory was propounded1 because they were not yet known4 ,but when the corpuscular theory of light was replaced by the theory of waves of an elastic ether1 geometric optics at first remained quite unchanged1 because the theory of straight lines of rays could be deduced from the new views also1 though not so easily and smoothly4 ,and geometric optics was then concerned with nothing but these straight lines1 in no wise with the question of their propagation4 ,it did not become clear until recently that this conception of straight lines of rays is incomplete1 though1 it is true1 it made a first approach toward the presentation of actual phenomena4 ,it fails when it comes to characterize the behavior of a pencil of rays of large aperture4 ,the old idea of a straight line of rays was to be replaced by a more complex concept with more varied characteristics1 namely1 the wave-surface4 ,the greater variety of this concept renders possible the presentation of the greater variety of the optical phenomena just mentioned4 ,and from it proceed the very considerable advances that have been made1 since the new theory was propounded1 in optical instruments1 especially the microscope and the photographic objective1 for the purposes of which pencils of rays of large aperture are required4 ,the astronomic objective with its small angle of aperture has not undergone particularly important improvements4 ,experience in every province of science is the same as in this4 ,science is not like a chain which snaps when only a single link proves to be weak4 ,it is like a tree1 or1 better still1 like a forest1 in which all sorts of changes or ravages go on without causing the whole to pass out of existence or cease to be active4 ,the relations between the various phenomena1 once they become known1 continue to exist as indestructible components of all future science4 ,it may come to pass1 in fact1 does come to pass very frequently1 that the form in which those relations were first expressed prove to be imperfect1 and that the relations cannot be maintained quite generally4 ,it turns out that they are subjected to other influences which change them because they had been unknown1 and which could not have been taken into consideration at the discovery and first formulation of these relations4 ,but no matter what changes science may undergo1 a certain residue of that first knowledge will remain and never be lost4 ,in this sense1 a truth that science has once gained has life eternal1 that is1 it will exist as long as human science exists4 ,applying this general notion to our case1 we have the following4 ,how far and how generally at any given time the relations of the various phenomena are summed up in fixed forms1 that is1 in natural laws1 will depend upon the stage attained by each of the special sciences4 ,but since science has been in existence it has yielded a certain number of such general laws1 and these1 though they have been filed down a good deal in form and expression1 and have undergone many corrections as to the limits of their application1 nevertheless have preserved their essence1 since they began their existence in the brains of human investigators4 ,the net of the relations of phenomena grows ever wider and more diversified1 but its chief features persist4 ,the same is true of an individual4 ,no matter how limited the circle of his knowledge1 it is a part of the great net1 and therefore possesses the quality by virtue of which the other parts readily join it as soon as they reach the consciousness and knowledge of the individual4 ,the man who thus enters the realm of science acquires advantages which may be compared to those of a telephone in his residence4 ,if he wishes to1 he may be connected with everybody else1 though he will make extremely limited use of his privilege1 since he will try to reach only those with whom he has personal relations4 ,but once such relations have been established1 the possibility of telephone communication is simultaneously and automatically established4 ,similarly1 every bit of knowledge that the individual appropriates will prove to be a regular part of the central organization1 the entire extent of which he can never cover1 though each individual part has been made accessible to him1 provided he wants to take cognizance of it4 ,the mere beginner in learning1 therefore1 when receiving the most elementary instruction in school1 or from his parents1 or even from his personal experiences in his surroundings1 is grasping one or more threads of the mighty net1 and can grope his way farther along it in order to draw an increasing area of it into his life and the field of his activity4 ,and this net has the valuable1 even precious quality of being the same that joins the greatest and most comprehensive intellects in mankind to one another4 ,the truths a man has once grasped he need never learn afresh so far as their actual content is concerned1 though not infrequently--especially in newer sciences--he may have to see the form of their presentation and generalization change4 ,for this reason it is of such especial importance for each individual from the first to perceive these unalterable facts and realize that they are unalterable and learn to distinguish them from the alterable forms of their presentation4 ,it is in this very regard that the incompleteness of human knowledge is most clearly revealed4 ,time and again in the history of science form has been taken for content1 and necessary changes of form--a merely practical question--have been confused with revolutionary modifications of the content4 ,thus1 each presentation of a science has its natural philosophic portion4 ,in text-books1 whether elementary or advanced1 the chapter on natural philosophy is found usually at the beginning of the book1 sometimes at the end1 in the form of a general introduction1 or general summary4 ,in the special works in which the latest advances of science are made known by the investigators1 the natural philosophic portions are usually to be found in the form of theses1 of principles1 which are not discussed1 often not even explicitly stated1 but upon the acceptance of which depend all the special conclusions that are drawn1 in the case in hand1 from the new facts or thoughts imparted4 ,whether at the beginning or at the end of the book1 these most general principles do not quite occupy the place that befits them4 ,if at the introduction of the text-book1 they are practically devoid of content1 since the facts they are meant to summarize are yet to be unfolded in the course of the presentation4 ,if at the end1 they come too late1 since they have already been applied in numerous instances1 though without reference to their general nature4 ,the best method is--and a good teacher always employs this method1 whether in the spoken or the written word--to let the generalizations come whenever the individual facts imparted require and justify them4 ,thus1 all instruction in natural sciences is necessarily interspersed with natural philosophy1 good or bad1 according to the clearheadedness of the teacher4 ,if we wish to obtain a perfect survey of a complex structure1 as1 for instance1 the confusion of streets in a large city1 we had better not try to know each street1 but study a general plan1 from which we learn the comparative situation of the streets4 ,so it is well for us in studying a special science to look at our general plan1 if for no other reason than to keep from losing our way when it may chance to lead through a quarter hitherto unknown4 ,this is the purpose of the present work4 ,,part ,i ,,general ,,theory ,,of ,,knowledge #a4 ,the ,formation of ,concepts4 ,to the human mind1 as it slowly awakens in every child1 the world at first seems a chaos consisting of mere individual experiences4 ,the only connection between them is that they follow each other consecutively4 ,of these experiences1 all of which at first are different from one another1 certain parts come to be distinguished by the fact that they are repeated more frequently1 and therefore receive a special character1 that of being familiar4 ,the familiarity is due to our recalling a former similar experience2 in other words1 to our feeling that there is a relation between the present experience and certain former experiences4 ,the cause of this phenomenon1 which is at the basis of all mental life1 is a quality common to all living things1 and manifesting itself in all their functions1 while appearing but rarely or accidentally in inorganic nature4 ,it is the quality by virtue of which the oftener any process has taken place in a living organism the more easily it is repeated4 ,here is not yet the place to show how almost all the characteristic qualities of living beings1 from the preservation of the species to the highest intellectual accomplishments1 are conditioned by this special peculiarity4 ,suffice it to say that because of this quality all those processes which are repeated frequently in any given living organism1 assume spontaneously1 that is1 from physiologic reasons1 a character distinguishing them essentially from those which appear only in isolated instances1 or sporadically4 ,if a living being is equipped with consciousness and thought1 like man1 then the conscious recollections of such uniform experiences form the enduring or permanent part in the sum-total of his experiences4 ,each time a complex event1 like the change of seasons1 for example1 which we know from experience repeats itself--each time a part of such an event reaches our consciousness1 we are prepared also for the other parts that experience teaches are connected with it4 ,this makes it possible for us to foresee future events4 ,what significance the foreseeing of future events has for the preservation and the development of the individual as well as the species can only be indicated here4 ,to give one instance1 it is our ability to foretell the coming of winter with the impossibility of obtaining food directly during the winter that causes us to refrain from at once using up all the food we have and to preserve it for the day of need4 ,the ability to foretell1 therefore1 becomes the foundation of the whole structure of economic life4 #b4 ,science4 ,the prophecy of future events based upon the knowledge of the details of recurring events is called science in its most general sense4 ,here1 as in most cases in which language became fixed long before men had a clear knowledge of the things designated1 the name of the thing is easily associated with false ideas arising either from errors that had been overcome or from other1 still more accidental1 causes4 ,thus1 the mere knowledge of past events is also called science without any thought of its use for prophesying future events4 ,yet a moment's reflection teaches that mere knowledge of the past which is not meant to1 or cannot1 serve as a basis for shaping the future is utterly aimless knowledge1 and must take its place with other aimless activities called play4 ,there are all sorts of plays requiring great acumen and patient application1 as for example the game of chess2 and no one has the right to prevent any individual from pursuing such games4 ,but the player for his part must not demand special regard for his activity4 ,by using his energies for his personal pleasure and not for a social purpose1 that is1 for a general human purpose1 he loses every claim to the social encouragement of his activity1 and must be content if only his individual rights are respected2 and that1 too1 only so long as the social interests do not suffer by it4 #c4 ,the ,aim of ,science4,these views are deliberately opposed to a very widespread idea that science should be cultivated for its own sake1 and not for the sake of the benefits it actually brings or may be made to bring4 ,we reply that there is nothing at all which is done merely for its own sake4 ,everything1 without exception1 is done for human purposes4 ,these purposes range from momentary personal satisfaction to the most comprehensive social services involving disregard of one's own person4 ,but in all our actions we never get beyond the sphere of the human4 ,if1 therefore1 the phrase for its own sake means anything1 it means that science should be followed for the sake of the immediate pleasure it affords1 that is to say1 as play 7as we have just characterized it71 and in the for-its-own-sake demand there is hidden a misunderstood idealism1 which1 on closer inspection1 resolves itself into its very opposite1 the degradation of science4 ,the element of truth hidden in that misunderstood phrase is1 that in a higher state of culture it is found better to disregard the immediate technical application in the pursuit of science1 and to aim only for the greatest possible perfection and depth in the solution of its individual problems4 ,whether this is the correct method of procedure and when it is so1 is solely a question of the general state of culture4 ,in the early stages of human civilization such a demand is utterly meaningless1 and all science is necessarily and naturally confined to immediate life4 ,but the wider and more complex human relations become1 the wider and surer must the ability to predict future events become4 ,then it is the function of prophesying science to have answers ready for questions which as yet have not become pressing1 but which with further development may sooner or later become so4 ,in the net-like interlacing of the sciences1 that is1 of the various fields of knowledge1 described in the introduction1 we must always reckon with the fact that our anticipation of what kind of knowledge we shall next need must always remain very incomplete4 ,it is possible to foresee future needs in general outline with more or less certainty1 but it is impossible to be prepared for particular individual cases which lie on the border line of such anticipation1 and which may sometimes become of the utmost importance and urgency4 ,therefore it is one of the most important functions of science to achieve as perfect an elaboration as possible of all the relations conceivable1 and in this practical necessity lies the foundation of the general or theoretical elaboration of science4 ,the ,science of ,concepts4 ,here the question immediately arises3 how can we secure such perfection8 ,the answer to this general preliminary question of all the sciences belongs to the sphere of the first or the most general of all the sciences1 a knowledge of which is presupposed for the pursuit of the other sciences4 ,since its foundation by the ,greek philosopher ,aristotle it has borne the name of logic1 which name1 etymologically speaking1 hints suspiciously at the word1 and the word1 as is known1 steps in where ideas are wanting4 ,here1 however1 we have to deal with the very science of ideas1 to which language bears the relation only of a means--and often an inadequate means--to an end4 ,we have already seen how1 through the physiologic fact of memory1 experiences are found in our consciousness which are similar1 that is1 partially coinciding with one another4 ,these coinciding parts are those concerning which we can make predictions1 for the very reason that they coincide in every single instance1 and they alone1 therefore1 constitute that part of our experience which bears results and hence has significance4 #d4 ,concrete and ,abstract4 ,such coinciding or repeated parts of similar experiences we call1 as already stated1 concepts4 ,but here1 too1 attention must immediately be drawn to a linguistic imperfection1 which consists in the fact that in such a group of coinciding experiences we designate by the same name both the isolated experience or the object of a special experience and the totality of all the coinciding experiences2 in other words1 all the similar experiences4 ,thus1 horse means1 on the one hand1 quite a definite thing which for the moment forms an object of our experience1 and1 on the other1 the totality of all possible similar objects which have been present in our former experiences1 and which we shall meet in our future experiences4 ,it is true that these two sorts of contents of consciousness bearing the same name are distinguished also as concrete and abstract1 and there is an inclination to attribute reality only to the first1 while the other1 as mere entities in thought1 are relegated to a lesser degree of reality4 ,as a matter of fact1 the difference1 though important1 is of quite another kind4 ,it is the difference between the momentary experience1 as opposed to the totality of the corresponding memories and expectations4 ,hence not so much a difference in reality as in presence4 ,however1 our observations have already made it apparent that presence alone never yields knowledge4 ,a necessary part of knowledge is the memory of former similar experiences4 ,for without such memory and the corresponding comparison1 it is quite impossible for us to get at those things which agree and which1 therefore1 may be predicted2 and we should stand before every one of our experiences with the helplessness of a new-born babe4,a ,a ,sometimes on suddenly awaking from a profound sleep a person finds himself for the moment deprived of his personal stock of memories1 unable to recall where and in what circumstances he is4 ,no one who has experienced such a condition can ever forget the terrifying sense of helplessness it brings4 #e4 ,the ,subjective ,part4 ,we shall therefore have to recognize realities in abstract ideas in so far as they must rest upon some experiences to be at all intelligible to us4 ,since the formation of concepts depends upon memories1 and these may refer1 according to the individual1 to very different parts of the same experience of different individuals1 concepts always possess an element dependent upon the individual1 or a subjective element4 ,this1 however1 does not consist in the addition by the individual of new parts not found in the experience1 but1 on the contrary1 in the different choice out of what is found in the experience4 ,if every individual absorbed all parts of the experience1 the individual1 or subjective1 differences would disappear4 ,and since scientific experience endeavors to make the absorption of experiences as complete as possible1 it aims nearer and nearer to this ideal by seeking to equalize the subjective deficiency of the individual memory through the collocation of as many and as various memories as possible1 thus filling in the subjective gaps in experience as far as possible and rendering them harmless4 #f4 ,empirical ,concepts4 ,first and unconditionally those concepts possess reality which always and without exception are based on experienced facts4 ,but we can easily make manifold arbitrary combinations of concepts from different experiences1 since our memory freely places them at our disposal1 and from such a combination we can form a new concept4 ,of course it is not necessary that our arbitrary combination should also be found in our past or future experiences4 ,on the contrary1 we may rather expect that there could be many more arbitrary combinations not to be found in experience than combinations later confirmed by experience4 ,the former are purposeless because unreal1 the latter1 on the contrary1 are of the utmost consequence because upon them is based the real aim of knowledge1 prediction4 ,the former are those which have brought the very reality of the concepts into ill repute1 while the latter show that the formation and the mutual reaction of the concepts practically constitute the entire content of all science4 ,it is of the greatest importance1 therefore1 to distinguish between the two kinds of concept combinations1 and the study of this differentiation forms the content of that most general of all the sciences which we have characterized as logic1 or1 better1 the science of concepts4 #g4 ,simple and ,complex ,concepts4 ,the formation of concepts consists1 as we have seen1 in the selection of those parts of different but similar experiences which coincide with one another and in the elimination of those that are different in kind4 ,the results of such a procedure may vary greatly according to the number and the difference of the experiences placed in relation with one another4 ,if1 for example1 we compare only a few experiences1 and if1 moreover1 these experiences are very similar to one another1 then the resulting concepts will contain very many parts that agree4 ,but at the same time they will have the peculiarity of not being applicable to other experiences1 since these are without some of the coinciding parts of that narrower circle4 ,thus1 for example1 the concept which a rustic chained to the soil all his life has of human work does not apply to the work of the city man4 ,a concept will embrace a larger number of individual cases in proportion as it contains fewer different parts4 ,and by systematically following out this thought we arrive at the conclusion that the concepts that are simple and have no different parts at all find the widest application or are the most general4 ,the elimination of the non-coinciding parts from the concept-forming experience is called abstraction4 ,obviously abstraction must be carried the farther the more numerous and the more varied the experiences from which the concepts are abstracted1 and the simplest concepts are the most abstract4 ,by looking back over the ground just traversed1 the less abstract ideas may also be regarded as the more complex in contradistinction to the simpler ones4 ,only we must guard against the error of literal interpretation and not suppose that the less simple concepts have really been compounded of the simpler ones4 ,in point of origin they actually existed first1 since the experience contains the ensemble of all the parts1 those which have been retained as well as those which have been eliminated4 ,it is only later1 by a characteristic mental operation1 after we have analyzed the more complex concept1 that is1 after we have disclosed the simpler concepts existing in it1 that we can compound it again2 in other words1 execute its synthesis4 ,these relations bear a striking resemblance to the relations known from chemistry to exist between substances1 namely1 between elements and compounds4 ,from the chaos of all objects of experimentation 7chemistry purposely limits itself to ponderable bodies7 the pure substances are sifted out--an operation corresponding to the formation of concepts4 ,the pure substances prove to be either simple or compound1 and the compounds are so constituted that they can each be reduced to a limited number of simple substances4 ,the simple substances1 or elements1 retain this quality of simplicity only until they are recalled2 that is1 until it has been proved that they1 too1 can be resolved into still simpler elements4 ,the same is true of the simple concepts4 ,they can claim simplicity only until their complex nature is demonstrated4 ,with all these similarities we must be extremely careful never to forget the differences existing alongside the agreements4 ,so hereafter we shall make no further use of the chemical simile4 ,it was brought into requisition merely in order to acquaint the beginner the more readily with the entire method of investigation by means of a more familiar field of thought and study4 ,it is quite certain1 however1 that side by side with the given similarities there are also radical differences4 ,moreover1 the notion of simple and complex concepts or ideas had been elaborated by ,john ,locke long before chemistry reached its present state of clearness concerning the concept of the elements4 ,nevertheless since then the relation has been completely reversed4 ,while the study of the chemical elements has in the meantime undergone great development1 so that not only have the elements of all the substances coming under the observation of the chemist been discovered1 but1 inversely1 many compound substances have been constructed from their elements1 not even an approach to such a development is apparent in the study of concepts4 ,on the contrary1 the whole matter has remained at about the same point as that to which ,john ,locke had brought it in the second half of the seventeenth century4 ,this is due above all to the opinion of the most influential philosophers1 that ,aristotle's logic1 or science of concepts1 is absolutely true as well as exhaustive and complete1 so that1 at the utmost1 what is left for later generations to do is only to make a change in the form in which the matter is presented4 ,it is true that in more recent times the grave error of this view is beginning to be recognized4 ,we realize that ,aristotle's logic embraces but a very small part of the entire field1 though in this part he displays the greatest genius4 ,but beyond this general recognition no great step forward has been made4 ,not even a provisional table of the elementary concepts has been propounded and applied since ,locke4 ,hence in the following investigation we shall have to speak of the elements or the simpler parts of a complex concept only in the sense that these concept elements are simpler as compared with the complex concepts1 but not in the sense that the simplest or truly elementary concepts have already been worked out4 ,it must be left to later investigators to find these1 and it may be expected that the reduction of some concepts until then considered elementary into still simpler ones will take place chiefly in times of great intellectual progress4 ,complex concepts can1 in the first place1 be formed from experience1 for in an empirical concept we meet with several conceptual component parts which can be separated from one another by a process of abstraction1 but are always found together in the given experiences4 ,for example1 the concept horse has originated from a very frequent1 similarly repeated experience4 ,on analysis it is found to contain a vast number of other concepts1 such as quadruped1 vertebrate animal1 warm-blooded1 hairiness1 and so on4 ,horse1 then1 is obviously a complex empirical concept4 ,on the other hand1 we can combine as many simple concepts as we please1 even if we did not find them combined in experience1 for in reality there is nothing to hinder us from uniting all the concepts provided by memory into any combinations we please4 ,in this way we obtain complex arbitrary concepts4 ,the task of science can now be even more sharply defined than before by the fact that it permits the construction of arbitrary concepts which in circumstances to be foreseen become empirical concepts4 ,this is another expression for prediction1 which we recognized as the characteristic of science4 ,it goes deeper than the previous definition1 because here the means for its realization are given4 #h4 ,the ,conclusion4 ,first let us consider the scientific import of the complex empirical concepts4 ,it consists in the fact that they accustom us to the coexistence of the corresponding elements of a concept4 ,so that when1 in a new experience1 we meet with some of these elements together1 we immediately suppose that we shall find in the same experience the other elements also which have not yet been ascertained4 ,such a supposition is called a conclusion4 ,a conclusion always exceeds the present experience by predicting an expected experience4 ,therefore1 the form of a conclusion is the universal form of scientific predication4 ,a conclusion must contain at least two concepts1 the one which is experienced1 and the one which1 on the basis of this experience1 is expected4 ,every complex empirical concept makes such a conclusion possible after it has been separated into simpler concepts4 ,and the simplest case is naturally the one in which there are only two parts1 or in which only two parts are taken into consideration4 ,to what extent such a conclusion is valid1 that is to say1 to what extent the experience produces the anticipated concept1 obviously depends upon the reply to a very definite fundamental question4 ,if in experience the union of the two parts of the concept occurs invariably1 so that one part of the concept is never experienced unless the other part is also experienced1 then there is the greatest probability that the expected experience will also have the same character1 and that the conclusion will prove valid or true4 ,to be sure1 there is no way of making certain that the coincident occurrence of the two concepts1 which experience has shown to be without exception hitherto1 will continue to be so also in the future4 ,for our only means of penetrating into the future consists in applying that conclusion from previous experiences to future experiences1 and it can therefore by no means claim absolute validity4 ,there are1 however1 different degrees of certainty1 or1 rather1 probability1 attaching to such a conclusion4 ,in experiences that occur but rarely the probability is that so far we have experienced only certain combinations of simple concepts1 while others1 though occurring1 have not yet entered within the limited circle of our experience4 ,in such a case a conclusion of the kind mentioned above may be right1 but there is also some probability of its being false4 ,on the other hand1 in experiences which happen extremely frequently and in the most diverse circumstances1 and in which we always find the constant and unexceptional combination1 the probability is very strong that we shall find the combination in future experiences also1 and the probability of the conclusion approaches practical certainty4 ,of course1 we can never quite exclude the possibility that new relations never as yet experienced might enter1 by which the conclusion which hitherto has always been true would now become false1 whether because the expectation entertained prove invalid in single instances or in all cases4 ,it follows from this that in general1 our conclusions will have the greater probability the more generally and the oftener the corresponding experiences have occurred and are occurring4 ,such concepts as are found consistently in many experiences otherwise different are called general concepts1 and therefore the probability of the conclusions described will be the greater the more general the concepts to which they refer4 ,this obtains to such a degree that we feel that certain very general conclusions must be true always and without exception1 and it is unthinkable to us that they can ever in any circumstances prove not valid4 ,such a statement1 however1 is never anything else than a hidden appeal to experience4 ,for the mere putting of the question1 whether the conclusion can also be false1 demonstrates that the opposite of what has proved to be the experience so far can be conceived1 and the assertion of its unthinkability only signifies that such an experience cannot be evoked in the mind by the memory for the very reason that1 as has been premised1 there are no such memories because the experiences did not exist4 ,but since1 on the other hand1 there is no hindrance to thinking any combinations of concepts at will1 we have not the least difficulty1 as everybody knows1 in thinking any sort of nonsense whatsoever4 ,only it is impossible to reproduce such combinations from memory4 ,the scientific conclusion1 therefore1 first takes the form3 if ,a is1 then ,b is also4 ,here ,a and ,b represent the two simple concepts which are known from experience to be found together in the more complex concept ,c4 ,the word is signifies here some empirical reality corresponding to the concepts4 ,the conclusion may therefore also be expressed1 somewhat more circumstantially and more precisely1 in this form3 if ,a is experienced1 the experience of ,b is also expected4 ,the evoking of this expectation1 which implies its justification1 is due to the recollection of the coincidence of the two concepts in former experiences1 and the probability depends1 in the manner described above1 upon the number of valid cases4 ,here it must be observed that even individual cases in which our expectations have been deceived do not for the most part lead us to regard the conclusion as generally untrue1 that is1 to abandon the expectation of ,b from ,a4 ,for we know that our experience is always incomplete1 that in certain circumstances we fail to notice existing factors1 and that1 therefore1 our failure to find that relation valid which1 on other occasions1 has been found to be valid1 may be attributed to subjective causes4 ,in case1 however1 of the repeated occurrence of such disappointments1 we will look elsewhere for relations between these and other elements of experience1 in order that thereafter we may foresee such cases also and include them in our anticipations4 #i4 ,the ,natural ,laws4 ,the facts just described have very frequently found expression in the doctrine of the laws of nature1 in connection with which we have often1 as in the man-made social or political laws1 conceived of a lawmaker1 who1 for some reasons1 or perhaps arbitrarily1 has ordained that things should be as they are and not otherwise4 ,but the intellectual history of the origin of the laws of nature shows that here the process is quite a different one4 ,the laws of nature do not decree what shall happen1 but inform us what has happened and what is wont to happen4 ,the knowledge of these laws1 therefore1 makes it possible for us1 as ,i have emphasized again and again1 to foresee the future in a certain degree and1 in some measure1 also to determine it4 ,we determine the future by constructing those relations in which the desired results appear4 ,if we cannot do so either because of ignorance or because of inaccessibility to the required relations1 then we have no prospect of fashioning the future according to our desires4 ,the wider our knowledge of the natural laws1 that is1 of the actual behavior of things1 the more likely and more numerous the possibilities for fashioning the future according to our desires4 ,in this way science can be conceived of as the study of how to become happy4 ,for he is happy whose desires are fulfilled4 ,in this conception the natural laws indicate what simpler concepts are found in complex concepts4 ,the complex concept water contains the simpler ones liquid1 a certain density1 transparency1 colorlessness1,b and many others4 ,the sentences1 water is a liquid1 water has a density of one1 water is transparent1 water is colorless1 or1 pale blue1 etc41 are so many natural laws4 ,b ,more precisely1 a very pale blue4 ,now what predictions do those natural laws enable us to make8 ,they enable us to predict that when we have recognized a given body as water by virtue of the above properties1 we are justified in expecting to find in the same body all the other known properties of water4 ,and so far experience has invariably confirmed such expectations4 ,furthermore1 we may expect that if in a given specimen of water we discover a relation which up to that time was unknown1 we shall find this relation also in all the other specimens of water even though they were not tested for that particular relation4 ,it is obvious how enormously this facilitates the progress of science4 ,for it is only necessary to determine this new relation in some one case accessible to the investigator to enable us to predict the same relation in all the other cases without subjecting them to a new test4 ,as a matter of fact1 this is the general method that science pursues4 ,it is this that makes it possible for science to make regular and generally