lllllll'' i li ll'llili; liilliillliiii! Hi! BOUGHT WITH THE INCOME FROM THE ■ ■ SAGE ENDOWMENT FUND THE GIFT OF m^nvu ^^ Sage ^,.-^.3.15.0^. 3]xcr,.|w,., 1357 Cornell University Library Q 175.085 1910 Natural philosophy; 3 1924 012 246 678 Cornell University Library The original of this book is in the Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/cletails/cu31924012246678 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 1910 Copyright, 1910, BY HENRY HOLT AND COMPANY Published November, 1910 THE OUINN & BOOEN CO. PRESS RAHWAY N. J. ^Ai The original or this book was published as volume I in Reclam's Bucher der NaTURWISSENSCH AFT . PREFACE The beginning of the twentieth century is marked by a sudden rise of interest in philosophy. This is especially manifest in the vast growth of philosophic literature. The present movement, it is noteworthy, is by no means a revival proceeding from the aca- demic philosophy traditionally represented at the universities, but has rather the original character of natural philosophy. It owes its origin to the fact that after the specialization of the last half century, the synthetic factors of science are again vigorously asserting themselves. 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 totality, must be regarded as the most prolific source of the present philosophic movement, just as it was the source of the natural philosophic endeavors a hundred years ago. But while that old natural philosophy soon ended in a boundless sea of speculation, the present move- ment gives promise of permanent results, because it is built upon an extremely broad basis of experi- ence. The laws of energy in the inorganic world and the laws of evolution in the organic world fur- vi Preface nish mental instruments for a conceptual elabora- tion of the material provided by science, instru- ments capable not only of unifying present knowl- edge, but also of evoking the knowledge of the future. If it is not permissible to regard this unification as exhaustive and sufficient for all time, yet there is still so much left for us to do in work- ing over the material we have on hand from the general points of view just mentioned, that the need for systematizing must be satisfied before we can turn our gaze upon things more remote. The present work is meant to serve as the first aid and guide in the acquisition of these compre- hensive notions of the external world and the inner life. It is not meant to develop or uphold a " sys- tem of philosophy." Through long experience as a teacher the writer has learned that those are the best pupils who soon go their own way. However, it is meant to uphold a certain method, that is, the scientific (or, if you will, the natural scientific), which takes its problems, and endeavors to solve its problems, from experience and for experience. If, as a result, several points of view arise that differ from those of the present day, and consequently de- mand a different attitude toward important matters in the immediate future, this very fact affords proof that our present natural philosophy does not lead away from life, but aims to form a part of our life, and has a right to. CONTENTS PAGE Introduction i PART I General Theory of Knowledge ii 1. The Formation of Concepts ii 2. Science 13 3. The Aim of Science 13 4. Concrete and Abstract 16 5. The Subjective Part 17 6. Empirical Concepts 18 7. Simple and Complex Concepts 19 8. The Conclusion . 24 9. The Natural Laws 28 10. The Law of Causation . . ... 31 11. The Purification of the Causal Relation ... 34 12. Induction ... 38 13. Deduction 40 14. Ideal Cases .... 44 15. The Determinateness of Things 47 16. The Freedom of the Will 50 17. The Classification of the Sciences .... 53 18. The Applied Sciences 57 PART II Logic, the Science of the Manifold, and Mathematics 61 19. The Most General Concept . . . 6i 20. Association . '-63 21. The Group ... 65 vii viii Contents PAGE 22. Negation . . 68 23. Artificial and Natural Groups ... 69 24. Arrangement of the Members . . 75 25. Numbers 78 26. Arithmetic, Algebra, and the Theory of Numbers 79 27. Co-ordination . . 80 28. Comparison ... 82 29. Numbers . . 85 30. Signs and Names . 86 31. The Written Language 89 32. Pasigraphy and Sound Writing ... 92 33. Sound Writing ... ... 96 34. The Science of Language .... 97 35. Continuity lOI 36. Measurement . . 107 37. The Function . 109 38. The Application of the Functional Relation U2 39. The Law of Continuity . . . . 113 40. Time and Space ... ... 118 41. Recapitulation 124 PART III The Physical Sciences 127 42. General 127 43. Mechanics 128 44. Kinetic Energy 132 45. Mass and Matter 136 46. Energetic Mechanics 138 47. The Mechanistic Theories . . . . 140 48. Complementary Branches of Mechanics . . 144 49. The Theory of Heat ... . . 147 50. The Second Fundamental Principle . . 150 51. Electricity and Magnetism 154 52. Light . 156 53. Chemical Energy 159 Contents ix PART IV PAGE The Biologic Sciences . 163 54- Life ... . 163 55. The Storehouse of Free Energy 168 56. The Soul ... . .... 171 57. Feeling, Thinking, Acting 174 58. Society . . 