valid progress through the labors of the most various investigators who work independently of one another1 and often know nothing of one another4 ,of course1 it must not be forgotten that such conclusions are always obtained in accordance with the following formula3 things have been so until now1 therefore we expect that they will be so in the future4 ,in every such case1 therefore1 there is the possibility of error4 ,thus far1 whenever an expectation was not realized1 it was almost always possible to find an explanation for the error4 ,either the inclusion of the special case in the general concept proved to be inadmissible because some of its other characteristics were absent1 or the accepted characterization of the concept required an improvement 7limitation or extension74 ,in other words1 one way or another1 there was a discrepancy between the concept and the experience1 and1 as a rule1 sooner or later it becomes possible for us to arrive at a better adjustment between them4 ,this general truth has often been interpreted to mean that in the end such an adjustment must of necessity always be possible to reach1 without exception2 in other words1 that absolutely every part of an experience can be demonstrated as conditioned by natural law4 ,evidently such an assertion far exceeds the demonstrable4 ,and even the usual conclusion cannot be applied here1 that because it has happened so in the past it will happen so in the future also4 ,for the part of our experiences that we can grasp by natural laws is infinitesimally small in comparison with that in which our knowledge still fails us entirely4 ,i will mention only the uncertainty in predicting the weather for only one day ahead4 ,moreover1 when we consider that until now only the easiest problems had been solved1 and naturally so1 because they were most accessible to the means at hand1 then we can readily see that experience offers no basis whatever for such a conclusion4 ,we must not say1 therefore1 that because we have been able so far to explain all experiences by natural laws it will be so in the future likewise4 ,for we are far from being able to explain all experiences4 ,in fact1 it is only a very small part that we have begun to investigate4 ,we are as little justified in saying that we have explained all the problems of our experience that have been subjected to scientific investigation4 ,we have by no means explained all of them4 ,every science1 even mathematics1 teems with unsolved problems4 ,so we must resign ourselves to the present status of human knowledge and ability1 and may at best express the hope founded upon previous experience1 that we shall be able to solve more and more of the incalculable number of problems of our experience without indulging in any illusions as to the perfection of this work4 #aj4 ,the ,law of ,causation4 ,by reason of its frequency and importance the mental process above described has been subjected to the most diverse investigations1 and that most general form of the scientific conclusion 7which we apply in ordinary life even much more frequently than in science7 has been raised1 under the name of the law of causation1 to a principle anteceding all experience and to the very condition making experience possible4 ,of this so much is true1 that through the peculiar physiological organization of man1 memory in the most general sense--the easier execution of such processes as have already repeatedly taken place in the organism1 as against entirely new kinds of processes--the formation of concepts 7of the recurring parts in the constantly changing variety of processes71 is especially stimulated and facilitated4 ,by it the recurring parts of experience step into the foreground1 and on account of their paramount practical importance for the security of life1 it may well be said in the sense of the theory of evolution and adaptation1 that the entire structure and mode of life of the organism1 especially of the human organism1 nay1 perhaps life itself1 is indissolubly bound up with that foresight and1 therefore1 with the law of causation also4 ,of course1 there is nothing in the way of calling such a relation an a priori relation1 if it is so desired4 ,as far as the individual is concerned it no doubt antedates all his experience1 since the entire organization which he inherits from his parents had already been formed under such an influence4 ,but that there can be forms or existence without such an attribute is shown by the whole world of the inorganic1 in which1 as far as our knowledge goes1 there is no evidence of either memory or foresight1 but only of an immediate passive participation in the processes of the world around them4,c ,c ,it cannot be objected that inorganic nature also is known to be subject to the law of causation4 ,the causal mode of regarding inorganic phenomena is a distinctly human one1 and nothing justifies the assertion that the same phenomena cannot be viewed in an entirely different manner4 ,further1 the circumstance that the causal relation is brought about by the peculiar manner in which we react upon our experiences1 has sometimes been expressed in this way--the relation of cause and effect does not exist in nature at all1 but has been introduced by men4 ,the element of truth in this is1 that a quite differently organized being1 it is to be supposed1 would be able to1 or would have to1 arrange its experiences according to quite different mutual relations4 ,but since we have no experience of such a being1 we have no possibility of forming a valid opinion of its behavior4 ,on the other hand1 we must recognize that it is possible1 at least formally1 to conceive also of kinds of experiences with no coinciding parts1 or a world in which there are no experiences at all with coinciding parts4 ,in such1 therefore1 prediction is impossible4 ,such a world will not call forth1 even in a being endowed with memory1 a conception and generalization of the various experiences in the shape of natural laws4 ,consequently we must recognize that in addition to the subjective factor in the formation of our knowledge of the world1 or that factor which is dependent upon our physico-psychical structure1 there is also the objective character of the world with which we must decidedly reckon1 or that character which is independent of us2 and that in so far the natural laws contain also objective parts4 ,to represent the relation clearly to our minds by a figure1 we may compare the world to a heap of gravel and man to a pair of sieves1 one coarser than the other4 ,as gravel passes through the double sieve pebbles of apparently equal size accumulate between the sieves1 the larger ones being excluded by the first sieve and the smaller ones allowed to pass by the second4 ,it would be an error to assert that all the gravel consisted of such pebbles of equal size4 ,but it would be equally false to assert that it was the sieves that made the pebbles equal4 #aa4 ,the ,purification of the ,causal ,relation4 ,if by experience we have found a proposition of the content1 ,if ,a is1 then ,b is also1 the two concepts ,a and ,b generally consist of several elements which we will designate as a1 a1 a1 a1 etc41 and as b1 b1 b1 b4 ,now the question arises1 whether or not all these elements are essential for the relation in question4 ,it is quite possible1 in fact1 even highly probable1 that at first only a special instance of the existing phenomena was found1 that is1 that the concept ,a1 which has been found to be connected with the concept ,b1 contains other determining parts which are not at all requisite to the appearance of ,b4 ,the general method of convincing oneself of this is by eliminating one by one the component parts of the concept ,a1 namely1 a1 a1 a1 etc41 and then seeing whether ,b still appears4 ,it is not always easy to carry out this process of elimination4 ,our greater or less ability to conduct such investigations depends upon whether we deal with things that are merely the objects of our observation1 and which we ourselves have not the power to change 7as1 for example1 astronomical phenomena71 or with things which are the objects of our experimentation1 and which we can influence4 ,in the latter case one or another factor is usually found which can be eliminated without the disappearance of ,b1 and then we must proceed in such a way as to form a corresponding new concept ,a from the factors recognized as necessary 7which new concept will be more general than the former ,a71 and to express the given proposition in the improved form3 ,if ,a is1 then ,b is also4 ,quite similar is the case with the other member of this relation4 ,it often happens that when a1 or a1 a is found1 somewhat different things appear1 which do not fit the concept as first constructed4 ,then we must multiply the experiences as much as possible in order to determine what constant elements are found in the concept ,b1 and to form from these constant elements the corresponding concept ,b4 ,the improved proposition will then read3 if ,a is1 then ,b is also4 ,this entire process may be called the purification of the causal relation4 ,by this term we express the general fact that in first forming such a regular connection1 the proper concepts are very seldom brought into relation with one another at once4 ,the cause of it is that at first we make use of existing concepts which had been formed for quite a different purpose4 ,it must therefore be regarded as a special piece of good fortune if these old concepts should at once prove suited to the new purpose4 ,furthermore1 the existing concepts are as a rule so vaguely characterized by their names1 which we must employ to express the new relation1 that for this reason also it is often necessary to determine empirically in what way the concept is to be definitely established4 ,the various sciences are constantly occupied with this work of the mutual adaptation of the concepts that enter into a causal relation4 ,by way of example1 we may take the self-understood proposition which we use when we call out to a careless child when it sticks its finger into the flame of a candle1 ,fire burns6 ,we discover that there are self-luminous bodies which produce no increase of temperature1 and therefore no sensation of pain4 ,we discover that there are processes of combustion that develop no light1 but heat enough to burn one's fingers4 ,and1 finally1 the scientific investigation of this proposition arrives at the general expression that1 as a rule1 chemical processes are accompanied by the development of heat1 but that1 conversely1 such processes may also be accompanied by the absorption of heat4 ,in this way that casual sentence which we call out to the child develops into the extensive science of thermo-chemistry when it is subjected to the continuous purification of the causal relation1 which is the general task of science4 ,it remains to be added that in this process of adapting concepts it is necessary also sometimes to follow the opposite course4 ,this is the case when exceptions are noticed in a relation as expressed for the time being2 when1 therefore1 the proposition if ,a is present1 then ,b is present also1 is in a great many instances valid1 but occasionally fails4 ,this is an indication that in the concept ,a an element is still lacking4 ,this element1 however1 is present in the instances that tally1 but absent in the negative cases1 and its absence is not noticed because it is not contained in ,a4 ,then it is necessary to seek this part1 and after it has been found1 to embody it in the concept ,a1 which thus passes into the new concept ,a4 ,this case is the obverse of the former one4 ,here the more suitable concept proves to be less general than the concept accepted temporarily1 while in the first case the improved concept is more general4 ,hence we formulate the rule3 exceptions to the temporary rule require a limitation1 while an unforeseen freedom requires an extension1 of the accepted concept4 #ab4 ,induction4 ,the form of conclusion previously discussed1 because it has been so1 ,i expect it will continue to be so in the future1 is the form through which each science has arisen and has won its real content1 that is1 its value for the judgment of the future4 ,it is called inference by induction1 and the sciences in which it is preponderatingly applied are called inductive sciences4 ,they are also called experiential or empirical sciences4 ,at the basis of this nomenclature is the notion that there are other sciences1 the deductive or rational sciences1 in which a reverse logical procedure is applied1 whereby from general principles admitted to be valid in advance1 according to an absolutely sure logical process1 conclusions of like absolute validity are drawn4 ,at the present time people are beginning to recognize the fact that the deductive sciences must give up these claims one by one1 and that they already have given them up to a certain extent2 partly because on closer study they prove to be inductive sciences1 and partly because they must forego the title and rank of a science altogether4 ,the latter alternative applies especially to those provinces of knowledge which have not been used in prophesying the future or cannot be so used4 ,to return to the inductive method--it is to be noted that ,aristotle1 who was the first to describe it1 proposed two kinds of induction1 the complete and the incomplete4 ,the first has this form3 since all things of a certain kind are so1 each individual thing is so4 ,while the incomplete induction merely says3 since many things of a certain kind are so1 presumably all things of this kind are so4 ,one instantly perceives that the two conclusions are essentially different4 ,the first lays claim to afford an absolutely certain result4 ,but it rests upon the assumption that all the things of the kind in question are known and have been tested as to their behavior4 ,this hypothesis is generally impossible of fulfilment1 since we can never prove that there are not more things of the same kind other than those known to us or tested by us4 ,moreover1 the conclusion is superfluous1 as it merely repeats knowledge that we have already directly acquired1 since we have tested all the things of the one kind1 hence the special thing to which the predication refers4 ,on the other hand1 the incomplete induction affirms something that has not yet been tested1 and therefore involves as a condition an extension of our knowledge1 sometimes an extremely important extension4 ,to be sure1 it must give up the claim to unqualified or absolute validity1 but1 to compensate1 it acquires the irreplaceable advantage of lending itself to practical application4 ,indeed1 in accordance with the scientific practice justified by experience1 described on p4 #bi1 the scientific inductive conclusion assumes the form3 because it has once been found to be so1 it will always be so4 ,from this appears the significance of this method for the enlargement of science1 which1 without it1 would have had to proceed at an incomparably slower pace4 #ac4 ,deduction4 ,in addition to the inductive method1 science has 7p4 #ch7 another method1 which1 in a sense1 should be the reverse of the inductive and is claimed to provide absolutely correct results4 ,it is called the deductive method1 and it is described as the method that leads from premises of general validity by means of logical methods of general validity to results of general validity4 ,as a matter of fact1 there is no science that does or could work in such a way4 ,in the first place1 we ask in vain1 how can we arrive at such general1 or absolutely valid1 premises1 since all knowledge is of empiric origin and is therefore equipped with the possibility of error as ineradicable evidence of this origin4 ,in the next place1 we cannot see how from principles at hand conclusions can be drawn the content of which exceeds that of these principles 7and of the other means employed74 ,in the third place1 the absolute correctness of such results is doubtful from the fact that blunders in the process of reasoning cannot be excluded even where the premises and methods are absolutely correct4 ,in practice it has actually come to pass that in the so-called deductive sciences doubts and contradictions on the part of the various investigators of the same question are by no means excluded4 ,to wit1 the discussion that has been carried on for centuries1 and is not yet ended1 over ,euclid's parallel theorem in geometry4 ,if we ask whether1 in the sense of the observations we have just made of the formation of scientific principles1 there is anything at all like deduction1 we can find a procedure which bears a certain resemblance with that impossible procedure and which1 as a matter of fact1 is frequently and to very good purpose applied in science4 ,it consists in the fact that general principles which have been acquired through the ordinary incomplete induction are applied to special instances which1 at the proposition of the principle1 had not been taken into consideration1 and whose connection with the general concept had not become directly evident4 ,through such application of general principles to cases that have not been regarded before1 specific natural laws are obtained which had not been foreseen either1 but which1 according to the probability of the thesis and the correctness of the application are also probably correct4 ,however1 the investigator1 bearing in mind the factor of uncertainty in these ratiocinations feels in each such instance the need for testing the results by experience1 and he does not consider the deduction complete until he had found confirmation in experience4 ,deduction1 therefore1 actually consists in the searching out of particular instances of a principle established by induction and in its confirmation by experience4 ,this conduces to the growth of science1 not in breadth1 but in profundity4 ,i again resort to the comparison ,i have frequently made of science with a very complex network4 ,at first glance we cannot obtain a complete picture of all the meshes4 ,so1 at the first proposition of a natural law an immediate survey of the entire range of the possible experiences to which it may apply is inachievable4 ,it is a regular1 important1 and necessary part of all scientific work to learn the extent of this range and investigate the specific forms which the law assumes in the remoter instances4 ,now1 if an especially gifted and far-seeing investigator has succeeded in stating in advance an especially general formulation of an inductive law1 it is everywhere confirmed in the course of the trial applications1 and the impression easily arises that confirmation is superfluous1 since it results simply in what had already been deduced4 ,in point of fact1 however1 the reverse is not infrequently the case1 that the principle is not confirmed1 and conditions quite different from those anticipated are found4 ,such discoveries1 then1 as a rule1 constitute the starting-point of important and far-reaching modifications of the original formulation of the law in question4 ,as we see1 deduction is a necessary complement of1 in fact1 a part of1 the inductive process4 ,the history of the origin of a natural law is in general as follows4 ,the investigator notices certain agreements in individual instances under his observation4 ,he assumes that these agreements are general1 and propounds a temporary natural law corresponding to them4 ,then he proceeds by further experimentation to test the law in order to see whether he can find full confirmation of it by a number of other instances4 ,if not1 he tries other formulations of the law applicable to the contradictory instances1 or exclusive of them1 as not allied4 ,through such a process of adjustment he finally arrives at a principle that possesses a certain range of validity4 ,he informs other scientists of the principle4 ,these in their turn are impelled to test other instances known to them to which the principle can be applied4 ,any doubts or contradictions arising from this again impel the author of the principle to carry out whatever readjustments may have become necessary4 ,upon the scientific imagination of the discoverer depends the range of instances sufficing for the formulation of the general inductive principle4 ,it also frequently depends upon conscious operations of the mind dubbed scientific instinct4 ,but as soon as the principle has been propounded1 even if only in the consciousness of the discoverer1 the deductive part of the work begins1 and the consequent test of the proposition has the most essential influence on the value of the result4 ,it is immediately evident that this deductive part is of all the more weight1 the more general the concepts in question are4 ,if1 in addition1 the inductive laws posited soon prove to be of a comparatively high degree of perfection1 we obtain the impression described above1 that an unlimited number of independent results can be deduced from a premise4 ,kant was keenly alive to the peculiarity of such a view1 which had been widely spread pre-eminently by ,euclid's presentation of geometry1 and he gave expression to his opinion of it in the famous question3 ,how are a priori judgments possible8 ,we have seen that it is not always a question of a priori judgments1 but also of inductive conclusions applied and tested according to deductive methods4 #ad4 ,ideal ,cases4 ,each experience may generally be considered under an indefinite number of various concepts1 all of which may be abstracted from that experience by corresponding observations4 ,accordingly an indefinite number of natural laws would be required for prophesying that experience in all its parts4 ,likewise the indefinite number of premises must be known through the application of which those natural laws acquire a certain content4 ,thus it seems as if it were altogether impossible to apply natural laws for the determination of a single experience to come1 and in a certain sense this is true 7p4 #cj74 ,for example1 when a child is born1 we are quite incapable of foretelling the peculiar events that will occur in its life4 ,beyond the statement that it will live a while and then die1 we can make only the broadest assertions qualified by numerous ifs and buts4 ,if1 in spite of this1 we arrange a very great part of our life and activity according to the prophecies we make in regard to numerous details in life1 basing them upon natural laws1 the question arises1 how we get over the difficulty1 or1 rather1 the impossibility just referred to4 ,the answer is1 that we repeatedly so find or can form our experiences that certain natural relations preponderatingly determine the experience1 while the other parts that remain undetermined fall into the background4 ,the prophecy will cover so considerable a part of the experience that we can forego previous knowledge of the rest4 ,we can foretell enough to render a practical construction of life possible1 and increasing experience1 whether the personal experience of the individual or the general experience of science1 constantly enlarges this controllable part of future experiences4 ,the procedure of science is similar to that of practical life1 though freer4 ,whenever an investigator seeks to test a natural law of the form3 if ,a is so1 then ,b is so1 he endeavors to choose or formulate the experiences in such a way that the fewest possible extraneous elements are present1 and that those that are unavoidable should exert the least possible influence upon the relation in question4 ,he never succeeds completely4 ,in order1 nevertheless1 to reach a conclusion as to the form the relation will take without extraneous influences1 the following general method is applied4 ,a series of instances are investigated which are so adjusted that the influence of the extraneous elements grows less and less4 ,then the relation investigated approaches a limit which is never quite reached1 but to which it draws nearer and nearer1 the less the influence of the extraneous elements4 ,and the conclusion is drawn that if it were possible to exclude the extraneous elements entirely1 the limit of the relation would be reached4 ,a case in which none of the extraneous elements of experience operate is called an ideal case1 and the inference from a series of values leading to the limit-value is an extrapolation4 ,such extrapolations to the ideal case are a quite natural procedure in science1 and a very large part of natural laws1 especially all quantitative laws1 that is1 such as express a relation between measurable values1 have precise validity only in ideal cases4 ,we here confront the fact that many natural laws1 and among them the most important1 are expressed as1 and taken to be1 conditions which never occur in reality4 ,this seemingly absurd procedure is1 as a matter of fact1 the best fitted for scientific purposes1 since ideal cases are to be distinguished by this1 that with them the natural laws take on the simplest forms4 ,this is the result of the fact that in ideal cases we intentionally and arbitrarily overlook every complication of the determining factors1 and in describing ideal cases we describe the simplest conceivable form of the class of experiences in question4 ,the real cases are then constructed from the ideal cases by representing them as the sum of all the elements that have an influence on the experience or the result4 ,just as we can represent the unlimited multitude of finite numbers by the figures up to ten1 so we can represent an unlimited quantity of complicated events by a finite number of natural laws1 and so reach a highly serviceable approximation to reality4 ,thus geometry deals with absolutely straight lines1 absolutely flat surfaces1 and perfect spheres1 though such have never been observed1 and the results of geometry come the closer to truth1 the more nearly the real lines1 surfaces1 and spheres correspond to the ideal demands4 ,similarly1 in physics1 there are no ideal gases or mirrors1 or in chemistry ideally pure substances1 though the expressed simple laws in these sciences are valid for only such bodies4 ,the non-ideal bodies of these sciences1 which reality presents in various degrees of approximation1 correspond the more closely to these laws1 the slighter the deviation of the real from the ideal4 ,and the same method is applied in the so-called mental sciences1 psychology and sociology1 in which the normal eye and a state with an entirely closed door are examples of such idealized limit-concepts4 #ae4 ,the ,determinateness of ,things4 ,a very widespread view and a very grave one1 because of its erroneous results1 is that by the natural laws things are unequivocally and unalterably determined down to the very minutest detail4 ,this is called determinism1 and is regarded as an inevitable consequence of every natural scientific generalization4 ,but an accurate investigation of actual relations produces something rather different4 ,the most general formulation of the natural law3 if ,a is experienced1 then we expect ,b1 necessarily refers in the first place only to certain parts of the thing experienced4 ,for perfect similarity in two experiences is excluded by the mere fact that we ourselves change unceasingly and one-sidedly4 ,consequently1 no matter how accurate the repetition of a former experience may be1 our very participation in it1 an element bound to enter1 causes it to be different4 ,therefore we deal with only a partial repetition of any experience1 and the common part is all the smaller a fraction of the entire experience1 the more general the concept corresponding to this part4 ,but the most general and most important natural laws apply to such very general ideas1 and accordingly they determine only a small part of the whole result4 ,other parts are determined by other laws1 but we can never point out an experience that has been determined completely and unequivocally by natural laws known to us4 ,for example1 we know that when we throw a stone1 it will describe an approximate parabolic curve in falling to the ground4 ,but if we should attempt to determine its course accurately1 we should have to take into consideration the resistance of the air1 the rotatory motion of the stone upon being thrown1 the movement of the earth1 and numerous other circumstances1 the exact determination of which is a matter beyond the power of all sciences4 ,nothing but an approximate determination of the stone's course is possible1 and every step forward toward accuracy and absoluteness would require scientific advances which it would probably take centuries to accomplish4 ,science1 therefore1 can by no means determine the exact linear course that the stone will take in its fall4 ,it can merely establish a certain broader path within which the stone's movement will remain4 ,and the path is the wider the smaller the progress science has made in the branch in question4 ,the same conditions prevail in the case of every other prediction based upon natural laws4 ,natural laws merely provide a certain frame within which the thing will remain4 ,but which of the infinitely numerous possibilities within this frame will become reality can never be absolutely determined by human powers4 ,the belief that it is possible has been evoked merely by a far-reaching method of abstraction on the part of science4 ,by assuming in place of the stone a non-extended point of mass and by disregarding all the other factors which in some way 7whether known or unknown7 exercise an influence on the stone's movement1 we can effect an apparently perfect solution of the problem4 ,but the solution is not valid for real experience1 merely for an ideal case1 which bears only a more or less profound similarity to the real4 ,it is only such an ideal world1 that is1 a world arbitrarily removed from its actual complexity1 that has the quality of absolute determinateness which we are wont to ascribe to the real world4 ,we might point to the method of abstraction generally adopted in science and to the extrapolation to ideal cases which has just been explained1 and regard the assertion of the absolute determinateness of events in the world as a justified extrapolation to the ideal case4 ,in other words1 we might say that we know all the natural laws and how to apply them perfectly to the individual instances4 ,in controversion of this it must be said that the ulterior justification of such ideal extrapolation is not yet feasible4 ,the justification lies in the demonstration that the real cases approximate the ideal the more closely the more we actualize our presumptions4 ,but in this case this is not feasible1 since1 for the greater part of our experiences1 we do not even know the approximate or ideal natural laws by the help of which we can construct such ideal cases4 ,for instance1 the whole province of organic life is at present essentially like an unknown land1 in which there are only a few widely separated paths ending in culs-de-sac4 #af4 ,the ,freedom of the ,will4 ,this relation explains why1 on the one hand1 we assume a far-reaching determinateness for many things1 that is1 for all those accessible to scientific treatment and regulation1 and why1 on the other hand1 we have the consciousness of acting freely1 that is1 of being able to control future events according to the relations they bear to our wishes4 ,essentially there is no objection to be found to a fundamental determinism which explains that this feeling of freedom is only a different way of saying that a part of the causal chain lies within our consciousness1 and that we feel these processes 7in themselves determined7 as if we ourselves determined their course4 ,nor can we prove this idea to be false1 that1 since the number of factors which influence each experience is indefinitely great and their nature indefinitely complex1 each event would appear to be determined in the eyes of an all-comprehensive intellect4 ,but to our finite minds an undetermined residue necessarily remains in each experience1 and to that extent the world must always remain in part practically undetermined to human beings4 ,thus1 both views1 that the world is not completely determined1 and that it really is1 though we can never recognize that it is1 lead practically to the same result3 that we can and must assume in our practical attitude to the world that it is only partially determined4 ,but if two different lines of thought in the whole world of experience everywhere lead to the same result1 they cannot be materially1 but merely formally or superficially1 different4 ,for those things are alike which cannot be distinguished4 ,there is no other definition of alikeness4 ,thus1 if we see that the age-long dispute between these two views always breaks out afresh without seeming to be able to reach an end1 this is readily understood1 from what has been said1 since the very same essential arguments which can be adduced of one view can be used as a prop for the other view1 because in their essential results the two are the same4 ,i have discussed this matter because it presents a very telling example of a method to be applied in all the sciences when dealing with the solution of old and ever recurrent moot questions4 ,each time we encounter such problems1 we must ask ourselves3 what would be the difference empirically if the one or the other view were correct8 ,in other words1 we first assume the one to be correct1 and develop the consequences accordingly4 ,then we assume the second to be correct and develop the consequences accordingly4 ,if in the two cases the consequences differ in a certain definite point1 we at least have the possibility of ascertaining the false view by investigating in favor of which case experience decides on this point4 ,however1 we may not conclude that by this the other view has been proved to be entirely correct4 ,it likewise may be false1 only with the peculiar quality that in the case in question it leads to the correct conclusions4 ,that such a thing is possible1 every one knows who has attentively observed his own experiences4 ,how often we act correctly in actual practice1 though we have started out on false premises6 ,the explanation of this possibility resides in the highly composite nature of each experience and each assumption4 ,it is quite possible--and1 in fact1 it is the general rule--that a certain view contains true elements1 but along with them false elements also4 ,in applications of the view where the true elements are the decisive factors1 true results are obtained1 despite the errors present4 ,likewise1 false results will be achieved where the false elements are decisive1 despite the true results that can be had1 or have been had1 elsewhere1 by means of the true elements4 ,hence1 in case of the confirmation1 we can only conclude that that portion of the view essential for the instance in question is correct4 ,one readily perceives that these observations find application in all provinces of science and life4 ,there are no absolutely correct assertions1 and even the falsest may in some respect be true4 ,there are only greater and lesser probabilities1 and every advance made by the human intellect tends to increase the degree of probability of experiential relations1 or natural laws4 #ag4 ,the ,classification of the ,sciences4 ,from the preceding observations the means may be drawn for outlining a complete table of the sciences4 ,however1 we must not regard it complete in the sense that it gives every possible ramification and turn of each science1 but that it sets up a frame inside of which at given points each science finds its place1 so that1 in the course of progressive enlargement1 the frame need not be exceeded4 ,the basic thought upon which this classification rests is that of graded abstraction4 ,we have seen 7p4 #ai7 that a concept is all the more general1 that is1 is applicable to all the more experiences1 the fewer parts or elementary concepts it contains4 ,so we shall begin the system of the sciences with the most general concepts1 that is1 the elementary concepts 7or with what for the time being we shall have to consider elementary concepts71 and1 in grading the concept complexes according to their increasing diversity1 set up a corresponding graded series of sciences4 ,one thing more is to be noted here1 that this graded series1 on account of the very large number of new concepts entering1 must produce a correspondingly great number of diverse sciences4 ,for practical reasons groups of such grades have been combined temporarily4 ,thereby a rougher classification1 though one easier to obtain a survey of1 has been made4 ,the most suitable and lasting scheme of this sort was originated by the ,french philosopher1 ,auguste ,comte1 since whom it has undergone a few changes4 ,below is the table of the sciences1 which ,i shall then proceed to explain3 ,i4 ,formal ,sciences4 ,main concept3 order ,logic1 or the science of the ,manifold ,mathematics1 or the science of ,quantity ,geometry1 or the science of ,space ,phoronomy1 or the science of ,motion ,,ii4 ,physical ,sciences4 ,main concept3 energy ,mechanics ,physics ,chemistry ,,iii4 ,biological ,sciences4 ,main concept3 life ,physiology ,psychology ,sociology ,as is evident1 we first have to deal with the three great groups of the formal1 the physical1 and the biological sciences4 ,the formal sciences treat of characteristics belonging to all experiences1 characteristics1 consequently1 that enter into every known phase of life1 and so affect science in the broadest sense4 ,in order immediately to overcome a widespread error1 ,i emphasize the fact that these sciences are to be considered just as experiential or empirical as the sciences of the other two groups1 as to which there is no doubt that they are empirical4 ,but because the concepts dealt with by the first group are so extremely wide1 and the experiences corresponding to them1 therefore1 are the most general of all experiences1 we easily forget that we are dealing with experiences at all2 and our very firmly rooted consciousness of the unqualified similarity of these experiences causes them to seem native qualities of the mind1 or a priori judgments4 ,nevertheless1 mathematics has been proved to be an empirical science by the fact that in certain of its branches 7the theory of numbers7 laws are known which have been found empirically and the deductive proof of which we have as yet not succeeded in obtaining4 ,the most general concept expressed and operative in these sciences is the concept of order1 of conjugacy or function1 the content and significance of which will become clear later in a more thorough study of the special sciences4 ,in the second group1 the physical sciences1 the arbitrariness of the classification becomes very apparent1 since these sciences are among the best known4 ,we are perfectly justified in regarding mechanics as a part of physics2 and in our day physical chemistry1 which in the last twenty years suddenly developed into an extended and important special science1 thrust itself between physics and chemistry4 ,the most general concept of the physical sciences is that of energy1 which does not appear in the formal sciences4 ,to be sure it is not a fundamental concept4 ,on the contrary1 its characteristic is undoubtedly that of compositeness1 or1 rather1 complexity4 ,the third group comprehends all the relations of living beings4 ,their most general concept1 accordingly1 is that of life4 ,by physiology is understood the entire science dealing with non-psychic life phenomena4 ,it therefore embraces what is called1 in the present often chance arrangement of scientific activities1 botany1 zoology1 and physiology of the plants1 animals1 and man4 ,psychology is the science of mental phenomena4 ,as such1 it is not limited to man1 even though for many reasons he claims by far the preponderating part of it for himself4 ,sociology is the science which deals with the peculiarities of the human race4 ,it may therefore be called anthropology1 but in a far wider sense than the word is now applied4 #ah4 ,the ,applied ,sciences4 ,it will be remarked that the grouping of the table gives no place at all in its scheme to certain branches of learning taught in the universities and equally good technical institutions4 ,we look in vain not only for theology and jurisprudence1 but also for astronomy1 medicine1 etc4 ,the explanation and justification of this is1 that for purposes of systematization we must distinguish between pure and applied sciences4 ,by virtue of their strictly conceptual exclusiveness the pure sciences constitute a regular hierarchy or graded series1 so that all the concepts that have been used and dealt with in the preceding sciences are repeated in the following sciences1 while certain characteristic new concepts enter in addition4 ,thus logic1 the science of the manifold1 exercises its dominion over all the other sciences1 while the specific concepts of physics and chemistry have nothing to do with it1 though they are of importance to all the biologic sciences4 ,through this graded addition of new 7naturally empiric7 concepts1 the construction of the pure sciences proceeds in strict regularity1 and their problems arise exclusively from the application of new concepts to all the earlier ones4 ,in other words1 their problems do not reach them accidentally from without1 but result from the action and reaction of their concepts upon one another4 ,at the same time there are problems that each day sets before us without regard to system4 ,these come from our endeavor to improve life and avert evil4 ,in the problems of life we are confronted by the whole variety of possible concepts1 and under the day's immediate compulsion we cannot wait1 if we are sowing crops or helping a sick man1 until physiology and all the other appropriate sciences have solved all the problems of plant growth and the changes of the human body and human energy4 ,when other signs fail1 we use the position of the stars for finding our way on the high seas4 ,in this manner we turn the teaching of the stars1 or astronomy1 into an applied science1 in which at first mechanics alone seemed to have a part4 ,later physics took a share in it1 then optics took a particularly prominent share1 and in recent times not only did chemistry find its way into astronomy1 but the specifically biologic concept of evolution was applied in astronomy with success4 ,thus1 side by side with the pure sciences are the applied1 which are to be distinguished from the pure sciences by the fact that they do not unfold their problems systematically1 but are assigned them by the external circumstances of man's life4 ,the pure sciences1 therefore1 almost always have a larger or smaller share in the tasks of the applied sciences4 ,for instance1 in building a bridge or railroad1 physical problems have to be taken into consideration as well as sociologic problems 7problems of trade71 and a good physician should be a psychologist as well as a chemist4 ,but since all the individual questions arising in the applied sciences may be considered essentially as problems of one or other pure science1 they need not be explicitly enumerated along with the pure sciences1 especially since their development is greatly dependent upon temporary conditions and is therefore incapable of simple systematization4 ,,part ,,ii ,,logic1 ,,the ,,science ,,of ,,the ,,manifold1 ,,and ,,mathematics #ai4 ,the ,most ,general ,concept4 ,if we try to conceive the whole structure of science according to the principle of the increasing complexity of concepts1 the first question which confronts us is1 ,what concept is the most general of all possible concepts1 so general that it enters into every concept formation and acts as a decisive factor8 ,in order to find this concept let us go back to the psycho-physical basis of concept formation1 namely1 memory1 and let us investigate what is the general characteristic determining memory4 ,we soon perceive that if a being were to lead an absolutely uniform existence1 no memories could be evoked4 ,there would be nothing by which the past could be distinguished from the present1 hence nothing by which to compare them4 ,so the primal phenomenon of conscious thought is the realization of a difference1 a difference between memory and the present1 or1 to put the same idea still more generally1 between two memories4 ,our experiences1 therefore1 are divided into two parts1 distinguished from each other4 ,in order to predicate something of a perfectly general nature concerning those parts1 without regard to their particular content1 we must1 in accordance with the means employed in human intercourse1 designate them by a name4 ,now in all human languages there is a great deal of arbitrariness and indefiniteness in the relations between the concepts and the names applied to them1 which render all accurate work in the study of concepts extremely difficult4 ,it is necessary1 therefore1 to state definitely in each particular instance with what conceptual content a given name is to be connected4 ,every experience in so far as it is differentiated from other experiences we shall call simply an experience without making a distinction between a so-called inner or outer experience4 ,many of the experiences remain isolated1 because they are not repeated in a similar form1 and so do not remain in our memory4 ,they depart from our psychic life once for all and leave no further consequences or associations4 ,but some experiences recur with greater or less uniformity1 and become permanent parts of psychic life4 ,their duration is by no means unlimited4 ,for even memories fade and disappear4 ,however1 they extend through a considerable part of life1 and that suffices to give them their character4 ,the aggregate of similar experiences1 hence of experiences conceptually generalized1 we shall call things4 ,a thing1 therefore1 is an experience which has been repeated1 and is recognized by us4 ,that is1 it is felt as repeated and conceptually comprehended4 ,in other words1 all experiences of which we have formed concepts are things1 and the concept of thing itself is the most general concept1 since1 according to its definition1 it includes all possible concepts4 ,its essence1 or determining characteristic1 lies in the possibility of differentiating any one thing from another4 ,things we do not differentiate we call the same1 or identical4 ,here we shall leave undecided the question whether this lack of differentiation occurs because we cannot1 or because we would not1 differentiate4 ,all experiences generalized into one concept are therefore felt or regarded as the same in reference to this concept4 ,now1 since concepts arise unconsciously as well as consciously1 the first is a case of identities which had been directly felt as such4 ,on the other hand1 in the second case1 the process is that of consciously disregarding or abstracting the existing differences in order to form a concept into which these do not enter4 ,this last process is applied in the highest degree possible in obtaining the concept thing4 #bj4 ,association4 ,the experience of the connection or relation between various things is also derived from the nature of our experiences in the most general sense4 ,when we recall a thing ,a1 another thing ,b comes to our mind1 the memory of which is called forth by ,a1 and vice versa4 ,the cause of this invariably lies in some experiences in which ,a and ,b occur together4 ,in fact1 ,a and ,b must have occurred together a number of times4 ,otherwise they would have disappeared from memory4 ,in other words1 it is the fact of the complex concept which appears in such connections between various things4 ,two things1 ,a and ,b1 which are connected with each other in such a way1 are said to be associated4 ,association in the most general sense means nothing more than that when we think of ,b we also have ,a in our consciousness1 and vice versa4 ,however1 we can at will make the association more definite1 so that quite definite thoughts or actions will be connected with the association of ,b4 ,these thoughts and actions are then the same for all the individual cases occurring under the concept ,a and ,b4 ,if we associate with the thing ,b another thing ,c1 we obtain a relation of the same nature as that obtained by the association of ,a and ,b4 ,but at the same time a new relation arises which was not directly sought1 namely1 the association of ,a to ,c4 ,if ,a recalls ,b1 and ,b recalls ,c1 ,a must inevitably recall ,c also4 ,this psychologic law of nature is productive of numberless special results4 ,for we can apply it directly to still another case1 the association of a fourth thing ,d to the thing ,c1 whereby new relations are necessarily established also between ,a and ,d as well as between ,b and ,d4 ,by positing the one relation ,c 3 ,d there arise two new relations not immediately given1 namely1 ,a 3 ,d and ,b 3 ,d4 ,the reason the other relations arise is because ,c was not taken free from all relations1 but had already attached to it the relations to ,a and ,b4 ,these relations of ,c1 therefore1 brought ,a and ,b into the new relation with ,d4 ,by this simplest and most general example we recognize the type of the deductive process 7p4 #da71 namely1 the discovery of relations which1 it is true1 have already been established by the accepted premises1 but which do not directly appear in undertaking the corresponding operations4 ,in the present case1 to be sure1 the deduction is so apparent that the recognition of the relations in question offers not the slightest difficulty4 ,but we can easily imagine more complicated cases in which it is much more difficult to find the actually existing relations1 and so in certain circumstances we may search for them a long time in vain4 #ba4 ,the ,group4 ,the aggregate of all individual things occurring in a definite concept1 or the common characteristics of which make up this concept1 is called a group4 ,such a group may consist of a limited or finite number of members1 or may be unlimited1 according to the nature of the concepts that characterize it4 ,thus1 all the integers form an unlimited or infinite group1 while the integers between ten and one hundred 7or the two-digit numbers7 form a limited or finite group4 ,from the definition of the group concept follows the so-called classic process of argumentation of the syllogism4 ,its form is3 ,group ,a is distinguished by the characteristic of ,b4 ,the thing ,c belongs to group ,a4 ,therefore ,c has the characteristic of ,b4 ,the prominent part ascribed by ,aristotle and his successors to this process is based upon the certainty which its results possess4 ,nevertheless1 it has been pointed out1 especially by ,kant1 that judgments or conclusions of such a nature 7which he called analytic7 have no significance at all for the progress of science1 since they express only what is already known4 ,for in order to enable us to say that the thing ,c belongs to group ,a1 we must already have recognized or proved the presence of the group characteristic ,b in ,c1 and in that case the conclusion only repeats what is already contained in the second or minor premise4 ,this is evident in the classic example3 ,all men are mortal4 ,caius is a man4 ,therefore ,caius is mortal4 ,for if ,caius's mortality were not known 7here we are not concerned how this knowledge was obtained71 we should have no right to call him a man4 ,at the same time the character of the really scientific conclusion based upon the incomplete induction becomes clear4 ,it proceeds according to the following form4 ,the attributes of the group ,a are the characteristics of a1 b1 c1 d4 ,we find in the thing ,c the characteristics a1 b1 c4 ,therefore we presume that the characteristic d will also be found in ,c4 ,the ground for this presumption is that we have learned by experience that the characteristics mentioned have always been found together4 ,it is for this reason1 and for this reason only1 that we may assume from the presence of a1 b1 c the presence of d4 ,in the case of an arbitrary combination1 in which it is possible to combine other characteristics1 the conclusion is unfounded4 ,but if1 on the other hand1 the formation of the concept ,a with the characteristics of a1 b1 c1 d has been caused by repeated and habitual experience1 then the conclusion is well founded2 that is1 it is probable4 ,as a matter of fact1 however1 that classic example which is supposed to prove the absolute certainty of the regular syllogism turns out to be a hidden inductive conclusion of the incomplete kind4 ,the premise1 ,caius is a man1 is based on the attributes a1 b1 c 7for example1 erect bearing1 figure1 language71 while the attribute d 7mortality7 cannot be brought under observation so long as ,caius remains alive4 ,in the sense of the classic logic1 therefore1 we are not justified in the minor premise1 ,caius is a man1 while ,caius is alive4 ,the utter futility of the syllogism is apparent1 since1 according to it1 it is only of dead men that we can assert that they are mortal4 ,from these observations it becomes further apparent that logic1 whether it is the superfluous classic logic or modern effective inductive logic1 is nothing but a part of the group theory1 or science of manifoldness1 which appears as the first1 because it is the most general member of the mathematical sciences 7this word taken in its widest significance74 ,but according to the hierarchic system in harmony with which the scheme of all the sciences had been consciously projected1 we cannot expect anything else than that those sciences which are needful for the pursuit of all other sciences 7and logic has always been regarded as such an indispensable science1 or1 at least1 art7 should be found collected and classified in the first science4 #bb4 ,negation4 ,when the characteristics a1 b1 c1 d of a group have been determined1 then the aggregate of all things existing can be divided into two parts1 namely1 the things which belong to the group ,a and those which do not belong to it4 ,this second aggregate may then be regarded as a group by itself4 ,if we call this group not-,a1 it follows from the definition of this group that the two groups1 ,a and not-,a1 together form the aggregate of all things4 ,this is the meaning and the significance of the linguistic form of negation4 ,it excludes the thing negated from any group given in a proposition1 and this relegates it to the second or complementary group4 ,the characteristic of such a group is the common absence of the characteristics of the positive group4 ,we must note here that the absence of even one of the characteristics a1 b1 c1 d excludes the incorporation of the thing into the group ,a1 while the mere absence of this characteristic suffices to include it in the group not-,a4 ,we can therefore by no means predicate of group not-,a that each one of its members must lack all the characteristics a1 b1 c1 d4 ,we can only say that each of its members lacks at least one of the characteristics1 but that one or some may be present1 and several or all may be absent4 ,from this follows a certain asymmetry of the two groups1 which we must bear in mind4 ,the consideration of this subject is especially important in the treatment of negation in the conclusions of formal logic4 ,as we shall make no special use of formal logic1 we need not enter into it in detail4 #bc4 ,artificial and ,natural ,groups4 ,the combination of the characteristics which are to serve for the definition of a group is at first purely arbitrary4 ,thus1 when we have chosen such an arbitrary combination1 a1 b1 c1 d1 we can eliminate one of the characteristics1 as1 for example1 c1 and form a group with the characteristics a1 b1 d4 ,such a group1 which is poorer in characteristics1 will1 in general1 be richer in members1 for to it belong1 in the first place1 all the things with the characteristics a1 b1 c1 d1 of which the first group consisted1 and in addition all the things which1 though not possessing c1 possess a1 b1 and d4 ,if we call such groups related as contain common characteristics1 though containing them in different members and combinations1 so that the definition of the one group can be derived from the other by the elimination or incorporation of individual characteristics1 then we can postulate the general thesis that in related groups those must be richer in members which are poorer in characteristics1 and inversely4 ,this is the precise statement of the proposition of the less definite thesis stated above4 ,for the purposes of systematization we have assumed that we can arbitrarily eliminate one or another characteristic of a group4 ,in experience1 however1 this often proves inadmissible4 ,as a rule we find that the things which lack one of the characteristics of a group will also lack a number of other characteristics2 in other words1 that the characteristics are not all independent of one another1 but that a certain number of them go together1 so that they are present in a thing either in common or not at all4 ,this case1 however1 can be referred to the general one first described1 by treating the characteristics belonging together as being one characteristic1 so that the group is defined solely by the independent characteristics4 ,then1 according to the definition1 we can1 without losing our connection with experience1 carry out that formal manifoldness of all possible related groups which yields what is called a classification of the corresponding things4 ,if for the determination of a group a definite number of independent characteristics is taken1 say1 a1 b1 c1 d1 and e1 then we have at first the narrowest or poorest group abcde4 ,by the elimination of one characteristic we obtain the five groups1 bcde1 acde1 abde1 abce1 and abcd4 ,if we omit one other characteristic we get ten different groups abc1 abd1 abe1 acd1 ace1 ade1 bcd1 bce1 bde1 cde4 ,likewise1 there are ten groups with two characteristics each1 and finally five groups with one characteristic each4 ,all these groups are related4 ,there is a science1 the ,theory of ,combinations1 which gives the rules by which1 in given elements or characteristics1 the kind and number of the possible groups can be found4 ,the theory of combinations enables us to obtain a complete table and survey of all possible complex concepts which can be formed from given simple ones 7whether they be really elementary concepts1 or only relatively so74 ,when in any field of science the fundamental concepts have been combined in this manner1 a complete survey can be had of all the possible parts of this science by means of the theory of combinations4 ,in order to present this process vividly to our minds1 let us take as an example the science of the chemical combination of substances which form an important part of chemistry4 ,there are about eighty elements in chemistry1 and this science has to treat of a7 each of the eighty elements by itself b7 all substances containing two elements and no more c7 all substances containing three elements d1 e1 f1 etc47 the substances containing four1 five1 and six1 etc41 elements1 until finally we reach a group 7not existing in experience7 embracing substances formed of all the elements4 ,that there is no such substance in the present scope of human knowledge has1 of course1 no significance for the structure of the scheme4 ,what is significant is the fact that the scheme really embraces and arranges all possible substances in such a way that we cannot conceive of any case in which a newly discovered substance cannot after examination immediately be classed with one of the existing groups4 ,to cite an example from another science4 ,physics1 it will be recalled1 may be considered to be the science of the different kinds of energy4 ,this science1 accordingly1 is divided first into the study of the properties of each energy1 and then into the study of the relations of two energies1 of three energies1 of four energies1 etc4 ,here1 too1 we may say that in the end there can be no physical phenomenon which cannot be placed in one of the groups so obtained4 ,of course1 neither in chemistry nor in physics does this mean that each new case will fall within the scheme obtained by the exhaustive combination of elementary concepts 7whether chemical elements or kinds of energy7 known at the time4 ,it is quite possible that a new thing under investigation contains a new elementary concept1 so that on account of it the scheme must be enlarged through the embodiment of this new element4 ,but simultaneously a corresponding number of new groups appear in the scheme1 and the investigator's attention is directed to the fact that he still has a reasonable prospect1 in favorable circumstances1 of discovering these new things also4 ,thus combinatory schematization serves not only to bring the existing content of science into such order that each single thing has its assigned place1 but the groups which have thereby been found to be vacant1 to which as yet nothing of experience corresponds1 also point to the places in which science can be completed by new discoveries4 ,from the above presentation it is apparent how from the two concepts thing and association alone a great manifoldness of various and regular forms can be developed4 ,they are purely empirical relations1 for the fact that several things can be combined in the graded series described above according to a fixed rule does not follow merely from the two concepts1 but must be experienced4 ,but1 on the other hand1 both concepts are so general that the experiences obtained in some cases can be applied to all possible experiences and may serve the purpose of classifying and making a general survey of them4 ,the above statements1 however1 have by no means exhausted the possibilities4 ,for it has been tacitly assumed that in the combination of several things the sequence according to which this combination takes place should not condition a difference of the result4 ,this is true of a number of things1 but not of all4 ,in order1 therefore1 to exhaust the possibilities the theory of combinations must be extended also to cases in which the sequence is to be taken account of1 so that the form ab is regarded as different from ba4 ,we will not undertake to work out the results of this assumption4 ,it is obvious that the manifoldness of the various cases is much greater than if we neglect the sequence4 ,on this point we have one more observation to make1 that further causes for diversity exist4 ,it is true that a chemical combination is not influenced by the sequence in which its elements enter the combination1 but there do occur with the same elements differences in their quantitative relations1 and thereby a new complexity is introduced into the system1 so that two or more similar elements can form different combinations according to the difference in the quantitative relations4 ,still1 even with this1 the actual manifoldness is not exhausted1 for from the same elements and with the same quantitative relations there can arise different substances called isomeric1 which1 for all their similarity1 possess different energy contents4 ,but the first scheme is not demolished1 nor does it become impracticable because of this increase of manifoldness4 ,what simply happens is that several different things instead of one appear in the same group of the original scheme1 the systematic classification of which necessitates a further schematization by the use of other characteristics4 #bd4 ,arrangement of the ,members4 ,since we have started from the proposition that all members of a group are different from one another1 we have perfect liberty to arrange them4 ,the most obvious arrangement according to which some one definite member is followed by a single other member and so forth 7as1 for example1 the arrangement of the letters of the alphabet7 is by no means the only mode of arrangement1 though it is the simplest4 ,besides this linear arrangement1 there is also1 for instance1 the one in which two new members follow simultaneously upon each previous one1 or the members may be disposed like a number of balls heaped up in a pyramid4 ,however1 we shall not have much occasion to occupy ourselves with these complex types of arrangement1 and can therefore limit our considerations at first to the simplest1 that is1 to the linear arrangement4 ,this simplest of all possible forms expresses itself in the fact that the immediately experienced things of our consciousness are arranged in this way4 ,in point of fact1 the contents of our consciousness proceed in linear order1 one single new member always attaching itself to an existing member4 ,this law1 however1 is not strictly and invariably adhered to4 ,it sometimes happens that our consciousness continues for a while to pursue the direction of thought it has once taken1 although a branching off had already taken place at a former point1 at which a new chain of thought had begun4 ,nevertheless1 one of these chains usually breaks off very soon1 and the linear character of the inner experience is immediately restored4 ,of certain specially powerful intellects it is recorded that they could keep up several lines of thought for a considerable length of time--,julius ,csar1 for instance4 ,the biologic peculiarity here mentioned of the linear juxtaposition of the contents of our consciousness has led to the concept of time1 which has been appropriately called a form of inner life4 ,that all our experiences succeed each other in time is equivalent to saying that our thought processes represent a group in linear arrangement4 ,as appears from the above observations1 this is by no means an absolute form1 unalterable for all times4 ,on the contrary1 a few highly developed individuals have already begun to emancipate themselves from it4 ,but the existing form is so firmly fixed through heredity and habit that it still seems impracticable for most men to imagine the succession of the inner experiences in a different way than by a line or by one dimension4 ,since1 on the other hand1 we have all learned to feel space as tri-dimensional1 although optically it appears to possess only two dimensions 7we see length and breadth1 and only infer thickness from secondary characteristics71 we come to recognize that the linear form by which we represent the succession of our experiences is a matter of adaptation1 and that because the change has been extremely slight in the course of centuries it produces the impression of being unalterable4,d ,d ,mathematicians who busy themselves a great deal with the formal theory of four-dimensional space1 seem to acquire a capacity for imagining this form as easily as the three-dimensional form with which we are all familiar4 ,therefore1 despite the oft-repeated statements to the contrary1 it is not impossible to imagine four-dimensional space4 ,only1 we must not attempt to represent to ourselves four-dimensional space in three-dimensional space1 especially not without a knowledge of its properties4 ,these discussions lead to a further difference that can exist in groups of linear arrangement4 ,while in the first example we chose1 the alphabet1 the sequence was quite arbitrary1 since any other sequence is just as possible1 the same cannot be said of experiences into which the element of time enters4 ,these are not arbitrary1 but are arranged by special circumstances depending upon the aggregate of things which co-operate in the given experiences4 ,while1 therefore1 a group with free members1 that is1 members not determined in their arrangement by special circumstances1 can be brought into linear order in very different ways1 there are groups in which only one of those orders actually occurs4 ,we see at once that in free groups the number of different orders possible is the greater1 the greater the group itself4 ,the theory of combinations teaches how to calculate these numbers which play a very important rle in the various provinces of mathematics4 ,the naturally ordered groups always represent a single instance out of these possibilities1 the source of which always lies outside the group concept1 that is1 it proceeds from the things themselves which are united into a group4 #be4 ,numbers4 ,an especially important group in the linear order is that of the integral numbers4 ,its origin is as follows3 ,first we abstract the difference of the things found in the group1 that is1 we determine1 although they are different1 to disregard their differences4 ,then we begin with some member of the group and form it into a group by itself4 ,it does not matter which member is chosen1 since all are regarded as equivalent4 ,then another member is added1 and the group thus obtained is again characterized as a special type4 ,then one more member is added1 and the corresponding type formed1 and so on4 ,experience teaches that never has a hindrance arisen to the formation of new types of this kind by the addition of a single member at a time1 so that the operation of this peculiar group formation may be regarded as unlimited or infinite4 ,the groups or types thus obtained are called the integral numbers4 ,from the description of the process it follows that every number has two neighbors1 the one the number from which it arose by the addition of a member1 and the other the number which arose from it by the addition of a member4 ,in the case of the number one with which the series begins1 this characteristic is present in a peculiar form1 the preceding group being group zero1 that is1 a group without content4 ,this number in consequence reveals certain peculiarities into which we cannot enter here4 ,now1 according to a previous observation 7p4 #fd71 not only does the order bring every number into relation with the preceding one1 but since this last for its part already possesses a great number of relations to all preceding1 these relations exert their influence also upon the new relation4 ,this fact gives rise to extraordinarily manifold relations between the various numbers and to manifold laws governing these relations4 ,the elucidation of them forms the subject of an extensive science4 #bf4 ,arithmetic1 ,algebra1 and the ,theory of ,numbers4 ,from this regular form of the number series numerous special characteristics can be established4 ,the investigations leading to the discovery of these characteristics are purely scientific1 that is1 they have no special technical aim4 ,but they have the uncommonly great practical significance that they provide for all possible arrangements and divisions of numbered things1 and so have instruments at hand ready for application to each special case as it arises4 ,i have already pointed out that in this lies the positive importance of the theoretical sciences4 ,for practical reasons the study of them must be as general as possible4 ,this science is called arithmetic4 ,arithmetic undergoes an important generalization if the individual numbers