179 Sg. Language and Intercourse 182 60. Civilization 184 Index 187 INTRODUCTION Natural science and natural philosophy are not two provinces mutually exclusive of each other. They belong together. They are like two roads leading to the same goal. This goal is the domina- tion of nature by man, which the various natural sciences reach by collecting all the individual actual relations between the natural phenomena, placing them in juxtaposition, and seeking to discover their interdependence, upon the basis of which one phenomenon may be foretold from another with more or less certainty. Natural philosophy accom- panies these specialized labors and generalizations with similar labors and generalizations, only of a more universal nature. For instance, while the science of electricity, as a branch of physics, deals with the relation of electrical phenomena to one another and to phenomena in other branches of physics, natural philosophy is not only concerned with the question of the mutual connection of all physical relations, but also endeavors to include in the sphere of its study chemical, biological, astro- nomical, in short, all the known phenomena. In other words, natural philosophy is the most general branch of natural science. 2 Introduction Here two questions are usually asked. First, how can we define the boundary line between natural philosophy and the special sciences, since, obviously, sharp lines of demarcation are out of the question? Secondly, how can we investigate and teach natural philosophy, when it is impossible for any one per- son to master all the sciences completely, and so obtain a bird's-eye view of the general relations be- tween all the branches of knowledge? To the be- ginner especially, who must first learn the various sciences, it seems quite hopeless to devote himself to a study that presupposes a command of them. Since a discussion of the two questions will af- ford an excellent preliminary survey of the work in hand, it will be well to consider them in detail. In the first place, the lack of complete and precise boundary lines is a general characteristic of all natural things, and science is a natural thing. If, for instance, we try to differentiate sharply between physics and chemistry, we are met with the same difficulty. So also in biology if we try to settle be- yond the shadow of a doubt the line of separation between the animal and the vegetable kingdoms. If, despite this well-known impossibility, we con- sider the division of natural things into classes and orders as by no means useless and do not discard it, but regard it as an important scientific work, this is practical proof that such classification pre- serves its essential usefulness, even if it does not attain ideal definiteness. For, this imperfection Introduction 3 notwithstanding, classification reaches its end, which is a comprehensive view, and thus a mastery, of the manifoldness of phenomena. For example, with the overwhelming majority of organic beings there is no doubt whether they are animals or plants. Similarly, most phenomena of inorganic nature can readily be designated as physical or chemical. For all such cases, therefore, the existing classification is good and useful. The few cases presenting dif- ficulty may very well be considered by themselves wherever they occur, and we need merely take cog- nizance of them here. It follows from this, to be sure, that classification will be all the better fitted to its purpose the less frequently such doubtful cases arise, 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 ones. In these matters it is much the same as when we look upon the waves on the surface of a large body of water. Our first glance tells us that a number of waves are rolling there; and from a point giving us a sufficiently wide outlook, we can count them and gauge their width. But where is the line of division between one wave and the next? We un- doubtedly see one wave following another, yet it is impossible for us to indicate precisely the end of one and the beginning of the next. Are we then to deduce that it is superfluous or unfeasible to desig- nate the waves as different? By no means. On 4 Introduction the contrary, in strictly scientific work we will en- deavor to find some suitable definition of the boundary line between two consecutive waves. It may then be called an arbitrary line, and in a de- gree arbitrary it will certainly be. But to the in- vestigator this does not matter. What concerns him is, if, with the help of this definition, wave lengths can be unequivocally determined, and if this is possible, he will use the definition as suitable to the purposes of science, without dismissing from his mind the idea that possibly some other definition may provide an even easier or sharper determination. Such an one he would instantly prefer to the old one. Thus we see that these questions of classification are not questions of the so-called " essence " of the thing, but pertain merely to purely practical arrange- ments for an easier and more successful mastery of scientific problems. This is an extremely important point of view, much more far-reaching than is ap- parent here at its first application. As to the second objection, I will admit its valid- ity. But here, too, we have a phenomenon appear- ing in all branches and forms of science. Therefore we must familiarize ourselves with it in advance. Science was created by man for man's purposes, and, consequently, like all