in a calculation are disregarded and abstract signs standing for any number at all are used in their place4 ,at first glance this seems superfluous1 since in every real numerical calculation the numbers must be reintroduced4 ,the advantage lies in this1 that in calculations of the same form1 the required steps are formally disposed of once for all1 so that the numerical values need be introduced only at the conclusion and need not be calculated at each step4 ,moreover1 the general laws of numerical combination appear much more clearly if the signs are kept1 since the result is immediately seen to be composed of the participating members4 ,thus1 algebra1 that is1 calculation with abstract or general quantities1 has developed as an extensive and important field of general mathematics4 ,by the theory of numbers we understand the most general part of arithmetic which treats of the properties of the numerical bodies formed in some regular way4 #bg4 ,co-ordination4 ,so far our discussion has confined itself to the individual groups and to the properties which each one of them exhibits by itself4 ,we shall now investigate the relations which exist between two or more groups1 both with regard to their several members and to their aggregate4 ,if at first we have two groups the members of which are all differentiated from one another1 then any one member of the one group can be co-ordinated with any one member of the other group4 ,this means that we determine that the same should be done with every member of the second group as is done with the corresponding member of the first group4 ,that such a rule may be carried out we must be able to do with the members of all the groups whatever we do with the members of one group4 ,in other words1 no properties peculiar to individual members may be utilized1 but only the properties that each member possesses as a member of a group4 ,as we have seen1 these are the properties of association4 ,first1 the co-ordination is mutual1 that is1 it is immaterial to which of the two groups the processes are applied4 ,the relation of the two groups is reciprocal or symmetrical4 ,further1 the process of co-ordination can be extended to a third and a fourth group and so on1 with the result that what has been done in one of the co-ordinated groups must happen in all4 ,if hereby the third group is co-ordinated with the second1 the effects are quite the same as if it were co-ordinated directly with the first instead of indirectly through the second4 ,and the same is true for the fourth and the fifth groups1 etc4 ,thus1 co-ordination can be extended to any number of groups we please1 and each single group proves to be co-ordinated with every other4 ,finally1 a group can be co-ordinated with itself1 each of its members corresponding to a certain definite other member4 ,it is not impossible that individual members should correspond to themselves1 in which case the group has double members1 or double points4 ,the limit-case is identity1 in which every member corresponds to itself4 ,this last case cannot supply any special knowledge in itself1 but may be applied profitably to throw light on those observations for which it represents the extreme possibility4 #bh4 ,comparison4 ,if we have two groups ,a and ,b1 and if we co-ordinate their members severally1 three cases may arise4 ,either group ,a is exhausted while there are members remaining in ,b1 or ,b is exhausted before ,a1 or1 finally1 both groups allow of a mutual co-ordination of all their members4 ,in the first case ,a is called1 in the broader sense of the word1 smaller than ,b1 in the second ,b is called smaller than ,a1 in the third the two groups are said to be of equal magnitude4 ,the expression1 ,b is greater than ,a1 is equivalent to the expression1 ,a is smaller than ,b1 and inversely4 ,it is to be noted that the relations mentioned above are true1 whether the members are considered as individually different from one another or whether the difference of the members is disregarded1 and they are treated as alike4 ,this comes from the fact that every definite co-ordination of a group can be translated into every other possible co-ordination by exchanging two members at a time in pairs4 ,since in this process one member is each time substituted for another1 and a gap therefore can never occur in its place1 the group in the new arrangement can be co-ordinated with the other group as successfully as in the old arrangement4 ,at the same time we learn from this that in every co-ordination of a group with itself1 independently of the arrangement of its members1 it must prove equal to itself4 ,by carrying out the co-ordination proof is further supplied of the following propositions3 greater than ,if group ,a is equal to group ,b smaller than greater than and group ,b is equal to group ,c smaller than greater than then group ,a is equal to group ,c smaller than ,from this it follows that any collection of finite groups whatsoever1 of which no one is equal to the other1 can always be so arranged that the series should begin with the smallest and end with the greatest1 and that a larger should always follow a smaller4 ,this order would be unequivocal1 that is1 there is only one series of the given groups which has this peculiarity4 ,as we shall soon see1 the series of integers is the purest type of a series so arranged4 ,in comparing two infinitely large groups by co-ordination1 it may be said on the one hand that never will one group be exhausted while the other still contains members4 ,accordingly1 it is possible to designate two unlimited or infinite groups 7or as many such groups as we please7 as equal to each other4 ,on the other hand1 the statement that in both groups each member of the one is co-ordinated with a member of the other has no definite meaning on account of the infinitely large number of members4 ,the definition of equality is therefore not completely fulfilled1 and we must not loosely apply a principle valid for finite groups to infinite groups4 ,this consideration1 which may assume very different forms according to circumstances1 explains the paradoxes of the infinite1 that is1 the contradictions which arise when concepts of a definite content are applied to cases possessing in part a different content4 ,if we wish to attempt such an application1 we must in each instance make a special investigation as to the manner in which the relations on their part change by the change of those contents 7or premises74 ,as a general rule we must expect that the former relations will not remain valid in these circumstances without any change at all4 ,in the course of these observations we have learned how co-ordination can be used for obtaining a number of fundamental and multifariously applied principles4 ,from this alone the great importance of co-ordination is evident1 and later we shall see that its significance is even more far-reaching4 ,the entire methodology of all the sciences is based upon the most manifold and many-sided application of the process of co-ordination1 and we shall have occasion to make use of it repeatedly4 ,its significance may be briefly characterized by stating that it is the most general means of bringing connection into the aggregate of our experiences4 #bi4 ,counting4 ,the group of integral numbers1 because of its fundamental simplicity and regularity1 is by far the best basis of co-ordination4 ,for while arithmetic and the theory of numbers give us a most thorough acquaintance with the peculiarities of this group1 we secure by the process of co-ordination the right to presuppose these peculiarities and the possibility of finding them again in every other group which we have co-ordinated with the numerical group4 ,the carrying out of such co-ordination is called counting1 and from the premises made it follows that we can count all things in so far as we disregard their differences4 ,we count when we co-ordinate in turn one member of a group after another with the members of the number series that succeed one another until the group to be counted is exhausted4 ,the last number required for the co-ordination is called the sum of the members of the counted group4 ,since the number series continues indefinitely1 every given group can be counted4 ,numerals have been co-ordinated with names as well as with signs4 ,the former are different in the different languages1 the latter are international1 that is1 they have the same form in all languages4 ,from this proceeds the remarkable fact that the written numbers are understood by all educated men1 while the spoken numbers are intelligible only within the various languages4 ,the purpose of counting is extremely manifold4 ,its most frequent and most important application lies in the fact that the amount affords a measure for the effectiveness or the value of the corresponding group1 both increasing and decreasing simultaneously4 ,a further number serves as a basis for divisions and arrangements of all kinds to be carried out within the group1 whereby liberal use is made of the principle that everything that can be effected in the given number group can also be effected in the co-ordinated counted group4 #cj4 ,signs and ,names4 ,the co-ordination of names and signs with numbers calls for a few general remarks on co-ordination of this nature4 ,the possibility of carrying out the formal operations effected in one of the groups upon the co-ordinated group itself facilitates to an extraordinary extent the practical shaping of the reality for definite purposes4 ,if by counting we have ascertained that a group of people numbers sixty1 we can infer without actually executing the steps that it is possible to form these men in six rows of ten1 or in five rows of twelve1 or in four rows of fifteen1 but that we cannot obtain complete rows if we try to arrange them in sevens or elevens4 ,these and numberless other peculiarities we can learn of the group of men from its amount1 that is1 from its co-ordination with the numerical group of sixty4 ,in co-ordination1 therefore1 we have a means of acquainting ourselves with facts without having to deal directly with the corresponding realities4 ,it is clear that men will very soon notice and avail themselves of so enormous an advantage for the mastery and shaping of life4 ,thus1 we see the process of co-ordination in general use among the most primitive men4 ,even the higher animals know how to utilize co-ordination consciously4 ,when the dog learns to answer to his name1 when the horse responds to the ,whoa and the ,gee of his driver there is in each case a co-ordination of a definite action or series of actions1 that is1 of a concept with a sign1 or1 in other words1 of a concept with a member of another group2 and in this there need not be the least similarity between the things co-ordinated with each other4 ,the only requirement is that on the one hand the co-ordinated sign should be easily and definitely expressed and be to the point1 and that1 on the other hand1 it should be easily understood1 that is1 comprehended by the senses and unmistakably differentiated from other signs co-ordinated with other things4 ,thus1 we find that the most frequent concepts of co-ordinated sound signs form the beginnings of language in the narrower sense4 ,it is very difficult to ascertain for what reasons the particular forms of sound signs have been chosen1 nor is it a matter of great importance4 ,in the course of time the original causes have disappeared from our consciousness and the present connection is purely external4 ,this is evident from the enormous difference of languages in which hundreds of different signs are employed for the same concept4 ,now it would be quite possible to solve the problem of co-ordinating with each group of concepts a corresponding group of sounds1 so that each concept should have its own sound1 or1 in other words1 that the co-ordination should be unambiguous4 ,it would not by any means be beyond human power to accomplish this1 if it were not for the fact that the concepts themselves are still in so chaotic a state as they are at present4 ,we have seen that the attempts of ,leibnitz and ,locke to draw up a system of concepts1 if only in broad outline1 have undergone no further development since4 ,even the most regulated concepts as well as the familiar concepts of daily life are in ceaseless flux1 while the co-ordinated signs are comparatively more stable4 ,but they1 too1 undergo a slow change1 as the history of languages shows1 and in accordance with quite different laws from those which govern the change of concepts4 ,the consequence is that in language the co-ordination of concepts and words is far from being unambiguous4 ,the science of language designates the presence of several names for the same concept and of several concepts for the same name by the words synonym and homonym4 ,these forms1 which have arisen accidentally1 signify so many fundamental defects of language1 since they destroy the principle of unambiguity upon which language is based4 ,in consequence of the false conception of its nature we have until now positively shrunk from consciously developing language in such a way that it should more and more approach the ideal of unambiguity4 ,such an ideal is in fact scarcely known1 much less recognized4 #ca4 ,the ,written ,language4 ,sound signs1 to be sure1 possess the advantage of being produced easily and without any apparatus1 and of being communicable over a not inconsiderable distance4 ,but they suffer under the disadvantage of transitoriness4 ,they suffice for the purpose of temporary understanding and are constantly being used for that4 ,if1 on the other hand1 it is necessary to make communications over greater distances or longer periods of time1 sound signs must be replaced by more permanent forms4 ,for this we turn to another sense1 the sense of sight4 ,since optic signs can travel much greater distances than sound signs without becoming indistinguishable1 we first have the optical telegraphs1 which find application1 though rather limited application1 in very varying forms1 the most efficient being the heliotrope4 ,the other sort of optic signs is much more generally used4 ,these are objectively put on appropriate solid bodies1 and last and are understood as long as the object in question lasts4 ,such signs form the written language in the widest sense1 and here1 too1 it is a question of co-ordinating signs and concepts4 ,what ,i have said concerning the very imperfect state of our present concept system is true also of these two groups4 ,on the other hand1 the written signs are not subject to such great change as the sound signs1 because the sound signs must be produced anew each time1 whereas the written signs inscribed on the right material may survive hundreds1 even thousands of years4 ,hence it is that the written languages are1 upon the whole1 much better developed than the spoken languages4 ,in fact1 there are isolated instances in which it may be said that the ideal has well-nigh been reached4 ,as we have already pointed out1 such a case is furnished by the written signs of numbers4 ,by a systematic manipulation of the ten signs #j #a #b #c #d #e #f #g #h #i it is not only possible to co-ordinate a written sign with any number whatsoever1 but this co-ordination is strictly unambiguous1 that is1 each number can be written in only one way1 and each numerical sign has only one numerical significance4 ,this has been obtained in the following manner3 ,first1 a special sign is co-ordinated to each of the group of numbers from zero to nine4 ,the same signs are co-ordinated with the next group1 ten to nineteen1 containing as many numbers as the first4 ,to distinguish the second from the first group1 the sign one is used as a prefix4 ,the third group is marked by the prefixed sign two1 and so on1 until we reach group nine4 ,the following group1 in accordance with the principle adopted1 has as its prefix the sign ten1 which contains two digits4 ,all the succeeding numbers are indicated accordingly4 ,from this the following result is assured3 ,first1 no number in its sequence escapes designation2 second1 never is an aggregate sign used for two or more different numbers4 ,both these circumstances suffice to secure unambiguity of co-ordination4 ,it is known that the system of rotation just described is by no means the only possible one4 ,but of all systems hitherto tried it is the simplest and most logical1 so that it has never had a serious rival1 and the clumsy notation with which the ,greeks and ,romans had to plague themselves in their day was immediately crowded out1 never to return again upon the introduction of the ,indo-,arabic notation1 which has made its way in the same form among all the civilized nations and constitutes a uniform part of all their written languages4 ,the comparison of the spoken and the written languages offers a very illuminating proof of the much greater imperfection of the language of words4 ,the number #ahfed is expressed in the ,english language by eighteen thousand six hundred and fifty-four1 that is1 the second figure is named first1 then the first1 the third1 the fourth1 and the fifth4 ,in addition1 four different designations are used to indicate the place of the figures1 -teen1 -thousand1 -hundred1 and -ty4 ,a more aimless confusion can scarcely be conceived4 ,it would be much clearer to name the figures simply in their sequence1 as one-eight-six-five-four4 ,besides1 this would be unambiguous4 ,if we should desire to indicate the place value in advance1 we could do so in some conventional way1 for example1 by stating the number of digits in advance4 ,this1 however1 would be superfluous1 and ordinarily should be omitted4,e ,e ,the usual designation of the larger groups1 ten1 hundred1 thousand1 million1 billion1 etc41 is also quite irrational4 ,if it is our object to secure expressions for place values in as few words as possible1 we find that the numbers of the form #ajbn1 in which n is a whole number1 must receive their own names1 that is1 #aj1 #ajj1 #aj1jjj1 #ajj1jjj1jjj etc4 ,in this way the problem of designating as many numbers as possible by as few words as possible is solved4 #cb4 ,pasigraphy and ,sound ,writing4 ,there are two possibilities for co-ordination between concepts and written signs4 ,either the co-ordination is direct1 so that it is only a matter of providing every concept with a corresponding sign1 or it is indirect1 the signs serving only the purpose of expressing the language sound4 ,in the latter case the written language is based entirely upon the sound language1 and the only problem1 comparatively easy to solve1 is to construct an unambiguous co-ordination between sound and sign4 ,the ,chinese script follows the direct process1 but all the scripts of the ,european-,american civilized peoples are based on the indirect process4 ,this1 it is true1 is the case only in ordinary1 non-scientific language1 while for science the ,european nations also have to a large extent built up a direct concept writing4 ,one example of this we have seen in the number signs4 ,musical notation furnishes another instance1 though by far not so perfect4 ,the use of the different keys destroys the unambiguous connection between the pitch and the note sign1 and the signatures placed at the beginning of a whole staff have the defect of removing the sign from the place where it is applied4 ,despite this imperfection musical notation is quite international1 and every one who understands ,european music also understands its signs4,f ,f ,it is not difficult to perfect musical notation with a view to unambiguity1 a thing which would greatly facilitate the study of music4 ,fundamentally we need not hesitate to recognize in concept writing or pasigraphy a more complete solution of the problem of sign arrangement4 ,even the very incomplete ,chinese pasigraphy renders possible written intercourse1 especially for mercantile purposes1 between the various ,east-,asiatic peoples who speak some dozens of different languages4 ,but each language community translates the common signs into its own words1 just as we do in the case of the number signs4 ,but in order that such a system of representation should be complete it must fulfil a whole series of conditions for which scarcely a remote possibility is to be discerned at present4 ,at first the concepts could simply be taken as found in the words and grammatical forms of the various languages1 and each one provided with an arbitrary sign4 ,such approximately is the ,chinese system4 ,but a system of that sort entails an extreme burdening of the memory1 which results both from the great number of words and from the necessity of keeping the signs within certain bounds of simplicity4 ,if we consider that the complex concepts are formed according to laws1 to a large extent still unknown1 from a relatively small number of elementary concepts1 we may attempt to build up the signs of the complex concepts by the combination of those of the elementary concepts according to corresponding rules4 ,then it would only be necessary to learn the signs for the elementary concepts and the rules of combination in order for us to be able to represent all the possible concepts4 ,this would provide even for the natural enlargement of the concept world1 since every new elementary concept would receive its sign and would then serve as the basis from which to deduce all the complex concepts dependent upon it4 ,in fact1 even should a concept hitherto regarded as elementary prove to be complex1 it would not be difficult to declare that its sign1 like the name of an extinct race1 is dead1 and after the lapse of sufficient time to use it for other purposes4 ,the numerical signs offer an excellent example for the elucidation of this subject1 and at the same time serve as a proof that in limited provinces the ideal has already been attained4 ,another very instructive example is furnished by the chemical formulas1 which1 though they use the letters of the ,european languages1 do not associate with them sound concepts1 but chemical concepts4 ,since the chemical concepts are co-ordinated with certain letters1 it is possible1 in the first place1 to denote the composition of all combinations qualitatively by the combination of the corresponding letters4 ,but since quantitative composition proceeds according to definite relations which are determined by a variety of specific numbers peculiar to each element and called its combining weight1 we need only add to the sign of the element the concept of the combining weight in order to represent in the second place the quantitative composition4 ,further1 the multiples mentioned can also be given4 ,since1 moreover1 there are various substances which1 despite equal composition1 possess different properties1 the attempt has been made to express this new manifoldness by the position of the element signs on the paper1 and in more recent times also by space representation4 ,and here1 too1 rules have been worked out in which the scheme affords a close approach to experience4 ,this example shows how1 by the constant increase of the complexity of a concept 7here the chemical composition71 ever greater and more manifold demands are made upon the co-ordinated scheme4 ,the form of expression first chosen is not always adequate to keep pace with the progress of science4 ,in this case it must be radically changed and formed anew to meet the new demands4 #cc4 ,sound ,writing4 ,in point of unambiguity of co-ordination phonetic writing is far more imperfect than concept writing4 ,it is obvious that in phonetic writing all the faults already present in the co-ordination between concept and sound are transferred to the written language4 ,to these are added the defects as regards unambiguity occurring in co-ordination between sound and sign from which no language is free4 ,in some languages1 in fact1 notably in ,english1 these defects amount to a crying calamity4 ,the principle of unambiguity would require that there should never be a doubt as to the way in which a spoken word is written1 and as little doubt as to the way in which a written word is spoken4 ,it needs no proof to show how often the principle is violated in every language4 ,in the ,german language the same sound is represented by f1 v1 and ph2 in the ,english by f and ph4 ,and in both ,german and ,english quite different sounds are associated with c1 g1 s1 and other letters4 ,the fact that orthographic mistakes can be made in the writing of any language is direct proof of its imperfection1 and the oftener this possibility occurs the more imperfect is the language in this respect4 ,we know that the spelling reforms begun in ,germany more than ten years ago and recently in ,america and ,england1 have for their object unambiguity in the co-ordination between sign and sound4 ,still it must be admitted that this tendency has not always been pursued undeviatingly4 ,a few innovations1 in fact1 undoubtedly represent a step backward4 #cd4 ,the ,science of ,language4 ,a comparison of our investigations--which we cannot present in detail but only indicate--with the science of language or philology as taught in the universities and in a great number of books1 reveals a great difference between them4 ,this academic philology makes a most exhaustive study of relations1 which from the point of view of the purpose of language are of no consequence whatever1 such as most of the rules and usages of grammar4 ,a study of this sort must naturally confine itself to a mere determination of whether certain individuals or groups of individuals have or have not conformed to these rules4 ,even the chief subject of modern comparative philology1 the study of the relations of the word forms to one another and their changes in the course of history1 both within the language communities and when transferred to other localities1 appear to be quite useless from the point of view of the theory of co-ordination4 ,for it is indeed of little moment to us to learn by what process of change1 as a rule utterly superficial1 a certain word has come to be co-ordinated with a concept entirely different from the one with which it had been previously co-ordinated4 ,of incomparably greater importance would be investigations concerning the gradual change of the concepts themselves1 although by no means as important as the real study of concepts4 ,to be sure1 such investigations are much more difficult than the study of word forms set down in writing4 ,nevertheless1 on account of a historical process1 which it would lead us too far afield to discuss1 an idea of such word investigations has been formed which is wholly disproportionate to their importance4 ,and if we ask ourselves what part such labors have taken in the progress of human civilization1 we are at a loss for an answer4 ,students of the science of language make a sharp distinction between it and the knowledge of language1 which is regarded as incomparably lower4 ,but while a knowledge of language is important in at least one respect1 in that it presents to us the cultural material set down in other languages1 or makes them accessible in translation to those who do not know foreign languages1 philology is of no service in this respect at all1 and the pursuit of it will seem as inconceivably futile to future science as the scholasticism of the middle ages seems to us now4 ,the unwarranted importance attached to the historical study of language forms is paralleled by the equally unwarranted importance ascribed to grammatical and orthographic correctness in the use of language4 ,this perverse pedantry has been carried to such lengths that it is considered almost dishonorable for any one to violate the usual forms of his mother tongue1 or even of a foreign language1 like the ,french4 ,we forget that neither ,shakespeare nor ,luther nor ,goethe spoke or wrote a correct ,english or ,german1 and we forget that it cannot be the object of a true cultivation of language to preserve as accurately as possible existing linguistic usage1 with its imperfections1 amounting at times to absurdities4 ,its real object lies rather in the appropriate development and improvement of the language4 ,we have already mentioned the fact that in one department1 orthography1 the true conception of the nature of language and of its development is gradually beginning to assert itself4 ,among most nations efforts are being made to improve orthography with a view to unambiguity1 and when once sufficient clearness is had as to the object aimed for in spelling1 there will be no special difficulty in finding the required means to attain it4 ,but in all the other departments of language we are still almost wholly without a conception of the genuine needs4 ,though the example of the ,english language proves that we can entirely dispense with the manifold co-ordinations in the same sentence as appearing in the special plural forms of the adjective1 verb1 pronoun1 etc41 yet the idea of consciously applying to other languages the natural process of improvement unconsciously evolved in the ,english language seems not to have occurred even to the boldest language reformers4 ,so strongly are we all under the domination of the schoolmaster ideal1 that is to say1 the ideal of preserving every linguistic absurdity and impracticability simply because it is good usage4 ,a twofold advantage will have been attained by the introduction of a universal auxiliary language 7p4 #ahc74 ,recently the efforts in that direction have made considerable progress4 ,in the first place it will provide a general means of communication in all matters of common human interest1 especially the sciences4 ,this will mean a saving of energy scarcely to be estimated4 ,in the second place1 the superstitious awe of language and our treatment of it will give way to a more appropriate evaluation of its technical aim4 ,and when by the help of the artificial auxiliary language1 we shall be able to convince ourselves daily how much simpler and completer such a language can be made than are the natural languages1 then the need will irresistibly assert itself to have these languages also participate in its advantages4 ,the consequences of such progress to human intellectual work in general would be extraordinarily great4 ,for it may be asserted that philosophy1 the most general of all the sciences1 has hitherto made such extremely limited progress only because it was compelled to make use of the medium of general language4 ,this is made obvious by the fact that the science most closely related to it1 mathematics1 has made the greatest progress of all1 but that this progress began only after it had procured both in the ,indo-,arabic numerals and in the algebraic signs a language which actually realizes very approximately the ideal of unambiguous co-ordination between concept and sign4 #ce4 ,continuity4 ,up to this point our discussions have been based on the general concept of the thing1 that is1 of the individual experience differentiated from other experiences4 ,here the fact of being different1 which1 as a general experience1 led to the corresponding elementary concept1 appeared in the foreground in accordance with its generality4 ,but in addition to it there is another general fact of experience1 which has led to just as general a concept4 ,it is the concept of continuity4 ,when1 for example1 we watch the diminution of light in our room as it grows dark in the evening1 we can by no means say that we find it darker at the present moment than a moment before4 ,we require a perceptibly long time to be able to say with certainty that it is now darker than before1 and throughout the whole time we have never felt the increase of darkness from moment to moment1 although theoretically we are absolutely convinced that this is the correct conception of the process4 ,this peculiar experience1 our failure to perceive individual parts of a change1 the reality of which we realize when the difference reaches a certain degree1 is very general1 and1 like memory1 is based upon a fundamental physiological fact4 ,it has already been noted by ,herbart1 but its significance was first recognized by ,fechner1 and has since then become generally known in physiology and psychology under the name of threshold4 ,next to memory the threshold determines the fundamental lines of our psychic life4 ,the threshold therefore means that whatever state we are in a certain finite amount of difference or change must be stepped over before we can perceive the difference or change4 ,this peculiarity appears in all our states or experiences4 ,we have already given an example for the phenomena of light and darkness4 ,the same is true of differences in color and of our judgments as to tone pitch and tone strength4 ,even the transition from feeling well to feeling ill is usually imperceptible1 and it is only when the change occurs in a very brief time that we become conscious of it4 ,the physical causes of these psychic phenomena need be indicated only in brief4 ,in all our experiences an existing chemico-physical state in our sense organs and in the central organ undergoes a change4 ,now experiments with physical apparatus have shown that such a process always requires a finite1 though sometimes a very small1 quantity of work1 or1 generally speaking1 energy1 before it can be brought about at all4 ,even the finest scale1 sensitive to a millionth of a gram1 remains stationary when only a tenth of a millionth is placed upon it1 although we can see a body of such minute weight under the microscope4 ,in the same way it requires a definite expenditure of energy in order to bring the sense organs1 or the central organ1 into action1 and all stimuli less than this limit or threshold produce no experience of their presence4 ,by this the difficult concept of continuity is evoked in our experience4 ,the transition from the light of day to the darkness of evening proceeds continuously1 that is1 at no point of the whole transition do we notice that the state just passed is different from the present one1 while the difference over a wider extent of the experience is unmistakable4 ,if we wish to bring vividly to our minds the contradiction to other habits of thought which this involves1 we need only to represent to ourselves the following instance4 ,i will compare the thing ,a at a certain time with the thing ,b1 which is so constructed that though objectively different from ,a1 the difference has not yet reached the threshold4 ,from experience1 therefore1 ,i must take ,a to be equal to ,b4 ,then ,i compare ,b with a thing ,c1 which is objectively different from ,b in the same way as ,a is from ,b1 though here1 too1 the difference is still within the threshold1 though very near it4 ,i shall also have to take ,b as equal to ,c4 ,but now if ,i compare ,a directly with ,c1 the sum of the two differences oversteps the threshold value1 and ,i find that ,a is different from ,c4 ,this1 then1 is a contradiction of the fundamental principle that if ,a ,b and ,b ,c1 ,a ,c4 ,this principle is valid for counted things1 which1 in consequence1 are discontinuous1 but not for continuous things susceptible by our senses4 ,if in spite of this it is applied to continuous things or magnitudes in the narrower sense1 we must bear in mind that it is just as much a case of an extrapolation to the non-existing ideal instance 7p4 #df7 as in the case of the other general principles1 which1 though they are