human achievements, possesses the indestructible quality of imperfection. But the mere fact that a successful working sci- ence exists, with the help of which human life Introduction 5 has been fundamentally modified, signifies that the quality of incompleteness in human learning is no hindrance to its efficiency. For what science has once worked out always contains a portion of truth, hence a portion of efficiency. The old corpuscular theory of light, which now seems so childishly in- complete to us, was adequate, none the less, for satisfactorily explaining the phenomena of reflection and refraction, and the finest telescopes have been built with its help. This is due to the true elements in it, which taught us correctly to calculate the di- rection of rays of light in reflection and refrac- tion. The rest was merely an arbitrary acces- sory which had to fall when new, contradictory facts were discovered. These facts could not have been taken into consideration when the theory was propounded, because they were not yet known. But when the corpuscular theory of light was replaced by the theory of waves of an elastic ether, geometric optics at first remained quite unchanged, because the theory of straight lines of rays could be deduced from the new views also, though not so easily and smoothly. And geometric optics was then con- cerned with nothing but these straight lines, in no wise with the question of their propagation. It did not become clear until recently that this conception of straight lines of rays is incomplete, though, it is true, it made a first approach toward the presentation of actual phenomena. It fails when it comes to characterize the behavior of a pencil of rays of 6 Introduction large aperture. The old idea of a straight line of rays was to be replaced by a more complex concept with more varied characteristics, namely, the wave- surface. The greater variety of this concept ren- ders possible the presentation of the greater variety of the optical phenomena just mentioned. And from it proceed the very considerable advances that have been made, since the new theory was pro- pounded, in optical instruments, especially the micro- scope and the photographic objective, for the pur- poses of which pencils of rays of large aperture are required. The astronomic objective with its small angle of aperture has not undergone particularly im- portant improvements. Experience in every province of science is the same as in this. Science is not like a chain which snaps when only a single link proves to be weak. It is like a tree, or, better still, like a forest, in which all sorts of changes or ravages go on without causing the whole to pass out of existence or cease to be active. The relations between the various phenomena, once they become known, continue to exist as indestructible components of all future science. It may come to pass, in fact, does come to pass very frequently, that the form in which those relations were first expressed prove to be imperfect, and that the relations cannot be maintained quite generally. It turns out that they are subjected to other influences which change them because they had been unknown, and which could not have been taken Introduction 7 into consideration at the discovery and first formula- tion of these relations. But no matter what changes science may undergo, a certain residue of that first knowledge will remain and never be lost. In this sense, a truth that science has once gained has life eternal, that is, it will exist as long as human science exists. Applying this general notion to our case, we have the following. How far and how generally at any given time the relations of the various phenomena are summed up in fixed forms, that is, in natural laws, will depend upon the stage attained by each of the special sciences. But since science has been in existence it has yielded a certain number of such general laws, and these, though they have been filed down a good deal in form and expression, and have undergone many corrections as to the limits of their application, nevertheless have preserved their es- sence, since they began their existence in the brains of human investigators. The net of the relations of phenomena grows ever wider and more diversified, but its chief features persist. The same is true of an individual. No matter how limited the circle of his knowledge, it is a part of the great net, and therefore possesses the quality by virtue of which the other parts readily join it as soon as they reach the cottsciousness and knowledge of the individual. The man who thus enters the realm of science acquires advantages which may be compared to those of a telephone in his residence. 