derived from experience1 nevertheless1 for practical purposes1 transcend experience in their use4 ,the examples cited above prove also that these relations are by no means confined to the judgments we derive on the basis of immediate sensations4 ,when by means of the scale we compare three weights1 the differences of which lie within the limit of its sensitiveness but approach closely to it1 we can arrive in a purely empirical and objective way also at the contradiction ,a ,b1 ,b ,c1 but ,a ,not ,c4 ,in weight and measurement1 therefore1 we hold fast to the principle that the relations cited have no claim to validity outside the limit of their possible errors4 ,accordingly1 though the non-equation of ,a ,not ,c can be observed1 the difference of both values cannot be greater than at utmost the sum of the two threshold values4 ,these considerations also give us a means of appraising the oft-repeated statement that in contradistinction to the physical laws the mathematical laws are absolutely accurate4 ,the mathematical laws do not refer to real things1 but to imaginary ideal limit cases4 ,consequently they cannot be tested by experience at all1 and the demands science makes on them lie in quite a different sphere4 ,their nature must be such that experience should approximate them infinitely1 if certain definite well-known postulates are to be more and more fulfilled1 and that the various abstractions and idealizations should be so chosen as not to contradict one another4 ,such contradictions have by no means always been avoided4 ,but we must not regard them as inherent in the inner organization of our mind1 as ,kant did4 ,these contradictions spring from careless handling of the concept technique1 by which postulates elsewhere rejected are treated as valid4 ,we have already come across an instance of such relations in the application of the concept of equality to unlimited groups 7p4 #hd74 ,we must be guided by the same rules of precaution in answering the question whether the things felt as continuous--for example1 space and time--are truly continuous1 or whether in the last analysis they must not be conceived of as discontinuous4 ,the various sense organs1 and still more1 the various physical apparatus with which we examine given states1 are of very varying degrees of sensibility1 that is1 the threshold for distinguishing the differences may be of very different magnitudes4 ,therefore1 a thing which is discontinuous for a sensitive apparatus will behave as if it were continuous with a less sensitive apparatus4 ,accordingly1 we shall find so many the more things continuous the less sharply developed our ability is to differentiate4 ,while this circumstance makes it possible that we should regard discontinuous things as continuous1 time relations in certain circumstances produce the opposite effect4 ,even if in a process the change is continuous but very rapid1 and the new state remains unchanged for a certain time1 we easily conceive of this sequence as discontinuous4 ,we cannot resist this view of the process when the change occurs in a shorter time than the threshold time of our mind for each step in the process4 ,but since this threshold changes with our general condition1 one and the same process can appear to us both continuous and discontinuous according to circumstances4 ,here1 therefore1 we have a cause through the operation of which1 with advancing knowledge1 more and more things will become recognized as continuous4 ,now if we turn to experience1 we find1 as the sum total of our knowledge1 that for the sake of expediency we approach everything with the presumption that it is continuous4 ,this aggregate experience finds its expression in such sayings as ,nature makes no jumps1 and similar proverbial generalizations4 ,but we must emphasize the fact once more that in deciding matters in this way we deal solely with questions of expediency1 not with questions of the nature of our mental capacity4 #cf4 ,measurement4 ,measuring is in a certain way the opposite of counting4 ,while1 in counting1 the things are regarded in advance as individual1 and the group1 therefore1 is a body compounded of discontinuous elements1 measuring1 on the other hand1 consists in co-ordinating numbers with continuous things1 that is1 in applying to continuous things a concept formed upon the hypothesis of discontinuity4 ,it lies in the nature of such a problem that the difficulty of adaptation must crop out somewhere in the course of its attempted solution4 ,this is actually shown by the fact that measurement proves to be an unconcluded and inconcludable operation4 ,if1 in spite of this1 measurement may and must justly be denoted as one of the most important advances in human thought1 it follows that those fundamental difficulties can practically be rendered harmless4 ,let us picture to ourselves some process of measurement--for example1 the determination of the length of a strip of paper4 ,we place a rule divided into millimeters 7or some other unit7 on the strip1 and then we determine the unit-mark at which the strip ends4 ,it turns out that the strip does not end exactly at a unit-mark1 but between two unit-marks4 ,and even if the rule is provided with divisions ten or a hundred times finer1 the case remains the same4 ,in most cases a microscopic examination will show that the end of the strip does not coincide with a division4 ,all that can be said1 therefore1 is that the length must lie between n and n #a units1 and even if a definite number is given1 the scientifically trained person will supplement this number by the sign f1 in which f denotes the possible errors1 that is1 the limit within which the given number may be false4 ,we see at once how the characteristic concept of threshold1 which has led to the conception of the continuous1 immediately asserts itself when in connection with discontinuous numbers4 ,the adaptation of the threshold to numbers can be carried as far as it is possible to reduce the threshold1 but the latter can never be made to disappear entirely4 ,the significance of measurement therefore lies in the fact that it applies the operation of counting with all its advantages 7see p4 #he7 to continuous things1 which as such do not at first lend themselves to enumeration4 ,by the application of the unit measure a discontinuity is at first artificially established through dividing the thing into pieces1 each piece equal to the unit1 or imagining it to be so divided4 ,then we count the pieces4 ,when a quantity of liquid is measured with a liter this general process is carried out physically4 ,in all other less direct methods of measurement the physical process is substituted by an easier process equally good4 ,thus1 in the example of the strip of paper we need not cut it up into pieces a millimeter in length4 ,the divided rule is available for comparing the length of any number of millimeters that happen to come under consideration1 and we need only read off from the figures on the rule the quantity of millimeters equal to the length of the strip1 in order to infer that the strip can be cut up into an equal number of pieces each a millimeter in length4 ,after it has been made possible to count continuous things in this way1 the numeration of them can then be subjected to all the mathematical operations first developed only for discrete1 directly countable things4 ,when we reflect that our knowledge of things has given them to us preponderatingly as continuous1 we at once see what an important step forward has been made through the invention of measurement in the intellectual domination of our experience4 #cg4 ,the ,function4 ,the concept of continuity makes possible the development of another concept of greater universality1 which can be characterized as an extension of the concept of causation 7p4 #ca74 ,the latter is an expression of the experience1 if ,a is1 ,b is also1 in which ,a is understood to be a definite thing at first conceived of as immutable4 ,now it may happen that ,a is not immutable1 but represents a concept with continuously changing characteristics4 ,then1 as a rule1 ,b will also be of that nature1 so that every special value or state of ,b corresponds to every special value or state of ,a4 ,here1 in place of the reciprocal relation of two definite things1 we have the reciprocal relation of two more or less extended groups of similar things4 ,if these things are continuous1 as is assumed here 7and which is extremely often the case71 both groups or series1 even though they are finite1 contain an endless quantity of individual cases4 ,such a relation between two variable things is called a function4 ,although this concept is used chiefly for the reciprocal relation of continuous things1 there is nothing to hinder its application to discrete things1 and accordingly we distinguish between continuous and discontinuous functions4 ,the intellectual progress involved in the conception of the reciprocal relation of entire series or groups to one another1 as distinguished from the conception of the relations between individual things1 is of the utmost importance and in the most expressive manner characterizes the difference between modern scientific thought and ancient thought4 ,ancient geometry1 for example1 knew only the cases of the acute1 right1 and obtuse angled triangle1 and treated them separately1 while the modern geometrician represents the side of the triangle as starting from the angle zero and traversing the entire field of possible angles4 ,accordingly1 unlike his colleague of old1 he does not ask for the particular principles bearing upon these particular cases1 but he asks in what continuous relation do the sides and angles stand to one another1 and he lets the particular cases develop from out of one another4 ,in this way he attains a much profounder and more effectual insight into the whole of the existing relations4 ,it is in mathematics in especial that the introduction of the concept of continuity and of the function concept arising from it has exercised an extraordinarily deep influence4 ,the so-called ,higher ,analysis1 or ,infinitesimal ,analysis1 was the first result of this radical advance1 and the ,theory of ,functions1 in the most general sense1 was the later result4 ,this progress rests on the fact that the magnitudes appearing in the mathematical formulas were no longer regarded as certain definite values 7or values to be arbitrarily determined71 but as variable1 that is1 values which may range through all possible quantities4 ,if we represent the relation between two things by the formula ,b f7,a71 expressed in spoken language by ,b is a function of ,a1 then in the old conception ,a and ,b are each individual things1 while in the modern conception ,a and ,b represent an inexhaustible series of possibilities embracing every conceivable individual case that may be co-ordinated with a corresponding case4 ,herein lies the essential advantage of the concept of continuity4 ,it is true that it also introduces into calculation the above-mentioned contradictions which crop up in the ever-recurring discussions concerning the infinitely great and the infinitely small4 ,the system introduced by ,leibnitz of calculating with differentials1 that is1 with infinitely small quantities1 which in most relations1 however1 still preserve the character of finite quantities from which they are considered to have been derived1 has proved to be as fruitful of practical results as it is difficult of intellectual mastery4 ,we can best conceive of these differentials as the expression of the law of the threshold1 which law gave rise to1 or made possible1 the relation between the continuous and the discrete4 #ch4 ,the ,application of the ,functional ,relation4 ,i have already shown 7p4 #cd7 how the first formulation of a causal relation which experience yields can be purified and elaborated by the multiplication of the experience4 ,the method described was based upon the fact that the necessary and adequate factors of the result were obtained by eliminating successively from the cause the various factors of which its concept was or could be compounded1 and by concluding from the result1 that is1 the presence or absence of the effect1 as to the necessity or superfluity of each factor4 ,obviously the application of this process presupposes the possibility of eliminating each factor in turn4 ,very often it is not possible1 and then in place of the inadequate method of the individual case the method of the continuous functional relation steps in with its infinitely greater effectiveness4 ,if in most cases we cannot eliminate the factors one by one1 there are very few instances in which it is not possible to change them1 or to observe the result in the automatically changed values of the factors4 ,but then we have the principle that for the causal relation all such factors are essential the change of which involves a change of the result4 ,it is clear that this signifies a generalization of the former and more limited method4 ,for the elimination of the factor means that its value is reduced to zero4 ,but now it is no longer necessary to go to this extreme limit2 it suffices merely to influence in some way the factor to be investigated4 ,it is true that here the difference in the result cannot be expressed with a yes or a no1 as before4 ,it can only be said that it has changed partly1 more or less4 ,from this it can be seen that the application of this process requires more refined methods of observation1 especially for measuring1 that is1 for determining values or magnitudes4 ,on the other hand1 we must recognize how much deeper we can penetrate into the knowledge of things by the application of the measuring process4 ,each advance in precision of measurement signifies the discovery of a new stratum of scientific truth previously inaccessible4 #ci4 ,the ,law of ,continuity4 ,from the fact that natural phenomena in general proceed continuously we can deduce a number of important and generally applicable conclusions which are constantly used for the development of science4 ,when a relation of two continuously varying values of the form ,a f7,b7 is conjectured1 we convince ourselves of its truth by observing for different values of ,a the corresponding values of ,b1 or reversely4 ,if we find that changes in the one correspond to changes in the other1 the existence of such a relation is proved1 at first only for the observed values1 though we never hesitate to conclude that for the values of ,a lying between the observed values1 but themselves not yet observed1 the corresponding values of ,b will also lie between the observed values4 ,for example1 if the temperature at a given place has been observed at intervals of two hours1 we assume without hesitancy that in the hours between when no observations were made1 the values lie between the observed values4 ,if we indicate the time in the usual manner by horizontal lines and the temperature for the general periods of time by longitudinal lines1 the law of continuity asserts that all these temperature points lie in a steady line1 so that when a number of points lying sufficiently near one another is known1 the points between can be derived from the steady line which may be drawn through the known points4 ,this very commonly applied process will yield the more accurate results the nearer the known points are to one another1 and the simpler the line4 ,the application of the law of continuity or steadiness1 therefore1 means no less than that it is possible1 from a finite1 frequently not even a very large1 number of individual results1 to obtain the means of predicting the result for an infinitely large number of unexamined cases4 ,the instrument derived from this law1 therefore1 is an eminently scientific one4 ,the value of this instrument is still greater if it succeeds in expressing the relation ,a f7,b7 in strict mathematical form4 ,first1 the result of the determination of a number of individual values of that function is represented as a table of co-ordinated values4 ,by the graphic process above described1 or by its equivalent1 the mathematical process of interpolation1 this table is so extended that it also supplies all the intermediate values4 ,but this is still a case of a mechanical co-ordination of the corresponding values4 ,often we succeed1 especially in the relation of simple or pure concepts1 in finding a general mathematical rule by which the magnitude ,a can be derived from the magnitude ,b1 and reversely4 ,this is the only instance in which we speak of a natural law in the quantitative sense4 ,thus1 for example1 we can observe what volume a given quantity of air occupies when successively subjected to different pressures4 ,if we arrange all these values together in a table1 we can also calculate the volume for all the intermediate pressures4 ,but on close inspection of the corresponding numbers of pressure and volume we notice that they are in inverse ratio1 or that when multiplied by one another their products will be the same4 ,if we denote the space by v and the pressure by p1 this fact assumes the mathematical form pv ,k1 in which ,k is a definite number depending upon the quantity of air1 the unit of pressure1 etc41 but remaining unchanged in an experimental series in which these factors stay the same4 ,the general functional equation ,a f7,b7 becomes the definite p ,k_/v4 ,and this formula enables us to determine by a simple calculation the volume for any degree of pressure1 provided the value of ,k has been once ascertained by experiment4 ,at first we have a right to such a calculation only within the province in which the experiments have been made1 and the simple mathematical expression of the natural law has for the time being no further significance than that of a specially convenient rule for interpolation4 ,but such a form immediately evokes a question which demands an experimental answer4 ,how far can the form be extended8 ,that there must be a limit is to be directly inferred from the consideration of the formula itself4 ,for if we let p #j1 then v infinity1 both of which lie beyond the field of possible experience4 ,similar considerations obtain in all such mathematically formulated natural laws1 and each time1 therefore1 we must ask what the range of validity of such an expression is1 and answer the question by experiment4 ,while in this discussion the mathematically formulated natural law seems to have the nature only of a convenient formula of interpolation1 we are nevertheless in the habit of regarding the discovery of such a formula as a great intellectual accomplishment1 which so impresses us that we frequently call it by the name of the discoverer4 ,now1 wherein lies the more significant value of such formulations8 ,it lies in the fact that simple formulas are discovered only when the conceptual analysis of the phenomenon has advanced far enough4 ,the very simplicity of the formula shows that the concept formation which is at the basis of it is especially serviceable4 ,in ,ptolemy's theory of the motion of the planets the means for calculating their positions in advance was given just as in the theory of ,copernicus4 ,but ,ptolemy's theory was based on the assumption that the earth stands still1 and that the sun and the other planets move4 ,the assumption that the sun stands still and that the earth and the other planets move greatly facilitates the calculation of the position of the planets4 ,in this lay the primary value of the advance made by ,copernicus4 ,it was not until much later that it was found that a number of other actual relations could be represented much more fittingly by means of the same hypothesis1 and thus the ,copernican theory has come to be generally recognized and applied4 ,the significance of the law of continuity and its field of application have by no means been exhausted by what has been said above4 ,but later we shall have a number of occasions to point out its application in special instances1 and so cause its use to become a steady mental habit with the beginner in scientific research4 #dj4 ,time and ,space4 ,time and space are two very general concepts1 though without doubt not elementary concepts4 ,for besides the elementary concept of continuity which both contain1 time has the further character of being one-seried or one-dimensional1 of not admitting of the possibility of return to a past point of time 7absence of double points7 and of absolute onesidedness1 that is1 of the fundamental difference between before and after4 ,this last quality is the very one not found in the space concept1 which is in every sense symmetrical4 ,on the other hand1 owing to the three dimensions it has a threefold manifoldness4 ,that despite this radical distinction in the properties of space and time all of our experiences can be expressed or represented within the concepts of space and time1 is very clear proof that experience is much more limited than the formal manifoldness of the conceivable4 ,in this sense space and time can be conceived as natural laws which may be applied to all our experiences4 ,here at the same time the subjective-human element of the natural law becomes very clear4 ,the properties of time are of so simple and obvious a nature that there is no special science of time4 ,what we need to know about it appears as part of physics1 especially of mechanics4 ,nevertheless time plays an essential rle in phoronomy1 a subject which we shall consider presently4 ,in phoronomy1 however1 time appears only in its simplest form as a one-seried continuous manifoldness4 ,as for space1 the presence of the three dimensions conditions a great manifoldness of possible relations1 and hence the existence of a very extensive science of bodies in space1 of geometry4 ,geometry is divided into various parts depending upon whether or not the concept of measurement enters4 ,when dealing with purely spacial relations apart from the concept of measurement it is called geometry of position4 ,in order to introduce the element of measurement a certain hypothesis is necessary which is undemonstrable1 and therefore appears to be arbitrary and can be justified only because it is the simplest of all possible hypotheses4 ,this hypothesis takes for granted that a rigid body can be moved in all directions in space without changing in measure4 ,or1 to state the inverse of this hypothesis1 in space those parts are called equal which a rigid body occupies1 no matter how it is moved about4 ,we are not conscious of the extreme arbitrariness of this assumption simply because we have become accustomed to it in school4 ,but if we reflect that in daily experience the space occupied by a rigid body1 say a stick1 seems to the eye to undergo radical changes as it shifts its position in space and that we can maintain that hypothesis only by declaring these changes to be apparent1 we recognize the arbitrariness which really resides in that assumption4 ,we could represent all the relations just as well if we were to assume that those changes are real1 and that they are successively undone when we restore the stick to its former relation to our eye4 ,but though such a conception is fundamentally practicable in so far as it deals merely with the space picture of the stick1 we nevertheless find that it would lead to such extreme complications with regard to other relations 7for example1 the fact that the weight of the stick is not affected by the change of the optic picture7 that we do better if we adhere to the usual assumption that the optical changes are merely apparent4 ,in this connection we learn what an enormous influence the various parts of experience exert upon one another in the development of science4 ,in every special generalization of experiences1 that is1 in every individual scientific theory1 our aim is not only to generalize this special group of experiences in themselves1 but at the same time to join such other experiences to them as expedience demands4 ,if the effect of this necessity is on the one hand to render the elaboration of an appropriate theory more difficult1 it has on the other hand the great advantage of affording a choice among several theories of apparently like value1 and thus making possible a more precise notion of the reality4 ,for example1 for the understanding of the mutual movements of the sun and the earth it is the same whether we assume that the sun moves about the earth or the earth about the sun4 ,it is not until we try to represent theoretically the position of the other planets that we see the economic advantage of the second conception1 and facts like ,foucault's experiment with a pendulum can be represented only according to this second conception in our present state of knowledge4 ,likewise1 the assumption on which scientific geometry goes1 that space has the same properties in all directions1 conflicts with immediate experience4 ,in immediate experience we make a sharp distinction between below and above1 although we are prepared to admit the homogeneity of space in the horizontal direction4 ,this is due1 as physics teaches1 to the fact that we are placed in a field of gravitation which acts only from above downward and which permits free horizontal turnings1 although it imparts a characteristic difference to the third direction4 ,since considerations of another kind enable us to place ourselves in a position in which we ignore this field of gravitation in the investigation of space1 geometry abstracts this element and disregards the corresponding manifoldness4 ,in the theory of the gravitation potential1 on the other hand1 this very manifoldness is made the subject of scientific investigation4 ,the common application of the concepts of space and time results in the concept of motion1 the science of which is called phoronomics4 ,in order to make this new variable subject to measurement we must arrive at an agreement or convention as to the way in which to measure time4 ,for since past time can never be reproduced we actually experience only unextended moments1 and have no means of recognizing or defining the equality of two periods of time by placing them side by side1 as we can in the case of spacial magnitudes4 ,we help ourselves by saying that in uninfluenced motions equal periods of time must correspond to the equal changes in space4 ,we regard the rotation of the earth on its axis and its revolution about the sun as such uninfluenced motions4 ,the two depend upon dissimilar conditions1 and the empirical fact that the relation of the two motions1 or the relation between the day and the year1 remains practically the same1 sustains that assumption1 and at the same time shows the expediency of the given definition of time4 ,analytic geometry1 the application of algebra to geometric relations1 occupies a noteworthy position1 from the point of view of method1 in the science of space4 ,it yields geometric results by means of calculation1 that is1 by the application of the algebraic material of symbols we can obtain data concerning unknown spacial relations4 ,an explanation is necessary of how by a method apparently so extraneous such results as these can be attained4 ,the answer lies again in the general principle of co-ordination1 which in this very case receives a particularly cogent illustration4 ,three algebraic signs1 x1 y1 and z1 are co-ordinated with the three variable dimensions of space4 ,first1 the same independent and constant variability is ascribed to these signs1 and1 further1 the same mutual relations are assumed to subsist between them as actually exist between the three-spacial dimensions4 ,in other words1 precisely the same kind of manifoldness is imparted to these algebraic signs as the spacial dimensions possess to which they are co-ordinated1 and we may therefore expect that all the conclusions arising from these assumptions will find their corresponding parts in the spacial manifoldness4 ,accordingly1 a co-ordinated spacial relation corresponds to every change of those algebraic formulas resulting from calculation1 and if such changes lead to an algebraically simple form1 then the spacial form corresponding to it must show an analogous simplicity4 ,here1 therefore1 we have a case such as was described under simpler conditions on p4 #hf of operations undertaken with one group and repeated correspondingly in the co-ordinated group4 ,and it is only the great difference in the things of which in this case the two groups are composed--spacial relations on the one side and algebraic signs on the other--that creates the impression of astonishment which was felt very strongly at the invention of this method1 and which is still felt by students with talent for mathematics when they first become acquainted with analytical geometry4 #da4 ,recapitulation4 ,before we proceed to consider the fundamentals of other sciences1 it is well to make a general rsum of the field so far traversed4 ,since the later sciences1 as we have already observed1 make use of the entire apparatus of the earlier sciences1 the mastery of them must be assured in order to render their special application possible4 ,this does not mean that one must have complete command of the entire range of those earlier sciences in order to pursue a later one4 ,mere human limitations would prevent the fulfilment of such a demand4 ,as a matter of fact1 successful work can be done in one of the later sciences even if only the most general features of the earlier ones have been clearly grasped4 ,nevertheless1 the rapidity and certainty of the results are very considerably increased by a more thorough knowledge of the earlier sciences1 and the investigator1 accordingly1 should seek a middle road between the danger of insufficient preparation for his special science and the danger of never getting to it from sheer preparation4 ,in any circumstances he must be prepared always1 even though it be in later age1 to acquire those fundamental aids so soon as he feels the need of them for carrying out any special work4 ,it is generally acceded that without logic the adequate pursuit of science is impossible4 ,nevertheless1 the opinion is widely current1 even among men of science1 that everybody has command of the needful logic without having studied it4 ,no more than a man can learn of himself to use the calculus1 even if he may have discovered unaided some of its elementary principles1 can he acquire certainty and readiness in the use of the logical rules generally necessary1 unless he has made the necessary studies4 ,it is true that the scientific works of the great pioneers and leaders in the special sciences furnish practical examples of such logical activity4 ,but complete freedom and security are acquired only on the basis of conscious knowledge4 ,we have now seen how1 from the physiological construction of our mental apparatus1 the process of concept formation and the experience of concept connections are the basis of the whole of mental life4 ,the laws of the mutual interaction of the most general or elementary concepts operated in the formation of the concepts1 thing1 group1 co-ordination4 ,here were found the fundamentals of logic or the science of concepts4 ,a special process of abstraction yielded the concept of number1 and with it the corresponding field of mathematics1 arithmetic1 algebra1 and the theory of numbers4 ,by means of the second fundamental fact of physiology1 the threshold1 another elementary fact was explained1 that of continuity4 ,the co-ordination of individual things under the influence of this concept was expanded into the co-ordination of continuous phenomena-series1 and yielded the correspondingly more general concept of the function4 ,from the application of the number concept to continuous things1 the idea of measurement resulted4 ,in mathematics the concept of continuity led to higher analysis and the theory of functions4 ,finally1 the concept of continuity proved to be an inexhaustible aid for the extension of scientific knowledge and for the formulation of natural laws in mathematical form4 ,,part ,,iii ,,the ,,physical ,,sciences #db4 ,general4 ,in the formal sciences we began the specialization of the object from the most general concept of thing conceivable1 possessing no other characteristic attribute than its capability of being distinguished from other things2 and we carried the specialization so far that we could follow in its movements an object definite as to time and space4 ,this object1 to be sure1 was defined only in that it occupied a definite space1 and accordingly had a definite form4 ,as a matter of fact1 the spacial thing of geometry and phoronomy reveals no further attributes4 ,it is here that the physical sciences enter into their dominion one after the other1 and fill the empty space of the geometric thing with definite attributes4 ,these are the secondary qualities of ,locke1 of which he assumed that they do not belong so much to the bodies themselves as that they merely appear to us so on account of the nature of our human sense organs4 ,now that our knowledge concerning the nature of those properties as well as the structure of our sense organs is much more thorough1 we have more definite ideas also of the subjective part of the corresponding experiences1 and in a large measure are able to separate it from the objective part4 ,all properties which physical bodies in contradistinction to geometric bodies possess can be traced back to a fundamental concept1 which1 in conjunction with the concepts explained in the former chapter1 serves to characterize and distinguish the physical structure4 ,for example1 the fact that we can distinguish cubes of equal size but of different material1 different temperature1 and different luminosity1 can be traced back always and entirely to the different kinds of energy acting in the geometric space in question4 ,the concept of energy1 therefore1 plays approximately the same rle in the physical sciences as the concept of thing in the formal sciences1 and the essentials of this new field of science are the comprehensive knowledge and development of this concept4 ,because of its great importance it has long been known and applied in individual forms4 ,but the systematization of the physical sciences relative to energy is a matter of only recent date4 #dc4 ,mechanics4 ,recently many scientists have taken exception to the traditional division of mechanics into statics1 or the science of equilibrium1 and dynamics1 or the science of motion1 because it does not correspond to the essence of the thing1 equilibrium being only the limit-case of motion4 ,however1 the classic presentations of this science are based on that division1 so that it must express an essential difference4 ,this difference we can clearly recognize through the application of the concept of energy to mechanics4 ,we then learn that statics is the science of work1 or the energy of position1 and that dynamics is the science of living force1 or of the energy of motion4 ,by work in the mechanical sense we mean the expenditure of force required for the locomotion of physical bodies4 ,while a cube of lead is geometrically equal to a cube of glass1 we experience a great difference between them when we lift them from the floor to a table4 ,we call the cube of lead heavier than the glass cube1 and we find it requires more work to raise the former than the latter4 ,for psychologic reasons this judgment becomes especially clear when the work required to lift the lead cube marks the limit of our physical capacity4 ,work depends not only upon the difference described above1 but also upon the distance through which it is exerted4 ,it increases in proportion as the distance increases4 ,in mechanics work is proportional both to the distance and to that peculiar property which in the given example we call weight4 ,but a more general concept has been formed for that property in the mechanical sense1 called force1 of which weight constitutes but a special instance4 ,whenever there is a resistance combined with a change of place we speak of a force1 and the product of the force and the distance we call work4 ,the cause of this kind of concept formation is the following3 ,there are a great number of different machines1 all of them possessing the peculiarity that work can be put into them at a definite place and taken out at another place4 ,now1 centuries of experience have shown that it is impossible to obtain more work from such mechanical machines than has been put into them4 ,as a matter of fact1 the work obtained is always less than the work put in1 and the two approach equality as the machine approaches perfection4 ,it is to such ideal machines1 therefore1 that the law of the conservation of work applies4 ,this law states that1 though a given quantity of work may be changed in the most manifold ways as to direction1 force1 etc41 it is impossible to change its quantity4 ,the reason we can judge of this fact with such certainty is because for many centuries a number of the ablest mechanicians have sought for a solution of the problem of perpetual motion1 that is1 for the construction of a machine from which more work can be gotten than is put into it4 ,all such attempts have failed4 ,but the positive result secured from these apparently futile efforts is the law of the conservation of work4 ,the greatness and importance of this result will become apparent in the further course of our study4 ,here for the first time we meet with a law expressing the quantitative conservation of a thing1 which may none the less undergo the most varied qualitative changes4 ,with the knowledge of this fact we involuntarily combine the notion that it is the same thing that passes through all these transformations1 and that it only changes its outward form without being changed in its essence4 ,such ideas1 it is true1 are widespread1 but they have a very doubtful side to them1 since they correspond to no distinct concept4 ,if we want to call the quantitative magnitude of the product of the force and distance the essence of work1 and the determination of the force and the distance according to magnitude and direction1 which come under consideration for each special value1 as its form1 then1 of course1 there is no objection to be made to mere nomenclature4 ,but we must bear in mind that the difference obtaining here lies exclusively in the fact that the amount of work measured quantitatively remains unchanged1 while its factors undergo simultaneous and opposite changes4 ,this discovery1 that there is a magnitude which can be quantitatively determined1 and which1 as experience shows1 remains unchanged1 however much its factors may change1 invariably results not only in a very simple and clear formulation of the corresponding natural law1 but also corresponds to the general tendency of the human mind to work out conceptually the permanent in change4 ,if1 in accordance with the word-sense1 we denote everything which persists under changing conditions by the name of substance1 we encounter in work the first substance of which we have attained knowledge in our scientific journeys4 ,in the history of the evolution of human thought this substance has been preceded by others1 especially by the weight and mass of ponderable bodies 7which are also subject to a law of conservation71 so that at present we are inclined to connect with the word substance a tacit secondary sense of ponderability4 ,but this is a remnant of the still very widely spread mechanistic theory of the universe1 which1 though it has almost finished its rle in physics1 will presumably continue to persist for a long time to come in the popularly scientific consciousness in accordance with the laws of collective thought4 #dd4 ,kinetic ,energy4 ,the law of the conservation of work is by no means true of all cases in which work is expended or converted1 but1 as has been said1 only of ideal machines1 that is1 of such cases which do not exist in reality4 ,but while in imperfect machines there is at least an approximation to this law1 there are besides countless normal cases in which we cannot even speak of an approximation4 ,when1 for example1 a stone falls to the ground from a certain height1 a certain quantity of work is expended1 which is equal to that by means of which the stone can be raised again to its original height4 ,this quantity of work apparently disappears entirely when the stone remains lying on the ground4 ,we shall discuss this case later4 ,or the falling of the stone can be so guided that it can lift itself again4 ,this happens1 for instance1 when1 by fastening the stone to a thread1 it is forced to move in a curved path1 or to perform pendular oscillations4 ,in that case1 it is true1 the stone will fall to the lowest point which the thread permits1 and so will there have lost its work without having done any other work in the meantime4 ,but it has entered a condition by virtue of which it raises itself again1 so that 7as before1 only in the ideal limit-case7 it reaches its former height1 and so has lost no work4 ,for this moment1 too1 then1 the law of the conservation of work obtains4 ,but in the meantime new relations have arisen4 ,what distinguishes the stone moving like a pendulum from the stone which simply falls is1 that at its lowest point it has not remained lying still1 but possesses a certain velocity4 ,by means of this it lifts itself again1 and after it has reached its former height1 it has lost its velocity4 ,therefore1 there is a reciprocal relation between the work which it loses and the velocity which it gains1 and the question may therefore be put1 ,how can this relation be represented mathematically8 ,experience teaches that in every such case a function of the velocity and of another property of the body1 called mass1 can be established in such a way that this function1 called the kinetic energy of the body1 increases precisely as much as the amount of work the body has expended1 and vice versa4 ,the sum of the kinetic energy of the body and of the work is therefore constant1 and the clearest mode of conceiving of this relation is by assuming that work can be transformed into kinetic energy and vice versa in such a way that given amounts of the two magnitudes are equal or equivalent to one another4 ,naturally1 this is only an abbreviated way of expressing the actual relations1 for it might just as well be assumed that the work really disappears and the kinetic energy really originates anew1 and that the disappearance of the one substance only happens regularly to coincide with the origin of the other4 ,but it is this regular conjunction of phenomena that constitutes the sole ground of every causal relation1 and in such a sense we are justified in regarding the disappearing work as the cause of the kinetic energy that arises1 and to designate this relation summarily as a transformation4 ,by the inclusion of cases in which work is converted into kinetic energy the law of the conservation of work therefore becomes the law of the conservation of the sum of work and kinetic energy4 ,we are thereby compelled to extend the concept of substance1 which at first contains only work1 to the sum of both magnitudes1 and to introduce a new name for this enlarged concept4 ,it will soon appear that all cases of imperfect machines1 in which work disappears without giving rise to an equivalent amount of kinetic energy1 can1 with a corresponding enlargement of the concept1 be likewise included in the law of conservation4 ,for experience has shown that in such cases something else arises1 heat1 light1 or electric force1 etc4 ,this generalized concept1 which embraces all natural processes and permits the sum of all corresponding values to be expressed by a law of conservation1 we call energy4 ,the law in question1 therefore1 is3 ,in all processes the sum of the existing energies remains unchanged4 ,the principle of the conservation of work in perfect machines proves to be an ideal special instance of this general law4 ,a perfect machine is one in which work changes into nothing but work of another kind1 and not into a different kind of energy4 ,then each side of the equation which expresses the general law of energy1 namely1 ,energy that has disappeared energy that has arisen1 contains only the magnitude of the work1 and expresses the law of the conservation of work4 ,if1 on the other hand1 as in the case of the pendulum1 the work increasingly changes part by part into kinetic energy1 and vice versa1 the equation during the first period is3 ,work that has disappeared kinetic energy that has arisen1 and during the second period in which the pendulum rises again1 ,kinetic energy that has disappeared work that has arisen4 ,thus1 while work can be called a substance only in a limited sense1 since its conservation is limited only to perfect machines1 we may call energy a substance unqualifiedly1 since in every instance of which we know the principle has been maintained that a quantity of any energy never disappears unless an equivalent quantity of another energy arises4 ,accordingly1 this law of the conservation of energy must be taken as a fundamental law of the physical sciences4 ,but not only do all the phenomena of physics1 including chemistry1 occur within the limits of the law of conservation1 but until the contrary is proved the law of conservation must also be regarded as operative in all the later sciences1 that is1 in all the activities of organisms1 so that all the phenomena of life must also take place within the limits of the law of conservation4 ,this corresponds to the general fact1 which ,i have emphasized a number of times1 that all the laws of a former science find application in all the following sciences1 since the latter can only contain concepts which by specialization1 that is1 by the addition of further characteristics1 have sprung from the concepts of the former or more general sciences4 #de4 ,mass and ,matter4 ,it has been noted above that kinetic energy depends upon another magnitude beside velocity4 ,a conception of its nature can be obtained when we try to put different bodies in motion4 ,in doing so the muscles of the arm perform certain quantities of work1 and we feel whether the quantities are greater or smaller4 ,in this way we obtain a clear consciousness of the fact that different bodies require quite different quantities of work for the same velocity4 ,the property which comes into play here is called mass1 and mass is proportional to the work which the various bodies require to attain the same velocity4 ,since the work and the velocity can be measured very accurately by appropriate means1 mass also lends itself to a correspondingly accurate measurement4 ,all known ponderable bodies have mass4 ,that means there is a regular connection between the property which makes a body tend to the earth with a certain definite force 7called weight7 and the property by virtue of which a body assumes certain velocities under the influences of motive causes4 ,we can readily conceive that it is possible for us to learn only of such bodies as are heavy1 that is1 bodies which are held by the earth1 since the others1 if they exist at all1 would naturally have left the earth long ago4 ,that all these bodies also have mass is to be explained in a similar way4 ,for a body of mass zero would at each impulse assume infinitely great velocity1 and could therefore never be the object of our observation4 ,consequently1 by reason of the physical conditions obtaining on the earth's surface1 the bodies known to us must combine both properties1 mass and weight4 ,the name given to this concept of the combined presence of mass and weight in space is matter4 ,experience shows that there is a law of conservation for these magnitudes also1 according to which whatever changes we may produce in bodies possessing weight and mass1 no change will occur in the sum of their weight and mass4 ,according to the nomenclature previously introduced we must therefore call weight and mass substances1 since they remain the same as to quantity1 no matter what changes they may undergo4 ,however1 it is usual to apply the name substance to the concept of matter composed of mass and weight4 ,in fact1 scientists often go so far as to limit the name to this single instance of the various laws of conservation1 and to take substance to mean exclusively the combination of mass and weight4 ,this is connected with the conception which we are about to discuss1 that all natural phenomena can ultimately be conceived as the motion of matter4 ,through the greater part of the nineteenth century this conception1 called scientific materialism1 was accepted almost without opposition4 ,at present it is being more and more recognized that it was only an unproved assumption1 which the development of science daily proves to be more untenable4 #df4 ,energetic ,mechanics4 ,in the light of our previous observations the branch of science traditionally known as mechanics appears as the science of work and of kinetic energy4 ,furthermore1 statics is shown to be the science of work1 while dynamics1 besides treating of kinetic energy in itself1 also treats of the phenomena of the change of work into kinetic energy1 and vice versa4 ,we shall find the same relation again later1 only in more manifold forms4 ,every branch of physics proves to be the science of a special kind of energy1 and to the knowledge of each kind of energy must be added the knowledge of the relations by which it changes to the other forms of energy and vice versa4 ,it is true that in the traditional division of physics this system has not been strictly carried out1 since an additional and very influential motive for classification has been the regard paid to the various human sense organs4 ,nevertheless this ground does not lie in the field of physics1 but in that of physiology1 and must1 therefore1 be abandoned in the interest of strict systematization4 ,of the physical sciences mechanics was the first to develop in the course of historical evolution4 ,a number of factors contributed to this end--the wide distribution of mechanical phenomena1 their significance to human life1 and the comparative simplicity of the principles of mechanics1 which made it possible to discover them at an early date4 ,most to be noted is1 that of all departments of physics mechanics is the first which lent itself to comprehensive mathematical treatment4 ,it is true that the mathematical treatment of mechanics was possible only after idealizing assumptions had been made--perfect machines and the like--so that the results of this mathematical treatment not infrequently had very little to do with reality4 ,the mistake of losing sight of the physical problem and of making mechanics a chapter of mathematics has not always been avoided1 and it is only in most recent times that the consciousness has again arisen that the classical mechanics1 in arbitrarily limiting itself to extreme idealized cases1 sometimes runs the risk of losing sight of the aim of science4 #dg4 ,the ,mechanistic ,theories4 ,because the evolution of mechanics antedates that of the other branches of physics1 mechanics has largely served as a model for the formal organization of the other physical sciences1 just as geometry1 which has been handed down to us from antiquity in the very elaborate form of ,euclid1 has largely been used as a model for scientific work in general4 ,such methods of analogy prove to be extremely useful at first because they serve as a guide to indicate when and where new sciences1 in which all possibilities are open1 can be got hold of4 ,but later on such analogies are apt to be harmful4 ,for each new science soon requires new methods1 by reason of the peculiar manifoldness which it has to deal with1 and the finding and the introduction of these new methods are easily delayed1 and1 as a matter of fact1 often have been delayed1 because scientists could not free themselves soon enough from the old analogy4 ,by its being based upon memory the human mind is so constructed that it cannot assimilate something entirely new4 ,the new must in some way be connected with the known in order that it may be organically embodied in the aggregate of concepts4 ,therefore1 it is the first involuntary impulse of our mind1 in the presence of new experiences or thoughts1 to look about for such points at which a linking of the unknown to the known seems possible4 ,in the case of mechanics this necessity for finding connecting links has acted in such a way that the attempt has been made1 and is still being made1 to conceive and represent all physical phenomena as mechanical4 ,the impulse to this was first given by the extraordinary successes which mechanics has attained in the generalization and prediction of the motions of the heavenly bodies4 ,the names of ,copernicus1 ,kepler1 and ,newton mark the individual steps in the mechanization of astronomy4 ,the cause of this lies in the fact that the heavenly bodies actually approximate very closely the ideal of the purely mechanical form with which classical mechanics deals4 ,these successes encourage the attempt to apply these mental instruments that were productive of such rich results to all other natural phenomena4 ,an old theory1 according to which all physical things are composed of the most minute solid particles of matter called atoms1 supported these tendencies and invited the attempt to regard the little world of atoms as subject to the same laws as had been found to apply so successfully to the great world of the stars4 ,thus we see how this mechanistic hypothesis1 the assumption that all natural phenomena can be reduced to mechanical phenomena1 comes as if it were a self-understood matter1 and with its claim to be a profound interpretation of nature it scarcely permits the question as to its justification to be raised at all4 ,and the effects here have been the same as ,i described above in cases in which inferences from analogy are accepted too extensively or too credulously4 ,while it is true1 no doubt1 that the mechanical hypothesis at first was fruitful of results in special research1 because it facilitated the putting of the question--for example1 we need think only of the atomic hypothesis in chemistry--later1 the efforts to find further hypothetic help for the inadequacies of the hypothesis that gradually came to light1 have not infrequently led scientific research to pseudo-problems1 that is1 to questions which are questions only in hypothesis1 but to which no actual reality can be shown to correspond4 ,such problems1 therefore1 are by their very nature insoluble1 and constitute an inexhaustible source of differences of scientific opinion4 ,the most flagrant of the injurious consequences of the mechanistic hypothesis appear in the scientific treatment of the mental phenomena4 ,ready as scientists were to represent all other life phenomena1 such as digestion1 assimilation1 and even generation and propagation1 as the consequence of an extremely complicated play of certain atoms1 their courage never went so far as to apply this principle to mental life and to consider that by mechanics the last word had been said on the subject4 ,it is because of this hesitancy to bring mental phenomena under the same mechanistic principle as all the other phenomena that the philosophical systems had to search for some other means to connect the mental world with the mechanical1 and the efforts of the philosophers to bring about this end have been most varied4 ,of the various doctrines that have come down to us1 that of the pre-established harmony proposed by ,leibnitz is in the ascendant in our day1 and is now called the theory of the psycho-physical parallelism4 ,according to this theory it is assumed that the mental world exists alongside1 and quite independent of1 the mechanical1 but that the things have been so prearranged that mental processes take place simultaneously with certain mechanical processes 7according to some1 with all mechanical processes7 in such a way that1 although the two series do not influence each other in the least1 they always correspond to each other precisely4 ,how such a relation has come about and how it is maintained remains unsaid1 or is left to future explanation4 ,we need only think of the content of this hypothesis with an unbiased mind to lose all relish for it at once4 ,in fact1 it has no other raison d'tre than the presumption that the mental and the mechanical world are opposed to each other4 ,as soon as we abandon the thesis that the non-mental world is exclusively mechanical1 we acquire the possibility again of finding for the theory of mental phenomena a constant and regular connection with the theories of all other phenomena1 especially with the phenomena of life4 ,therefore it will be found most expedient in every respect1 instead of rendering scientific research one-sided and almost blind to nonconforming facts by preconceived hypotheses1 such as the mechanistic hypothesis1 to seek1 as hitherto1 from step to step1 the new elements of manifoldness which must be taken account of in the progressive upbuilding of science and to limit ourselves faithfully to them in the formation of general ideas4 #dh4 ,complementary ,branches of ,mechanics4 ,the field of pure or classical mechanics is limited to the above two kinds of energy1 work and kinetic energy1 though these do not exhaust the manifoldness of the mechanical energies4 ,accordingly1 other branches of mechanics dealing with the corresponding phenomena are added to the classical mechanics described above4 ,if by mechanical energies we understand all energies in which changes of space are connected with changes of energy1 there are as many different forms as there are spacial concepts that seem applicable4 ,form1 ,volume1 and ,surface of bodies in space are especially recognizable as the field of action for energy1 which shows different properties or manifoldnesses according to each of these relations4 ,the energy of form is manifested in bodies 7solid or rigid bodies7 that maintain a definite shape because every change of shape is connected with work or with the expenditure of some other energy4 ,if the changes are small1 the bodies are of such a nature that they return to their former condition of their own accord after the force exerted upon them has ceased to act4 ,this property is called elasticity4 ,however1 the theory of elasticity1 which has been extensively and rationally developed1 is regarded as belonging rather to mathematical physics in general than to mechanics in particular4 ,in greater changes of shape the energy of form1 or elastic energy1 passes into other forms1 and the body does not return to its former shape after the force has been removed4 ,other bodies have no energy of form 7or only in an infinitesimally slight degree71 so that they allow of changes of form without the expenditure of work1 but their volume can be changed only by work4 ,these are divided into two classes4 ,first1 the liquids1 which have a definite volume 7corresponding to the definite shape of solids71 the changes of which in every sense1 both compression and expansion1 require work4 ,secondly1 the gases with volume energy in only one sense of the word1 in which only the compression of volume requires work1 while in expansion a certain amount of work is thrown off4 ,such bodies can exist only so long as the expenditure of their volume energy by spontaneous expansion is prevented by the presence of a counter energy1 as1 for example1 the elasticity of the walls of a vessel4 ,this tendency is called pressure4 ,finally1 there are energy qualities at the surfaces between various kinds of bodies which come into play at the change of these surfaces4 ,they always lie in such a direction that the enlargement of the surfaces requires work1 and hence1 by reason of the law of conservation of energy1 cannot proceed by itself4 ,in cases where there has been an inverse kind of energy present1 that is1 one which diminishes with increasing surface1 it also has been active as a rule1 thus bringing about the disappearance of the existing boundaries4 ,since the seat of this kind of energy is in the surfaces 7or superficies71 it is called surface-energy4 ,the phenomena depending upon it manifest themselves most clearly at the surface boundaries between liquids and gases4 ,they are called capillary phenomena4 ,this strange name1 derived from the word capilla1 hair1 has its origin in the fact that because of surface-energy liquids rise in tubes which they wet1 and the narrower the tube the higher they rise4 ,if the lumen of the tube is as fine as a hair1 a considerable rise can be observed4 ,this is the entire connection between the name and the thing4 ,the mechanics of liquids is called hydromechanics1 that of gases1 aeromechanics1 after the most familiar liquid1 water1 and the most familiar gas1 air4 ,the study of surface-energy under the name of the capillary theory forms part of theoretical physics4 ,while formerly this branch1 too1 was regarded as a working part1 or1 rather1 as a playing part1 of mathematical problems1 in more recent times extensive experimental research has made its entry in this province also1 and has demonstrated the necessity of passing from the former abstractions or idealizations1 which were carried altogether too far1 to a better and profounder regard for the actually existing complexities4 #di4 ,the ,theory of ,heat4 ,the various forms of energies the aggregate of which is comprehended in physics1 have very different special characters4 ,a systematic investigation has not yet been made of the characters of manifoldness by which1 for example1 work is distinguished from heat1 electrical energy from kinetic energy1 etc41 nor of what are the essential properties peculiar to each individual energy4 ,we feel certain that differences do exist1 for otherwise the energies could not be distinguished1 and we feel certain that these differences are very important1 for doubt seldom arises as to the kind of energy to which a certain phenomenon is to be assigned4 ,but just as we have no systematic table of the elementary concepts1 so we are still without a systematic natural history of the forms of energy in which the peculiarities of every species are characterized1 and in which the entire material is so arranged according to these characteristics that we can take a general survey of it4 ,as regards heat energy1 its foremost and most striking characteristic is its physiological effect4 ,in our skin there are organs for the perception of heat as well as of cold1 that is1 for temperatures above and below the temperature of the skin4 ,however1 the temperature that these organs can bear without injury to themselves is of a very small range1 beyond which physical apparatuses of all kinds must be used1 such as thermometers4 ,heat is the simplest kind of energy from the point of view of manifoldness4 ,every heat quantity is marked by a temperature1 just as a kinetic energy is marked by velocity4 ,but while a velocity is determined in space so that velocities of equal magnitude have in addition a threefold infinite manifoldness in reference to direction1 a temperature is characterized completely and unambiguously by a simple number1 the degree of temperature4 ,two temperatures of equal degree can in no wise be distinguished1 since temperature possesses no other possible manifoldness than degree4 ,the same property is found in heat energy itself4 ,in heat energy we measure the quantity of energy itself and call it the heat quantity1 while in some of the other kinds of energy1 only the factors into which they can be divided are measured1 and no habitual conception of the energy itself is developed4 ,a heat quantity is likewise fully indicated by its measure number4 ,that heat is an energy1 that is1 that it is developed in equal quantities from other kinds of energy1 and can change back again into them1 is a discovery which1 despite its fundamental and general character1 was not made before the forties of the nineteenth century4 ,as often happens in cases of important scientific advances1 the same idea came simultaneously to a number of investigators4 ,the first to grasp and fully comprehend this idea was ,julius ,robert ,mayer of ,heilbronn1 who published his results in #ahdb4 ,mayer not only showed that the imperfect machines 7p4 #acd71 which limit the validity of the law of the conservation of work1 owe this peculiarity to the fact that they transform a part of the work into heat1 and that when we take account of this part1 the law of conservation holds perfectly good1 but he also calculated1 with extraordinary acumen1 the mechanical equivalent of heat from the then existing data of physics4 ,that is to say1 he determined how many units of heat 7in the measure then in use7 correspond to a unit of work 7in its specific measure7 in the change from one to the other1 and back4 ,and this fundamental knowledge of the existence of a quantitatively unchangeable substance1 arising from work1 and capable of being transformed into it1 ,mayer did not limit in its application merely to heat4 ,he was the first to construct a table1 which he made as complete as possible1 of all the forms of energy then known1 and to assert and prove the possibility of their reciprocal change into each other4 ,in view of this relation of the quantitative equivalent of the various forms of energy when transformed into one another1 an attempt is being made at present to measure them all with the same unit4 ,that is1 some easily obtained quantity of energy is arbitrarily chosen as a unit and it is determined that in every other form of energy the unit shall be equal to the quantity obtained from that unit on its transformation into the energy in question4 ,for formal reasons the kinetic energy of a mass of two grams which moves with the velocity of one centimeter in a second has been chosen as the unit4 ,it is called erg1 an abbreviation of energy4 ,the amount is very small1 and for technical reasons #ajaj times greater unit is used4 ,to raise the temperature of a gram of water one degree a quantity of energy equal to #da1hcj1jjj ergs is required4 #ej4 ,the ,second ,fundamental ,principle4 ,another fundamental discovery has been made in connection with the heat form of energy1 which1 like the law of conservation1 relates to all forms of energy1 but has found its first and most important application in heat4 ,while the law of conservation answers the question1 how much of the new form of energy is developed if a given quantity of energy changes1 but gives no clue as to when such a change occurs1 this second law asserts the condition under which such changes arise1 and is therefore called the second fundamental principle4 ,the discovery of this law antedates ,mayer's discovery of the law of conservation by about twenty years1 and was made by a ,french military engineer1 ,sadi ,carnot1 who died soon afterward without having lived to see the recognition his great work obtained4 ,carnot asked himself the question1 ,upon what does the action of the steam engine1 which had just then come into use1 depend8 ,this led him first to the more general question of the action of heat engines in general4 ,he found that no heat engine could work unless the heat dropped from a higher to a lower temperature1 just as no water wheel can work unless the water flows from a higher to a lower level1 and he determined the conditions which an ideal heat engine must fulfil1 that is1 a machine in which the greatest possible value in work is obtained from heat4 ,however1 an ideal machine of this nature can be constructed in very different ways1 and ,carnot's discovery consists in the recognition of the fact that the quantity of work obtained from the heat unit does not at all depend upon the peculiar construction of the ideal machine1 but is determined solely by the temperature between which the heat transition takes place4 ,this follows from the following considerations3 ,in the first place an ideal engine must be reversible1 that is1 it must be capable of working both ways1 changing heat into work and work back into heat4 ,now1 if we have two ideal engines between the same temperatures1 and if we assume that engine ,a produces more work from the same quantity of heat than engine ,b1 then let ,a move one way and let ,b move the other way with the work obtained from ,a4 ,since ,b produces less work from a given amount of heat1 hence more heat from an equal amount of work1 there will in the end be more heat at the higher temperature than was originally there4 ,but experience teaches that there is no means in nature by which heat in the absence of concomitant change could be caused to rise to a higher temperature4 ,therefore an engine so constructed as to produce this result is impossible1 ,and ,b cannot be of such a nature as to produce less work from the same quantity of heat than ,a4 ,the reverse is also impossible4 ,for then we need merely couple the engines in the reverse way in order to obtain the same effect4 ,therefore1 since ,b can do neither less nor more work than ,a1 the two must do the same amount of work--which was to be proved4 ,it is obvious that this process of proof is similar to that by which the law of conservation was established4 ,because the arbitrary creation of energy from nothing is impossible there must be definite and immutable relations of change between the forms of energy4 ,because energy at rest does not spontaneously pass into conditions in which it can do work1 the efficiencies of the machines must have definite and unchangeable values4 ,if1 for example1 we could cause heat of its own accord to rise to a higher temperature1 we could also construct a perpetual motion machine which would always yield work at no expense4 ,but this perpetual motion would not be one that creates work out of nothing1 but one that extracts it from energy at rest4 ,a perpetual motion machine of this nature1 too1 is1 according to our experience1 impossible1 and this impossibility forms the content of the second fundamental principle4 ,on the face of it this apparently self-evident proposition does not reveal how fruitful of results it is when applied to the discovery of simple but not obvious relations4 ,it can only be said here that the deductions from this principle form the chief content of the extensive science of thermodynamics1 which deals with the changes of heat into other forms of energy4 ,we must only emphasize the fact that the application of this law1 as was already observed in stating it1 is not confined to the changes of heat alone4 ,it is a law rather which finds application in all the forms of energy4 ,for in every form of energy there is a property which corresponds to temperature in heat1 and upon the equality or the inequality of which depends whether the energy in question is at rest or ready for transformations4 ,this property is called the intensity of the energy4 ,in work1 for instance1 it is force1 in volume-energy it is pressure4 ,if once the intensity in a body is equal1 its energy is at rest1 and it never again moves of its own accord4 ,another form in which to present these relations is to make a distinction between free energy and energy at rest4 ,if we have a heat quantity the temperature of which is higher than that of the surrounding objects1 it can be used to do work only until its temperature has dropped to that of the surrounding objects4 ,although energy in abundance is still present1 there is no longer any energy capable of change1 or free energy4 ,since differences of temperature1 like other differences of intensity1 have a constant tendency to diminish1 the amount of free energy on earth is constantly decreasing1 and yet it is only this free energy that has value4 ,for since all phenomena depend upon change of energy1 and change of energy is possible only through free energy1 free energy is the condition of all phenomena4 #ea4 ,electricity and ,magnetism4 ,while the knowledge of heat energy goes back to the most ancient periods of civilization1 electrical and magnetic energies are relatively young acquisitions4 ,the highly developed technical application of both with the rich harvests they have yielded belongs exclusively to most recent times4 ,both these forms of energy1 like those discussed above1 are connected in the main with ponderable matter1 but in a much slighter and less regular measure4 ,while it is not possible as yet to render any given body free of heat 7although lately the absolute zero point has been considerably approximated71 freedom from electrical and magnetic energy is the normal condition of most bodies4 ,this is connected with the peculiarity that electrical and magnetic properties are decidedly bi-symmetrical or polar4 ,this property is not found in any other form of energy1 and can serve as the special scientific characteristic of electricity and magnetism4 ,this peculiarity shows itself in the concepts of positive and negative magnetism1 and positive and negative electricity1 and is due to the fact that two equal opposite quantities of electricity or magnetism1 when added together1 do not produce double their value1 but nullify each other4,g ,g ,for the sake of the layman it must be observed that those quantities are not energy magnitudes but factors of the electrical and magnetic energies4 ,energy itself in its various forms is an exclusively positive magnitude1 and the result of the additions of their various amounts is always the sum1 never the difference1 of their numerical values4 ,by the negative sign is understood the energy expended in contradistinction to the energy received4 ,it is therefore nothing more than the indication of a mathematical operation4 ,the fact that electrical and magnetic energies generally exist only in a transitory state 7with the notable exception of the magnetic condition of the earth7 is probably the cause of our not having developed a sense organ for them1 especially since their phenomena as they occur in nature have only occasionally and in very rare instances 7thunderstorms7 an influence upon us4 ,on the other hand1 the modern development of electrotechnics is based upon that property of electrical energy by virtue of which large quantities of it can be conducted along a thin wire over great distances without any considerable loss1 and at the point desired can be easily changed into any other forms of energy4 ,but since the collection and conservation of large quantities of electrical energy is hardly possible technically1 the electrical apparatus must be so constructed that the quantities each time required should be produced at the moment they are used4 ,the chief source of electricity is the chemical energy of coal1 which is first transformed into heat1 then into mechanical energy1 and finally into electrical energy4 ,this extremely roundabout process is necessary because a method technically practicable of transforming the chemical energy of coal directly into electrical energy has not yet been invented4 ,on the other hand1 mechanical energy can be easily and completely changed into electrical energy4 ,upon this is based the exploitation of much water power1 the energy of which could not be utilized but for the great capacity for change of the electrical form4 #eb4 ,light4 ,the case of light in our day seems to be similar to that of sound1 which1 although it has its special sense organ in man1 is yet no particular form of energy1 but has been found to be a combination of mechanical energies in an oscillatory or mutually changing state4 ,it seems highly probable that light1 too1 is not a special form of energy1 but a peculiar oscillatory combination of electrical and magnetic energies4 ,it is true that the circle of proof is not yet quite closed1 but the gaps have become so small that the above conclusion may at any rate be accepted as highly probable4 ,however that may be1 light is an energy which1 according to the known laws1 travels through space with tremendous rapidity4 ,we will call it radiant energy1 since the part optically visible1 to which alone the name light in its original sense belongs1 represents an extremely small portion of a vast field1 the properties of which change quite continuously from one end to the other4 ,radiant energy is characterized as an oscillatory or wave-like process4 ,so long as this fact was unknown 7up to the beginning of the nineteenth century7 it was thought that light consisted of minute spherical particles1 which shot through space in a straight line with the tremendous velocity mentioned above4 ,later1 in order to explain its wave nature1 which in the meantime has come to be recognized1 it was assumed to be due to the elastic vibrations of an all-pervading thing called ether1 of which we know nothing else4 ,this elastic undulatory theory has been abandoned in our time in favor of an electromagnetic theory supported by quite considerable experiential grounds4 ,whether it will be spared the fate that has overtaken the older theories 7or rather hypotheses7 of light cannot as yet be predicted with any degree of certainty4 ,radiant energy is of very marked importance in human relations4 ,as light it serves1 with the aid of the corresponding receiving organs1 the eyes1 as a more manifold means of intercommunication between our bodies and the outer world than any other form of energy4 ,the energy quantities penetrating to us from the extreme limits of the world space mark the outermost limits of which we have knowledge in any way whatsoever1 and finally the energy quantities radiating to us from the sun constitute the supply of free energy at the expense of which all organic life on earth is maintained4 ,even the chemical energy stored up in coal represents nothing else than accumulations of former sun radiation1 which had been transformed by the plants into the permanent form of chemical energy4 ,very recently other newly discovered forms of radiant energy have been added to light4 ,they are produced in manifold circumstances1 and some bodies emit them constantly4 ,the scientific elaboration of these extremely manifold and unusual phenomena has not yet been carried so far that they can be reduced to a doubt-free system4 ,but so much1 it seems1 is already apparent1 that they are presumably not purely new forms of energy1 but rather very composite phenomena which may yield one or more new energies as component parts4 ,but despite the peculiarity of these new rays1 nothing certain has as yet been proved against the law of conservation itself4 #ec4 ,chemical ,energy4 ,since chemical energy is only one of several forms of energy1 there seems to be no justification for allotting it to a special science1 since all the other forms of energy must be incorporated in physics4 ,but the actual existence of chemistry as a special science which has already many subdivisions is justified in the first place by the external fact that in practical life and in industry chemistry occupies a very wide field comparable1 if not superior1 to that of the whole of physics4 ,in the next place1 from the psychological point of view1 it is found that the chemist's methods of reasoning and working are so different from those of the physicist that a division seems to be in order for that reason also4 ,finally1 there is in the nature of chemical energy itself an important distinction which marks it off from the other forms4 ,while1 for example1 there is only one form of heat or of kinetic energy1 and in electricity there are only the two forms of polar opposites1 chemistry1 even after the greatest theoretical reduction1 possesses at least about eighty forms4 ,that is1 it possesses as many forms as there are chemical elements4 ,the experiential law1 that the elements cannot be changed into one another1,h also limits the corresponding changes of the chemical energies into one another1 and thus characterizes the independence of these various forms4 ,from this results a disproportionately greater manifoldness of relations1 which find their expression in the many thousands of the individualized chemical substances or combinations4 ,h ,lately changes of elements into one another have been observed in individual instances1 but in such peculiar circumstances that for the present we need not consider these discoveries1 which have only just begun4 ,this great manifoldness and the slight regularity hitherto found in connection with the properties and reciprocal relations of the numerous chemical elements renders modern chemistry more a descriptive than a rational science4 ,it was no more than twenty years ago that an earnest and successful attempt was begun to apply the stricter methods of physics to the investigation of chemical phenomena4 ,these labors1 so far as they have gone1 have yielded a great many far-reaching and comprehensive principles4 ,the significance of chemistry in human life is twofold4 ,in the first place the energy of the human body1 just as that of all other living organisms1 depends chiefly upon the action of chemical energies in the most manifold forms4 ,of all the physical sciences1 therefore1 chemistry is the most important for biology1 particularly for physiology4 ,in the second place1 as ,i have emphasized a number of times1 it possesses the peculiar property which enables it to be preserved for a long time without passing into other forms and being dissipated4 ,furthermore1 energy in this form permits of the most powerful concentration4 ,more of chemical energy can be stored in a given space than of any other form of energy4 ,both these properties1 then1 may be considered as the reason why organic beings are constituted chiefly by means of chemical energy4 ,at any rate1 it is due to these two peculiarities that chemical energy serves as the primary source for almost all the energy used in industry4 ,further1 the manifoldness of chemical energy is the cause of the peculiar manner in which it is transformed into other forms4 ,in the other forms of energy the transformation can be effected by the body itself4 ,nothing else is required4 ,if a stone is thrown and it hits against a wall1 it loses its kinetic energy1 the greater part of which changes into heat4 ,but in order to liberate the chemical energy of1 say1 coal1 the coal alone is not sufficient2 another chemical substance is required1 the oxygen of the air4 ,the interaction of the two substances produces a new substance1 and it is only during this process that a corresponding part of the chemical energy is liberated4 ,there are a few chemical processes also 7allotropic and isomeric changes7 in which a single substance without the co-agency of another substance can give off energy4 ,but the quantity of energy thus obtained is infinitely small as compared to that liberated by the interaction of two or more substances4 ,because of the necessity of two or more substances to co-operate in giving off chemical energy1 the opportunity for the transformation of chemical energy is less than for the transformation of the other forms of energy1 and this is the main reason why it can be conserved so long and so easily4 ,all that is necessary is to prevent contact with another substance4 ,this is a problem1 it is true1 which from the point of view of strict theoretical rigor it is almost impossible to solve4 ,in practice1 however1 it can be easily solved for periods of time long enough at least to require special means to enable us to recognize that it is only a temporary and not a fundamental solution4 ,scientifically expressed1 the cause of this is that the diffusion of the various substances in one another can theoretically never be completely eliminated1 while on the other hand the velocity of the diffusion over distances measured only by decimeters is extremely low4 ,,part ,,iv ,,the ,,biologic ,,sciences #ed4 ,life4 ,among the bodies in our environment that are ponderable and have mass the animate beings are so strikingly distinguished from the inanimate that in most cases we have not the slightest doubt whether a body belongs to the one kind or to the other1 even if in some cases we happen not to be familiar with its peculiar form4 ,in the first place1 therefore1 we must answer the question in a general way and tell what the distinguishing peculiarities are that mark them off one from the other4 ,the first peculiarity is this1 that living organisms are not stable but stationary forms4 ,this distinction is based upon the fact that a stable form is at rest or unchangeable in all its parts1 while a stationary body1 though it seems unchangeable in its form1 internally undergoes a constant change of its parts4 ,thus1 a brass faucet is a stable body1 since it not only preserves its form and function permanently1 but consists at all times of the same material and shows the same peculiarities1 such as stains1 defects in form1 etc4 ,it cannot be said1 it is true1 that it will remain completely unchanged for all time4 ,its metal suffers a gradual chemical and mechanical deterioration4 ,but this is not essential to the existence of the faucet1 since the deterioration varies greatly with circumstances1 and if conditions are ideal it can be reduced to zero4 ,on the other hand1 the jet of water flowing from the faucet is a stationary body4 ,in favorable circumstances it can assume a constant form1 so that at a hasty glance it might be taken for a stable glass rod4 ,on closer examination it will be found that the parts of water of which it is formed are not the same at any given instant as the instant before1 each part that has flowed away being replaced by another just as large following it4 ,from this difference in the nature of the two bodies results a difference in their behavior4 ,if ,i make a mark on the faucet with a file1 the mark remains permanent4 ,but even if ,i sever the entire water jet with a knife1 the cut is healed the next moment1 because by reason of the continuous flow of the water1 the severed place is instantly eliminated from the body4 ,owing to this nature peculiar to stationary bodies1 they have the capacity of being healed or of regeneration4 ,for a body to continue permanently in a stationary condition the material of which it is composed must be permanently supplied4 ,if we turn off the faucet1 the water jet immediately disappears or dies4 ,evidently1 therefore1 a stationary body can subsist by its own means only if it has the property or capacity to provide itself continually with the necessary material4 ,this material consists in the main of ponderable or chemical substances of definite physical and chemical properties1 and thus the change of substance1 metabolism1 appears as a necessary property of the stationary body4 ,in order1 however1 that metabolism should take place we must have free energy1 or energy having the capacity to work1 since it is only free energy that can cause substances to change1 just as every phenomenon in the world implies the equalization of free energy4 ,for a stationary body to exist independently1 therefore1 it must have the property of being able spontaneously to possess itself of the necessary substances and of free energy4 ,but since1 as we have already said1 the energy of organisms is stored up and used in the main in the form of chemical energy1 the two tasks which a stationary body has to perform1 that of meeting the need for substances and for energy1 are as a rule externally combined4 ,in organisms these two necessities combined are called nutrition1 and thus we recognize in the capacity for self-acquisition of nutrition another essential property of organisms4 ,a third essential property of organisms is the capacity for reproduction1 for the bringing forth of similar beings4 ,it is never impossible that the balance between the receipts and expenditures of a stationary body should1 in consequence of some external causes1 be disturbed1 even when under normal conditions it possesses the property of self-nutrition4 ,if the disturbance remains below a certain point1 then1 as we have already stated1 regeneration sets in4 ,but the disturbance may rise above that point1 in which case the body ceases to exist1 or dies4 ,then a similar body will not arise unless the manifold necessities that have led to the origin of the first will combine again to produce the second4 ,that such a thing is possible1 that1 in fact1 it often happens1 is shown1 for example1 by the waves of the ocean1 which have a stationary character since1 while they are composed of constantly changing masses of water1 their form remains unchanged4 ,the waves are destroyed in the breakers1 but arise again and again through the action of the wind upon the surface of the water4 ,but the more complex such bodies are the less easily they are formed1 while once they have been formed and have found the conditions of their existence1 their preservation is much easier4 ,beings1 therefore1 which have the capacity to form similar bodies out of themselves regularly and at the right time can preserve their species much more easily than those in which this property is absent4 ,death has to a great extent lost its power over beings capable of reproduction4 ,by way of illustration let us take another stationary thing1 a flame4 ,a flame is not an organism because it is not self-sustaining4 ,yet it multiplies itself4 ,and while a single little flame soon dies out1 the sea of flame of a burning forest1 which started from a single small flame1 is well-nigh inextinguishable1 and it cannot be fought in any other way than by letting it die its natural death and burn to the end4 ,thus1 while the fulfilment of the first two conditions1 the stationary change and the self-supply of food1 could produce bodies1 which would be able to exist for a longer or shorter period1 but which at some time would have to give way to other bodies of different form and nature1 the capacity for reproduction creates the condition that forms of the same species continue to exist even after the existence of the individual has ceased4 ,these three properties constitute the essential characteristics of animate things or organisms4 ,that the organisms are all constructed upon the basis of chemical energy is a fact of experience which may be understood to imply that the other forms of energy are not capable of producing the above-mentioned conditions4 ,this is due to the properties of chemical energy to which ,i have already called attention3 its great concentration and1 at the same time1 its capacity for prolonged preservation4 ,that chemical energy is the only form of energy suitable to life is obvious from the fact that in airship navigation1 for example1 the kinetic energy required for steering can be supplied only in the form of gasoline or hydrogen1 that is1 in the form of chemical energy1 because any of the other forms would be much too heavy4 ,the flight of a bee or the swimming of a dolphin cannot be conceived of except as brought about through chemical energy4 ,that this chemical energy is essentially that of carbon has also been established by experience1 although it is not quite universal1 for the sulphur bacteria found their household upon the energy of sulphur4 ,the cause of the preference of carbon is again to be sought in its special fitness for the purpose1 due1 on the one hand1 to its wide distribution1 and1 on the other hand1 to the exceeding manifoldness of its combinations4 ,finally1 the construction of the organisms from a peculiar combination of solid and liquid substances can be proved to be equally due to technical relations4 ,these three last-named peculiarities are therefore to be regarded as the special characteristics of the organisms with which we are acquainted on the surface of the earth in the conditions there prevailing4 ,we need not regard them conceptually as unchangeable or irreplaceable4 ,but the first three characteristics1 namely1 the stationary nature1 self-supply of nutrition1 and reproduction1 we may regard as the essential characteristics of organisms4 ,they constitute the frame within which everything must be found which we should recognize as living in the widest sense4 #ee4 ,the ,storehouse of ,free ,energy4 ,if we ask whence the organisms obtain the free energy which they require for the maintenance of their stationary existence1 the answer is that solar radiation alone furnishes this supply4 ,without this permanent supply the free energies upon the earth1 so far as our knowledge goes1 would long ago have reached a state of equilibrium1 and the earth's bodies would be stable1 that is1 dead and not stationary and living4 ,it is comprehensible1 therefore1 that machines should have evolved in the organism for transforming the radiant energy of the sun into a permanent form1 and1 as we have already learned1 chemical energy is permanent1 while radiant energy is an extremely transitory form of energy1 that is1 it changes very readily4 ,the very fact that1 owing to the change from day to night1 the supply of radiant energy periodically ceases1 makes the storing-up of energy for the night necessary to the existence of a form dependent upon it4 ,thus1 we recognize in the photochemical processes1 that is1 in the transformation of radiant energy into chemical energy1 the foundation of life on earth4 ,this work is done by the plants1 which thus provide a store of free energy not only for their own needs but also for all the other organisms which possess themselves directly or indirectly of the plant-chemical supplies in order to utilize them for their individual purposes4 ,in this manner nourishment in the widest sense is secured for all organisms1 being based upon the regular supply of free energy derived from the sun4 ,this also explains the great chemical similarity of all organisms1 which could not subsist if they were not so constructed as to be able to utilize the chemical energy in the form in which it is provided by the plants4 ,of the great stream of free energy poured out from the sun into cosmic space the earth receives an extremely small portion 7corresponding to the bit of space it occupies in the heavenly sphere as seen from the sun71 and the plants collect and store up only a very small fraction of this portion received by the earth4 ,measurements have shown that in most favorable circumstances a plant leaf changes only about #a_/ej of the radiant energy it receives into chemical energy4 ,if we consider that only a small part of the surface of the earth is covered with plants and that during the winter no energy from the sun is stored up at all1 we perceive what infinite possibilities for development there still are in arresting and storing up free energy4 ,the part stored up by the plants flows from these into the countless streams1 brooks1 and veins of the other organisms1 to end finally as used-up energy1 or energy at rest4 ,this energy is at rest1 it is true1 only in relation to the earth's surface4 ,we do not know whether the radiation from the earth1 which at present amounts to about as much as the radiation from the sun to the earth1 is in its turn somewhere utilized4 ,while the free energy is poured out in such a stream in one direction1 the ponderable substances of which the organisms are made up circulate through plants and animals and back again4 ,this is especially true of carbon1 which is freed from its combination with oxygen1 that is1 from carbonic acid1 by the sun energy transformed in the plants4 ,while carbon serves to build up the plant body and represents its supply of chemical energy1 the oxygen is returned to the air4 ,these two substances are again chemically combined in the various organisms and the quantities of energy which were necessary for their decomposition are again available for the manifold functions of life4 ,the product of the chemical combination1 carbonic acid1 returns to the air and is ready for renewed decomposition in the plants4 ,thus1 the entire mechanism of life can be compared to a water-wheel4 ,the free energy corresponds to the water1 which must flow in one direction through the wheel in order to provide it with the necessary amount of work4 ,the chemical elements of the organisms correspond to the wheel1 which constantly turns in a circle as it transfers the energy of the falling water to the individual parts of the machine4 #ef4 ,the ,soul4 ,our observations so far have shown the organisms to be extremely specialized individual instances of physico-chemical machines4 ,now we have to take into consideration a property which seems markedly to distinguish them from the lifeless machines1 and which we have already encountered in the very beginning of our treatise4 ,it is the property which we there called memory1 and which we will define in a very general way as the quality by virtue of which the repetition in organisms of a process which has taken place a number of times is preferred to new processes1 because it originates more easily and proceeds more smoothly4 ,it is readily apparent that by this property the organisms are enabled to travel on the sea of physical possibilities as if equipped with a keel1 by which the voyage is made stable and the keeping of the course is assured4 ,if we ask whether this is exclusively a quality of organisms the question cannot be answered affirmatively4 ,inanimate bodies also have something like the quality of adaptation4 ,an accurate clock attains its valuable qualities only after it has been going for some time1 and the best violin is raw until it has been broken in4 ,an accumulator must be formed before it can do its normal amount of work4 ,all these processes are due to the fact that the repetition of the same process improves the action1 that is1 it facilitates or increases it4 ,adaptation or memory1 then1 is not limited to organisms4 ,in inanimate things1 however1 this property is comparatively rare4 ,memory1 therefore1 is to be regarded as another property of organisms representing an extreme specialization of the inorganic possibilities4 ,this is an important point of view for what follows4 ,in the first place1 this property of adaptation facilitates and assures nourishment4 ,if we take the fundamental idea developed by ,darwin1 that that predominates in the world which by virtue of its properties endures the longest time1 then it is evident that a body which teleologically preserves and elaborates its nourishment will live longer than a similar body without this property4 ,moreover1 by the general process of adaptation1 these teleological properties come to be more greatly developed and more readily exercised in the body that lives longer1 so that its long life gives it another advantage over its rival4 ,thus we can understand how this property of adaptation1 which at first is to be conceived of as a purely physico-chemical quality is found developed in all organisms4 ,in its most primitive forms the quality of adaptation gives rise to the phenomena of reaction1 or to reflex actions1 that is1 to a series of processes in the organism in response to the stimulus of an outward energy4 ,this response is made in furtherance of the life of the organism4 ,reactions that serve a certain end1 that is1 teleological reactions1 can naturally be developed to such stimuli alone to which the organism is frequently and regularly subjected4 ,this is why adaptation to unusual phenomena is generally lacking1 and in relation to them the organisms are often extremely unfit4 ,the typical example of this is the moth1 which flies into the light and is burned4 ,as the reactions become more fixed they develop into longer and more complicated series1 which then appear to us as instinctive actions4 ,but here1 too1 we find the characteristic unsuitability when unwonted circumstances arise1 even if the teleologic reactions to stimuli become more manifold4 ,finally1 there are the conscious acts which appear to us to be the highest degree of the series4 ,it is with the teleologic regulation of these conscious acts1 including the very highest activities of mankind1 that this book deals4 ,they are distinguished from instinctive action by the fact that they no longer proceed in a single and definite series1 but are combined at need in the most manifold ways4 ,but the fundamental fact1 namely1 that actions are based upon the repetition of coinciding experiences1 at once appears here also1 since the basis of the entire conscious life of the soul1 the formation of concepts1 is made possible only through repetition4 ,thus1 we are justified in regarding the various degrees of mental activity from the simplest reflex manifestation to the highest mental act as a connected series of increasingly manifold and purposive actions proceeding from the same physico-chemical and physiological foundation4 #eg4 ,feeling1 ,thinking1 ,acting4 ,for good reasons it is generally assumed that the organisms have not always been what they are now1 but have developed from previous simpler forms4 ,it is undecided whether originally there were one or several forms from which the present forms sprang1 nor is it known how life first made its appearance on earth4 ,so long as the various assumptions with regard to this question have not led to decisive1 actually demonstrable differences in the results1 a discussion of it is fruitless1 and therefore unscientific4 ,the usual word evolution is non-purposive in so far as it signifies the appearance of something already existing4 ,another conception is better according to which the influence of changed conditions of existence has yielded the most important factor of change4 ,the change that the organisms undergo is always in a definite direction4 ,more and more complex and manifold forms are evolved1 and the evolution of these forms is characterized by an ever greater specialization of the functions of life1 so that every specially developed organ comes to perform but one function4 ,it is true that by this means the organism is better fitted to perform those functions1 but at the same time it grows more susceptible to injury1 since its existence depends upon the proper simultaneous activity of many different organs4 ,such an evolution1 therefore1 can occur only when the general conditions of life have grown steadier1 so that the danger of disturbance becomes less4 ,we are accustomed to regard changes in this direction as higher developments1 and the progressive simplifications of the organization 7as for example in parasites7 as backward steps4 ,since our opinion as to what constitutes a higher and a lower organism is doubtless arbitrary1 let us ask whether it is not possible to find an objective standard by which to measure the relative perfection of the different organisms4 ,the question must be answered in the affirmative when we take into consideration the following4 ,since the quantity of available free energy upon the earth is limited1 the organism which transforms the energy at its disposal more completely and with the least loss into the forms of energy necessary for the function of life1 must be regarded as the more perfect organism4 ,in fact1 we observe that with increasing complexity of the organisms there is for the most part also an increasing improvement in that direction1 and we can therefore speak of some beings as more perfect than others4 ,this view-point is especially significant in the evaluation of human progress1 appearing1 as it does1 as the general standard of all civilization4 ,the perfection of the organism shows itself in relation to the outer world in the development of the sense organs4 ,while a single-celled animal reacts almost exclusively to chemical1 sometimes also to optical1 stimuli1 and receives these with the entire surface of its body1 special parts of the body develop more and more toward perfection4 ,these are the parts that respond with special ease to the appropriate stimuli1 that is1 react to them with an increasingly smaller expenditure of energy4 ,then the points at which the stimuli are received are separated from those in which the reaction occurs1 and the two are connected by conducting paths1 the nerves1 in which an energy process takes place4 ,our present knowledge of this process still leaves much to be desired4 ,it is a process which moves with fairly great but by no means extraordinary rapidity 7about ten to thirty meters per second7 along the conducting paths4 ,at the one end of this path it is caused by actions of various kinds1 chiefly that of the specific energy1 for which the sense organ is developed4 ,at the other end it discharges specific effects4 ,there is no doubt that here we have in each instance a case of energy transformation connected with a discharge1 that is1 with the action of other energies which lie at the ends ready for change4 ,hence there is no equivalence between the different kinds of energy1 the discharging and the discharged1 mostly not even a proportional relation1 although both increase and decrease simultaneously4 ,what the form of the energy is that is propagated in the nerves is unknown4 ,it can be either a special form which arises only under the conditions here present 7just as1 for example1 a galvanic stream develops only under definite chemical and spacial conditions71 or a special combination of known energies1 as in sound and probably in light4 ,some day1 it is likely1 we shall have a more accurate knowledge of the nerve process which will solve the question4 ,when such a process is caused by some energy impulse from without1 it may produce various results4 ,in the simplest case it discharges the corresponding reaction1 just as the leaves of the sensitive plant close when they are touched4 ,or it may give rise to a series of processes following one another like the instinctive actions4 ,or1 finally1 it may bring about a series of inner processes which lead to an extreme differentiation of slight differences of this stimulus and to a corresponding graded reaction with the anticipation of success4 ,we call this conscious thinking1 willing1 and acting4 ,through the age-long effect of the blunder committed by ,plato in making a fundamental distinction between mental life and physical life1 we experience the utmost difficulty in habituating ourselves to the thought of the regular connection between the simplest physiological and the highest intellectual acts4 ,moreover1 this contrast has been accentuated by the mechanical hypothesis4 ,if we abandon the mechanical hypothesis and adhere to the summarization of experience free from all hypotheses1 as represented in the science of energy1 this contrast disappears4 ,for even if we concede the impossibility of conceiving thought as mechanical1 there is no difficulty in conceiving of it as energetic1 especially since we know that mental work is connected with expenditure of energy and exhaustion just as physical work is4 ,however1 the elucidation of this subject lies almost entirely in the future since the idea just developed has but only begun to influence scientific work in this field4 ,but judging from the results that have already been obtained we may hope for a speedy development4 #eh4 ,society4 ,the external circumstance that as an organism multiplies the new being must come to life in the proximity of the older one1 is in itself cause for the formation of closed groups confined to certain localities by animal organisms of the same species4 ,but they become scattered if the advantage of their living together is not such as to outweigh the disadvantage of having a narrow field of competition for the means of sustenance4 ,thus we see different plants and animals behaving differently in this respect4 ,while some species live in as great isolation as possible1 others form communities1 even if there is no mechanical tie to hold them together by a common integument4 ,since the second case is true of man in a highly marked degree1 his social characteristics and needs form a large and important part of his life4 ,and since1 further1 the socialization of man makes continuous headway with increasing civilization--we need but think of the development of the former little groups and tribes into states and the present very active internationalization of the most important affairs of mankind1 especially of the sciences--the social problems also occupy an ever larger place in the organization of human life4 ,what distinguishes man most essentially from the other animals1 even the most advanced1 is his capacity for perfection1 which in the lower animal can be paralleled at best by its capacity for self-preservation4 ,while the organization of the animals within the short period of which we have any historical knowledge has to all appearances remained essentially unchanged1 the world of mankind has changed in quite a remarkable way4 ,this change consists in an increasing subjection of the external world to human purposes1 and rests upon the increasing socialization of his capacities4 ,memory and heredity 7the latter being but an extension of memory to the offspring1 which is to be conceived of as a part of the older organism7 secures in the first place only the preservation of the stock and the renewed development of the new individual in the average type4 ,if a specially favored individual succeeds in accomplishing greater achievements1 he may in favorable circumstances transmit this capacity for higher attainments to his offspring4 ,but such individuals gain an advantage in the struggle for existence only if the other sides of their activity do not suffer curtailment as a result4 ,with the limited amount of energy at the individual's disposal every extraordinary accomplishment involves a corresponding one-sidedness1 and as soon as a certain measure is slightly overstepped1 it will cause a reduction of the other functions which will render the individual less fit in the struggle for existence4 ,but this is true only so long as an individual must live by himself4 ,as soon as he forms part of a social organization which benefits by his particular activity1 the organization compensates for the personal disadvantages by its collective activity1 and a social community not only finds room for such special developments1 but it even encourages and promotes them4 ,we have already seen that such manifestations occur within the organism itself4 ,higher functions1 depending upon the higher susceptibility of the sense organs1 can only be attained at the expense of the general functions by the organ in question4 ,we observe this fact in all socially organized beings1 like bees and ants1 which display a high degree of specialization in the functions of the individual subordinate groups2 the specialization often being carried so far that the individual groups can no longer subsist by themselves alone4 ,it is only the organization as a whole that is capable of permanent existence4 ,while the evolution of such superior functions involves a corresponding differentiation1 and therefore a division and separation of the superior functions within the social structure1 the necessity for communication and for mutual support results in an approximation of the individuals and the groups4 ,in every society1 therefore1 the centrifugal and the centripetal forces work simultaneously in co-operation and in opposition to one another4 ,while the extreme specialization on the one hand seems to make for the best individual functioning1 on the other hand it renders the entire collective structure much more dependent1 and therefore much more subject to injury1 as is shown by the example of the queen bee1 whose departure threatens the existence of the entire hive4 ,thus a medium degree of differentiation will as a general rule produce the most permanent social structure4 #ei4 ,language and ,intercourse4 ,the essential value of the social organization resides in the fact that the work of the individual1 in so far as it is adapted to it1 accrues to the benefit of the collective whole4 ,for this it is absolutely essential that the members of the collectivity should be able to have intercourse with one another in order that every part of the general activity may be communicated to the others4 ,this intercourse is obtained through language in the most general sense4 ,we have already learned that the essence of language consists in the co-ordination of concept to sign4 ,the social application of language demands that the signs co-ordinated to the concepts in use should be the same for all the members of the social organization4 ,only in this way can the members make themselves mutually understood4 ,but intelligible means of communication and division of labor impart to the social knowledge that is set down in writing a kind of independent existence4 ,many centuries ago the possibility ceased for one person to store in his memory the entire stock of human knowledge4 ,nowadays we have men who are versed only in single parts of separate sciences1 and the aggregate knowledge appears at first to be a unity existing only in thought4 ,but because this knowledge is set down in signs which endure far beyond the life of the individual and at the appropriate moment can unfold its entire power even after a long period of inactivity1 it has acquired an existence of a social character independent of the individual4 ,for although it survives the individual1 it cannot survive the death of human society4 ,as the socialization of all mankind advances to ever greater unities1 the linguistic limitations sprung from former stages of evolution prove to be a hindrance4 ,the mother tongue1 of course1 forms the first and most important entry for the individual to the common store of knowledge4 ,but in view of the linguistic limitation of which ,i have just spoken the efforts in our day are carried on with renewed zeal to create a universal auxiliary language 7p4 #ajj7 by means of which intercourse should be made possible beyond the language boundaries4 ,there have already been gratifying results4,i ,i ,at the present time ,ido is the best4 ,it is a highly practicable artificial language1 and its advocates have succeeded in organizing it to insure its normal development4 ,an older and still rather widespread form called ,esperanto has failed to organize itself so as to insure its development and it must inevitably die out4 #fj4 ,civilization4 ,everything which serves the social progress of mankind is appropriately called civilization or culture1 and the objective characteristic of progress consists in improved methods for seizing and utilizing the raw energies of nature for human purposes4 ,thus it was a cultural act when a primitive man discovered that he could extend the radius of his muscle energy by taking a pole in his hand1 and it was another cultural act when a primitive man discovered that by throwing a stone he could send his muscle energy a distance of many meters to the desired point4 ,the effect of the knife1 the spear1 the arrow1 and of all the other primitive implements can be called in each case a purposive transformation of energy4 ,and at the other end of the scale of civilization the most abstract scientific discovery1 by reason of its generalization and simplification1 signifies a corresponding economy of energy for all the coming generations that may have anything to do with the matter4 ,thus1 in fact1 the concept of progress as here defined embraces the entire sweep of human endeavor for perfection1 or the entire field of culture1 and at the same time it shows the great scientific value of the concept of energy4 ,if we consider further that1 according to the second fundamental principle1 the free energy accessible to us can only decrease1 but not increase1 while the number of men whose existence depends directly on the consumption of a due amount of free energy is constantly on the increase1 then we at once see the objective necessity of the development of civilization in that sense4 ,his foresight puts man in a position to act culturally4 ,but if we examine our present social order from this point of view1 we realize with horror how barbarous it still is4 ,not only do murder and war destroy cultural values without substituting others in their place1 not only do the countless conflicts which take place between the different nations and political organizations act anticulturally1 but so do also the conflicts between the various social classes of one nation1 for they destroy quantities of free energy which are thus withdrawn from the total of real cultural values4 ,at present mankind is in a state of development in which progress depends much less upon the leadership of a few distinguished individuals than upon the collective labor of all workers4 ,proof of this is that it is coming to be more and more the fact that the great scientific discoveries are made simultaneously by a number of independent investigators--an indication that society creates in several places the individual conditions requisite for such discoveries4 ,thus we are living at a time when men are gradually approximating one another very closely in their natures1 and when the social organization therefore demands and strives for as thorough an equalization as possible in the conditions of existence of all men4 ,,index ,above and below1 distinction between1 #aba ,abstract1 concrete and1 #af ff4 ,abstraction1 #bj ,action1 conscious1 #agd2 instinctive1 #agd ,adaptation1 #agb ff4 ,aeromechanics1 #adg ,algebra1 #hj ,alikeness1 definition of1 #ea ff4 ,allotropic changes1 #afa ,analysis1 infinitesimal1 #aaa ,analytic geometry1 #abb ff4 ,analytic judgments1 #ff ,anthropology1 #eg ,ants1 specialization of1 #aha ,applied sciences1 #eg ff4 ,a priori judgments1 #dd ,aristotle1 #ch1 #ff ,aristotle's logic1 #bb ,arithmetic1 #gi ff4 ,assertions1 never absolutely correct1 #ec ,association1 #fc ff41 #ha ,astronomic objective1 #f ,astronomy as an applied science1 #eh ,atomic hypothesis in chemistry1 #adb ,atoms1 #ada ,bees1 specialization of1 #aha ,biological sciences1 #ee2 life most general concept in1 #ef ,botany1 #ef ,csar1 ,julius1 #gf ,capillary phenomena1 #adf ,capillary theory1 #adg ,carbon1 its circulation through plants and animals1 #aga2 life based on the energy of1 #afh ,carbonic acid1 #aga ,carnot1 ,sadi1 #aea ,causal relation1 purification of1 #cd ff4 ,causation1 the law of1 #ca ff4 ,chemical combinations1 #ga ff42 quantitative relations in1 #gd ,chemical energy1 #aei ff42 capable of powerful concentration1 #afa2 different forms of1 #aei ,chemical formulas represent concepts not sounds1 #ie ,chemistry1 #bj1 #dg1 #ee2 significance of1 #afj ff4 ,chinese script based on direct co-ordination1 #ic ,civilization1 #ahd ff4 ,classification1 not definite1 #b2 purpose of1 #b-d ,classification of the sciences1 #ec ff4 ,collective activity1 #aha ,combination1 sequence in1 #gc ff4 ,combinations1 theory of1 #ga ,combinatory schematization1 #gc2 in chemistry1 #ga ff42 in physics1 #gb ,communication1 #aha ,community among plants and animals1 #agi ,comparison1 #hb ,comte1 ,auguste1 #ed ,concept1 the most general1 #fa ff4 ,concepts1 arbitrary1 #bc2 complex1 #bc2 complex empirical1 #bc2 definition of1 #af2 empirical1 #ah2 formation of1 #ai2 general1 #bf2 in ceaseless flux1 #hh2 science of1 #ae ff41 #abb2 simple1 #bj2 simple and complex1 #ai ff4 ,conclusion1 the1 #bd ff42 analytic1 #ff2 scientific1 #bg1 #cj1 #ff ff4 ,concrete and abstract1 #af ff4 ,conjugacy1 most general concept in formal sciences1 #ef ,conscious action1 #agd ,conscious thinking1 willing1 and acting1 #agh ,conservation of energy1 the law of the1 #ace ff4 ,conservation of matter1 #ach ,conservation of the sum of work and kinetic energy1 the law of the1 #acd ,conservation of work1 the law of the1 #acj ,conservation1 quantitative1 #aca ,continuity1 #aja ff42 the law of1 #aac ff4 ,co-ordinated signs1 change in1 #hh ff4 ,co-ordination1 #hj ff42 a means of obtaining facts without dealing directly with the corresponding realities1 #hg2 between concept and word not unambiguous1 #hi2 between concept and written sign1 direct and indirect1 #ib ff42 identity the limit case in1 #hb2 integral numbers the best basis of1 #he2 in use among primitive men and higher animals1 #hg2 its importance1 #he2 methodology of the sciences based upon1 #he2 of numbers with signs1 #ij ff42 possibility of unambiguous1 #hh ,copernican theory1 #aag ff4 ,copernicus1 #aag1 #ada ,corpuscular theory of light1 #e1 #aeg ,counting1 #he ff42 defined1 #he2 purpose of1 #hf ,culture1 see ,civilization ,darwin1 his fundamental theory1 #agc ,deduction1 #dj ff42 the process of1 #da ff4 ,deductive sciences1 #ch ,determinateness1 absolute1 only in ideal world1 #ej ,determinateness of things1 the1 #dg ff4 ,determinism1 #dh1 #ea ,differential ,calculus1 see ,differentials ,differentials1 #aab ,double numbers or double points in a group1 #hb ,dynamics1 #abh ff42 definition of1 #aci ,elasticity1 #ade ,elastic undulatory theory of light1 see ,wave theory of light ,electricity1 principal source of1 #aef ,electricity and magnetism1 #aed ff4 ,electromagnetic theory of light1 #aeg ff4 ,electrotechnics1 #aef ,empirical sciences1 #ch ,energetic mechanics1 #ach ff4 ,energy1 a substance1 #acf2 at rest1 #aed2 free1 #aed2 importance of concept of1 #abh2 in nerves1 #agg2 the most general concept in the physical sciences1 #ef2 of form1 #ade2 of volume1 #ade ,energy intensity1 #aec ,erg1 definition of1 #aej ,esperanto1 #ahc1 note ,euclid1 #dd1 #adj ,european-,american scripts based on indirect co-ordination1 #ic ,experience1 incompleteness of1 #bg2 more limited than the conceivable1 #aah ,experiences1 distinguished by being familiar1 #ca2 limited knowledge of1 #ca ,experiential sciences1 see ,empirical sciences ,extrapolation1 #df1 #ej1 #ajd ,familiarity due to recalling former similar experiences1 #aa ,fechner1 #ajb ,feeling1 thinking1 acting1 #agd ff4 ,force1 #abi ff41 #aec ,formal sciences1 #ed2 are empirical sciences1 #ee2 order most general concept in1 #ef ,foucault's pendulum experiment1 #aba ,freedom of the will1 #ej ff4 ,frequency of process facilitates repetition1 #aa ff4 ,function1 #aji ff42 continuous and discontinuous1 #aaj2 most general concept in formal sciences1 #ef ,functional relation1 the application of the1 #aab ff4 ,functions1 the theory of1 #aaa ,fundamental principle1 the second1 #aej ff4 ,gases1 #ade ,generalization1 suitable place for1 in text-books1 #i ff4 ,geometry1 #dg1 #ed1 #aai1 #abg2 ancient and modern methods of1 #aaj ff4 ,goethe1 #ii ,good usage in language1 #ajj ,grammatical correctness1 importance attached to1 #ii ,grammatical rules1 #ig ,gravitation potential1 the1 #aab ,group1 the1 #fe ff42 double members or double points in1 #hb2 linear arrangement of members of1 #ge ff4 ,groups1 artificial and natural1 #fi ff42 closed1 among animals1 #agi2 infinite1 equality of1 #hd2 related1 #fi ff42 unequivocal order of1 #hc ,heat1 mechanical equivalent of1 #adi2 theory of1 #adg ff4 ,heat energy1 #adh ff4 ,heat engine1 #aea2 ideal1 #aea ff4 ,heat quantity1 #adh ff4 ,heliotrope1 #ij ,herbart1 #ajb ,heredity1 #ahj ,higher analysis1 #aaa ,homonym1 #hi ,hydromechanics1 #adg ,ideal cases1 #dd ff4 ,ideal machines1 #acb ,identity1 the limit case in co-ordination1 #hb ,ido1 #ahc1 note ,imperfection1 indestructible quality of science1 #d ,incompleteness1 no hindrance to efficiency of science1 #e ,indestructibility of matter1 see ,conservation of matter ,indo-,arabic notation1 #ia ,induction1 #ch2 the complete and the incomplete1 #ci ,inductive sciences1 #ch ,inference1 by induction1 #ch2 from analogy1 #adj ,infinitesimal analysis1 #aaa ,inorganic world1 lack of memory and foresight in1 #cc ,insoluble problems1 #adb ,instinctive action1 #agd ,intercourse1 language and1 #ahb ff4 ,isolation among plants and animals1 #agi ,isomeric1 #gd ,isomeric changes1 #afa ,judgments1 analytic1 #ff ,kant1 #dd1 #ff1 #aje ,kepler1 #ada ,kinetic energy1 #acb2 and work1 their sum constant1 #acc ff42 transformed into work and vice versa1 #acd ,knowledge1 aim of1 #ai2 individual1 compared to telephone1 #g ff42 limited1 #ca2 possibility of error in1 ineradicable1 #dj2 social character of1 #ahc ,language1 beginnings of1 #hh2 defective in co-ordination1 #if2 distinction between science and knowledge of1 #ih2 good usage in1 #ajj2 and intercourse1 #ahb ff42 needless inflections in1 #ii ff42 of words more imperfect than written language1 #ib2 purpose of its cultivation1 #ii2 the science of1 #ig ff42 unambiguity the ideal of1 #hi2 a universal auxiliary1 #ajj2 written1 #hi ff4 ,leibnitz1 #hh2 his doctrine of pre-established harmony1 #adc2 inventor of differentials1 #aab ,life1 #afc ff42 the most general concept in the biological sciences1 #ef ,light1 #e1 #aef ff4 ,liquids1 #ade ,locke1 ,john1 #ba ff41 #hh2 his elaboration of the notion of simple and complex ideas1 #ba2 his secondary qualities1 #abg ,logic1 #ed1 #fg ff42 content of1 #ai2 definition of1 #ae ff4 ,luther1 #ii ,magnetism1 electricity and1 #aed ff4 ,man1 compared to pair of sieves1 #cd2 his capacity for perfection1 #ahj ,manifold1 the science of the1 #ed ,mass1 #acb ff41 #acf ff42 a substance1 #ach ,mathematical laws1 accuracy of1 #aje ,mathematics1 #ed2 an empirical science1 #ee2 influence on1 of concept of continuity1 #aaa2 its progress after introduction of ,indo-,arabic numerals and algebraic signs1 #aja ,matter1 definition of1 #ach ,mayer1 ,julius ,robert1 #adi2 his discovery of the law of conservation1 #aea ,measurement1 #ajg ,mechanical energies1 #add ,mechanics1 #ee1 #abh ff42 complementary branches of1 #add ff42 definition of1 #ach2 early development of1 #aci2 energetic1 #ach ff42 the first branch of physics treated mathematically1 #aci2 pure or classical1 #add ,mechanistic hypothesis1 the1 as an interpretation of all natural phenomena1 #adb2 especially injurious in study of mental phenomena1 #adb ,mechanistic theories1 #adj ff4 ,mechanistic theory of the universe1 #acb ,mechanization of astronomy1 #ada ,memory1 #af1 #cb1 #ahj2 definition of1 #agb2 general characteristic of1 #fa2 lack of1 in inorganic world1 #ec ,metabolism1 #afe ,methodology of the sciences based upon co-ordination1 #he ,microscope1 #f ,motion1 the science of1 #ed1 #abb2 uninfluenced1 #abb ,musical notation1 #ic ,names1 arbitrariness of1 #fb2 signs and1 #hf ff4 ,natural laws1 #bh ff42 definition of1 #bh2 their extent dependent upon stage of knowledge in each science1 #g2 their usual origin1 #db ff42 prediction from1 only approximate1 #dh ,natural philosophy1 definition of1 #a2 importance of1 in study of science1 #aj2 place of1 in text-books1 #i ff4 ,negation1 #fh ff4 ,nerves1 #agg ,nervous discharge1 #agg ,newton1 ,sir ,isaac1 #ada ,number groups1 unlimited1 #gh ,numbers1 #gh ff42 theory of1 #hj ,numerals1 co-ordination of1 with signs1 #hf ,numerical names different in different languages1 #hf ,numerical signs international1 #hf ,nutrition1 #afe ,objective1 astronomic1 #f2 photographic1 #f ,objective character of the world1 #cd ,optical telegraph1 #ij ,optics1 geometric1 #e ,optic signs1 #ij ,order1 most general concept in formal sciences1 #ef ,organisms1 standard for measuring relative perfection of1 #agf2 stationary forms1 #afc ,orthography1 efforts to improve1 #ii2 ,english1 defective in co-ordination1 #if2 exaggerated importance of correctness in1 #ii2 mistakes in1 #ig2 reform of1 #ig ,parabolic curve1 #dh ,paradoxes of the infinite1 #hd ,pasigraphy1 #ib ff42 ,chinese system of1 #id ,permanent in change1 the1 #aca ,perpetual motion1 #acj ,perpetual motion machine1 #aec ,philology1 #ig ff4 ,philosophy1 limited progress in1 #aja ,phonetic writing1 #cc ff4 ,phoronomy1 #ed1 #aai1 #abb1 #abg ,photochemical processes1 foundation of terrestial life1 #afi ,photographic objective1 #f ,physical sciences1 #ee ,physics1 #dg1 #ee2 each branch of1 treats of a special kind of energy1 #aci the science of the different kinds of energy1 #gb2 ,physiology1 #ee ff4 ,plato1 his distinction between mental and physical life1 #agh ,polarity of electricity and magnetism1 #aee ,political organizations1 conflicts between1 #ahe ,prediction1 #ab ,pre-established harmony1 #adc ,pressure1 #adf1 #aed ,progress1 depends on collective labor1 #ahe2 economy of energy1 #ahd2 evaluation of1 #agf ,pseudo-problems in science1 #adb ,psychology1 #dg1 #ee ff4 ,psycho-physical parallelism1 #adc ,ptolemy's system1 #aag ,pure science1 #eg ,quantity1 the science of1 see ,mathematics1 #ed ,radiant energy1 #aeg2 its importance to man1 #aeh ,rational sciences1 see ,deductive sciences ,rays1 straight lines of1 #e ,reaction1 teleological1 #agc ,reality1 #af ff4 ,reflection1 #e ,reflex action1 #agc ,refraction1 #e ,repetition1 basis of conscious life1 #agd ,reproduction1 #afe ff4 ,roman notation1 #ia ,science1 aim of1 #ac ff42 comparison of1 to a network1 #db2 comparison of1 to a tree or forest1 #f2 definition of1 #ac2 eternal truth of1 #f ff42 for its own sake1 #ac ff42 the facts of1 unalterable1 #h ff42 the function of1 #bc1 #cg2 importance of theoretical1 #ae2 its procedure1 #de2 the study of happiness1 #bh ,sciences1 the table of the1 #ed ff4 ,scientific discoveries1 independent simultaneous1 #ahe ,scientific instinct1 #dc ,scientific materialism1 #ach ,scientific written language based on direct co-ordination1 #ic ,self-preservation1 #ahj ,sense organs1 #agf ff4 ,shakespeare1 #ii ,signs and names1 #hf ff4 ,social characteristics1 importance of1 #agi ff4 ,social classes1 conflicts between1 #ahe ,socialization of human capacities1 #ahj ,social order still barbarous1 #ahe ,social organization1 #ahj2 how best obtained1 #ahb2 its tendency to equalize conditions1 #ahe2 secures permanence among specialized individuals1 #aha ,social problems1 #agi ff4 ,society1 #agi ff42 centrifugal and centripetal forces in1 #aha ff42 division of functions in1 #aha ,sociology1 #dg1 #ee1 #eg ,solar radiation1 #afi ,soul1 the1 #aga ff4 ,sound signs1 advantage and disadvantage of1 #hi ff4 ,sound writing1 #cc ff41 #ib ff4 ,space1 four-dimensional1 #gg1 note2 homogeneity of1 in horizontal direction1 #aba2 the science of1 #ed2 symmetrical and tri-dimensional1 #aah2 time and1 #aah ff42 tri-dimensional1 #gf ,specialization1 one-sidedness of1 #ahj ff4 ,spelling reform1 #ig ,stable forms1 #afc ,statics1 #abh ff42 definition of1 #ach ff4 ,stationary bodies1 capable of regeneration1 #afd ,stationary forms1 #afc ,substance1 #acb ,surface-energy1 #adf ,syllogism1 the1 classic method of argumentation1 #fe ff4 ,synonym1 #hi ,table of the sciences1 #ed ff4 ,telegraph1 optical1 #ij ,teleological properties of organisms1 #agc ,teleological reaction1 #agc ,telescope1 #e ,temperature1 #adh ,theoretical science1 importance of1 #ae ,theory of functions1 #aaa ,theory of numbers1 #hj ,thermo-chemistry1 #cg ,thermo-dynamics1 #aec ,thing1 definition of1 #fb ff4 ,thought conceived of as energetic1 #agh ,threshold1 #ajb ,time1 a form of inner life1 #gf2 measurement of1 #abb2 one-seried1 or one-dimensional1 #aah2 and space1 #aah ff4 ,unambiguity1 in language1 #hi2 of co-ordination of numbers to signs1 #ij ,universal auxiliary language1 #ajj1 #ahc ,velocity1 #acc ,volume energy1 #ade ,war1 #ahe ,wave surface1 #f ,wave theory of light1 #e1 #aeg ,weight1 #acb1 #acg ff42 a substance1 #ach ,work1 mechanical1 #abi2 product of the force and the distance1 #acj2 a substance in a limited sense1 #acf ,written language1 #hi ff4 ,written signs1 #ij ,zoology1 #ef 99 99 99 99 99 ,american ,public ,problems ,,edited ,,by ,,ralph ,,curtis ,,ringwalt ,,immigration3 ,and ,its ,effects ,upon the ,united ,states ,by ,,prescott ,f4 ,,hall1 ,a4,b41 ,,ll4,b41 ,secretary of the ,immigration ,restriction ,league4 #cic pp4 #a4ej net4 ,by mail1 #a4fe4 ,should prove interesting to everyone4 ,very readable1 forceful and convincing4 ,mr4 ,hall considers every possible phase of this great question and does it in a masterly way that shows not only that he thoroughly understands it1 but that he is deeply interested in it and has studied everything bearing upon it4--,boston ,transcript4 ,a readable work containing a vast amount of valuable information4 ,especially to be commended is the discussion of the racial effects4 ,as a trustworthy general guide it should prove a godsend4--,n4 ,y4 ,evening ,post4 ,earnest and unprejudiced4444 ,cannot fail to be of great assistance in clarifying and setting on a solid foundation the ideas of people who are now becoming convinced that the problems of immigration in the nation and the municipality will soon reach a more acute stage than ever before4--,philadelphia ,press4 ,an auspicious omen of the worth of ,messrs4 ,henry ,holt and ,company's recently announced series on ,american ,public ,problems4444 ,mr4 ,hall has been in close touch with the immigration movement and he writes with a grasp and a fullness of information which must commend his work to every reader4444 ,a handbook 444 to which one may turn conveniently for information for which he would otherwise be obliged to search through many a dusty document4--,the ,world ,to-day4 ,,the ,,election ,,of ,,senators ,by ,professor ,,george ,h4 ,,haynes1 ,author of ,representation in ,state ,legislatures4 #cjj pp4 #a4ej net4 ,by mail #a4fe4 ,shows the historical reasons for the present method1 and its effect on the senate and senators1 and on state and local government1 with a detailed review of the arguments for and against direct election4 ,a timely book4444 ,prof4 ,haynes is qualified for a historical and analytical treatise on the subject of the ,senate4 --,n4 ,y4 ,evening ,sun4 ,well worth reading1 and unique because it is devoted wholly to the election of senators and to the deliberations of the ,senate4 --,boston ,transcript4 ,able and dispassionate1 and ought to be widely read4 --,new ,york ,commercial4 ,of considerable popular as well as historical interest4--,dial4 ,henry ,holt and ,company #bi ,,west #bc;,d ,,street ,,new ,,york ,r4 ,m4 ,,johnston',s ,,leading ,,american ,,soldiers ,biographies of ,washington1 ,greene1 ,taylor1 ,scott1 ,andrew ,jackson1 ,grant1 ,sherman1 ,sheridan1 ,mc,clellan1 ,meade1 ,lee1 ,stonewall ,jackson1 ,joseph ,e4 ,johnson4 ,with portraits4 #a vol4 #a4ge net2 by mail #a4hh4 ,the first of a new series of biographies of leading ,americans4 ,performs a real service in preserving the essentials4--,review of ,reviews4 ,very interesting4444 ,much sound originality of treatment1 and the style is clear4--,springfield ,republican4 ,,eliza ,r4 ,,scidmore',s ,,as ,,the ,,hague ,,ordains ,journal of a ,russian ,prisoner's ,wife in ,japan4 ,illustrated from photographs4 #a4ej net1 by mail #a4fb4 ,holds a tremendous human interest4444 ,author writes with wit and a delightfully feminine abandon4--,outlook4 ,this surprisingly outspoken volume 444 could have been written only by an extraordinarily able woman who knew the inside of ,russian politics and also had actual experience in ,japanese war hospitals4--,chicago ,record-,herald4 ,w4 ,f4 ,,johnson',s ,,four ,,centuries ,,of ,,the ,,panama ,,canal ,with #af illustrations and #f colored maps4 #c4jj net2 by mail1 #c4bg4 ,the most thorough and comprehensive book on the ,panama ,canal4--,nation4 ,,john ,l4 ,,givens' ,,making ,a ,,newspaper ,the author was recently with the ,new ,york ,evening ,sun4 #a4ej net2 by mail #a4fb4 ,some seventy-five leading newspapers praise this book as the best detailed account of the business1 editorial1 reportorial and manufacturing organization of a metropolitan journal4 ,it should be invaluable to those entering upon newspaper work and a revelation to the general reader4 ,,the ,,open ,,road ,,the ,,friendly ,,town ,compiled by ,e4 ,v4 ,lucas4 ,full gilt1 illustrated cover linings1 each 7cloth7 #a4ej2 7leather7 #b4ej4 ,pretty anthologies of prose and verse from ,british and ,american authors1 respectively for wayfarers and the urbane4 99 99 99 ,if the reader will send his name and address the publishers will send1 from time to time1 information regarding their new books4 ,,henry ,,holt ,,and ,,company ,,publishers 7x-'#jg7 ,,new ,,york ,,recent ,,volumes ,,in ,,the ,,american ,,nature ,,series 7,prospectus on request7 ,,shell-,,fish ,,industries ,by ,,james ,l4 ,,kellogg of ,williams ,college4 ,large #abmo4 ,illustrated by half-tones and original drawings4 ,just published4 #a4ge net4 ,covers classification1 propagation and distribution4 ,for the person who eats oysters1 clams or scallops1 there is information on their structure1 life-histories and habits4 ,a chapter is devoted to shell-fish as collectors and carriers of disease organisms4 ,the oyster culturist will find the life history of bivalves1 a comparison of various culture methods1 and a description of oyster fields in various parts of the world4 ,several facts concerning the habits of bivalves1 here presented for the first time1 will be of interest to naturalists4 ,,fish ,,stories3 ,alleged and ,experienced1 with a ,little ,history1 ,natural and ,unnatural ,by ,,charles ,f4 ,,holder1 ,author of ,the ,log of a ,sea ,angler1 etc41 and ,,david ,,starr ,,jordan1 ,author of ,a ,guide to the ,study of ,fishes1 etc4 ,with colored plates and many illustrations from photographs4 #a4ge net4 ,a delightful miscellany1 telling about fish of the strangest kind1 with scientific description melting into accounts of personal adventure4 ,nearly everything that is entertaining in the fish world is touched upon and science and fishing are made very readable4--,new ,york ,sun4 ,,insect ,,stories ,by ,,vernon ,l4 ,,kellogg4 ,illustrated1 #a4ej net4 ,strange1 true stories1 primarily for children1 but certainly for those grown-ups who like to read discriminatingly to their children4 ,the author is among a few scientific writers of distinction who can interest the popular mind4 ,no intelligent youth can fail to read it with delight and profit4--,the ,nation4 ,,the ,,life ,,of ,a ,,fossil ,,hunter ,by ,,charles ,h4 ,,sternberg1 ,with introduction by ,prof4 ,h4 ,f4 ,osborn1 #dh ,illustrations1 #a4fj net4 ,the most interesting autobiography of the oldest and best known explorer in this field4 ,one of the most interesting books to be found anywhere4--,william ,allen ,white4 ,,the ,,fresh ,,water ,,aquarium ,,and ,,its ,,inhabitants ,by ,,otto ,,eggeling and ,,frederick ,,ehrenberg4 ,a ,guide for the ,amateur ,aquarist4 ,with #ajj illustrations1 large #abmo1 #b4jj net4 ,the best guide to the aquarium4--,the ,independent4 ,,henry ,,holt ,,and ,,company ,,publishers ,,new ,,york ,,the ,,theory ,,of ,,the ,,theatre ,and ,other ,principles of ,dramatic ,criticism ,by ,,clayton ,,hamilton4 ,author of ,materials and ,methods of ,fiction4 #a4ej net2 by mail1 #a4fj4 ,,contents3 ,,the ,,theory ,,of ,,the ,,theatre4--,what is a ,play8--,the ,psychology of ,theatre ,audiences4--,the ,actor and the ,dramatist4--,stage ,conventions in ,modern ,times4--,economy of ,attention in ,theatrical ,performances4--,emphasis in the ,drama4--,the ,four ,leading ,types of ,drama3 ,tragedy and ,melodrama2 ,comedy and ,farce4--,the ,modern ,social ,drama4 ,,other ,,principles ,,of ,,dramatic ,,criticism4--,the ,public and the ,dramatist4--,dramatic ,art and the ,theatre ,business4--,the ,happy ,endings in the ,theatre4--,the ,boundaries of ,approbation4--,imitation and ,suggestion in the ,drama4--,holding the ,mirror up to ,nature4--,blank ,verse on the ,contemporary ,stage4--,dramatic ,literature and ,theatric ,journalism4--,the ,intention of ,performance4--,the ,quality of ,new ,endeavor4--,the ,effect of ,plays upon the ,public4--,pleasant and ,unpleasant ,plays4--,themes in the ,theatre4--,the ,function of ,imagination4 ,,dramatists ,,of ,,to-,,day ,,rostand1 ,,hauptmann1 ,,sudermann1 ,,pinero1 ,,shaw1 ,,phillips1 ,,maeterlinck ,by ,,prof4 ,,edward ,,everett ,,hale1 ,,jr41 of ,union ,college4 ,with gilt top1 #a4ej net4 7,by mail1 #a4fj47 ,an informal discussion of their principal plays and of the performances of some of them4 ,the volume opens with a paper ,on ,standards of ,criticism1 and concludes with ,our ,idea of ,tragedy1 and an appendix of all the plays of each author1 with dates of their first performance or publication4 ,new ,york ,evening ,post3 ,it is not often nowadays that a theatrical book can be met with so free from gush and mere eulogy1 or so weighted by common sense 444 an excellent chronological appendix and full index 444 uncommonly useful for reference4 ,dial3 ,noteworthy example of literary criticism in one of the most interesting of literary fields4444 ,well worth reading a second time4 ,,the ,,german ,,drama ,,of ,,the ,,nineteenth ,,century ,by ,,georg ,,witkowski4 ,translated by ,,prof4 ,l4 ,e4 ,,horning4 #abmo4 #a4jj4 ,kleist1 ,grillparzer1 ,hebbel1 ,ludwig1 ,wildenbruch1 ,sudermann1 ,hauptmann1 and minor dramatists receive attention4 ,new ,york ,times ,review3 ,the translation of this brief1 clear1 and logical account was an extremely happy idea4 ,nothing at the same time so comprehensive and terse has appeared on the subject1 and it is a subject of increasing interest to the ,english-speaking public4 ,,henry ,,holt ,,and ,,company ,,publishers ,,new ,,york 99 99 99 99 99 ,transcriber's ,notes3 ,bold text is denoted by equal signs4 ,the caret indicates that the following character or expression is superscripted4 ,mid-sentence capital letters are used by the ,author to indicate the beginning of a quote or question1 which terminates at the end of the sentence4 ,typographical errors corrected3 p4 #ajj3 approprate changed to appropriate 7444 to a more appropriate evaluation 44474 p4 #ajh3 meassure changed to measure 7,by the application of the unit measure 44474 p4 #ahd3 correspondng changed to corresponding 7444 signifies a corresponding economy 44474 p4 #aia3 ,a single period deleted from index4 ,p4 #ahh1 #ahi3 limit-case changed to limit case 7#b occurrences71 to mirror text 7#c occurrences74 ,alphabetical sequencing adjusted in index3 ,p4 #ahi3 ,two ',energy' entries moved after ,energetic mechanics4 ,p4 #aia3 ,photographic objective moved below ,photochemical processes4 ,p4 #aia3 ,physics3 ,the order of the sub-entries swapped4 ,p4 #aib3 ,pure science moved down four places to end of ,p entries4 ,p4 #aic3 ,two ',teleological' entries moved after ,telegraph1 optical4