8 Introduction If he wishes to, he may be connected with every- body else, though he will make extremely limited use of his privilege, since he will try to reach only those with whom he has personal relations. But once such relations have been established, the pos- sibility of telephone communication is simultaneously and automatically estabhshed. Similarly, every bit of knowledge that the individual appropriates will prove to be a regular part of the central organization, the entire extent of which he can never cover, though each individual part has been made accessible to him, provided he wants to take cognizance of it. The mere beginner in learning, therefore, when receiving the most elementary instruction in school, or from his parents, or even from his personal ex- periences in his surroundings, is grasping one or more threads of the mighty net, 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 activity. And this net has the valuable, even precious quality of being the same that joins the greatest and most comprehensive intellects in mankind to one another. The truths a man has once grasped he need never learn afresh so far as their actual content is con- cerned, though not infrequently — especially in newer sciences — he may have to see the form of their presentation and generalization change. For this reason it is of such especial importance for each in- dividual from the first to perceive these unalterable facts and realize that they are unalterable and learn Introduction 9 to distinguish them from the alterable forms of their presentation. It is in this very regard that the in- completeness of human knowledge is most clearly revealed. Time and again in the history of science form has been taken for content, and necessary changes of form — a merely practical question — have been confused vi^ith revolutionary modifications of the content. Thus, each presentation of a science has its natural philosophic portion. In text-books, whether ele- mentary or advanced, the chapter on natural philoso- phy is found usually at the beginning of the book, sometimes at the end, in the form of a " general introduction," or " general summary." In the spe- cial works in which the latest advances of science are made known by the investigators, the natural philosophic portions are usually to be found in the form of theses, of principles, which are not dis- cussed, often not even explicitly stated, but upon the acceptance of which depend all the special conclu- sions that are drawn, in the case in hand, from the new facts or thoughts imparted. Whether at the beginning or at the end of the book, these most gen- eral principles do not quite occupy the place that be- fits them. If at the introduction of the text-book, they are practically devoid of content, since the facts they are meant to summarize are yet to be unfolded in the course of the presentation. If at the end, they come too late, since they have already been ap- plied in numerous instances, though without refer- lo Introduction ence to their general nature. The best method is — and a good teacher always employs this method, whether in the spoken or the written word — to let the generalizations come whenever the individual facts imparted require and justify them. Thus, all instruction in natural sciences is neces- sarily interspersed with natural philosophy, good or bad, according to the clearheadedness of the teacher. If we wish to obtain a perfect survey of a complex structure, as, for instance, the confusion of streets in a large city, we had better not try to know each street, but study a general plan, from which we learn the comparative situation of the streets. So it is well for us in studying a special science to look at our general plan, if for no other reason than to keep from losing our way when it may chance to lead through a quarter hitherto unknown. This is the purpose of the present wort. PART I GENERAL THEORY OF KNOWLEDGE I. The Formation of Concepts. To the human mind, as it slowly awakens in every child, the world at first seems a chaos consisting of mere in- dividual experiences. The only connection between them is that they follow each other consecutively. Of these experiences, all of which at first are dif- ferent from one another, certain parts come to be distinguished by the fact that they are repeated more frequently, and therefore receive a spe- cial character, that of being familiar. The famil- iarity is due to our recalling a former similar ex- perience; in other words, to our feeling that there is a relation between the present experience and certain former experiences. The cause of this phe- nomenon, which is at the basis of all mental life, is a quality common to all living things, and mani- festing itself in all their functions, while appearing but rarely or accidentally in inorganic nature. It is the quality by virtue of which the oftener any process has taken place in a living organism the more easily it is repeated. Here is not yet the place to show how almost all the characteristic qualities of living II 12 General Theory of Knowledge beings, from the preservation of the species to the highest intellectual accomplishments, are conditioned by this special peculiarity. Suffice it to say that be- cause of this quality all those processes which are re- peated frequently in any given living organism, as- sume spontaneously, that is, from physiologic rea- sons, a character distinguishing them essentially from those which appear only in isolated instances, or sporadically. If a living being is equipped with consciousness and thought, like man, then the conscious recollections of such uniform experiences form the enduring or per- manent part in the sum-total of his experiences. Each time a complex event, like the change of seasons, for example, which we know from experi- ence repeats itself — each time a part of such an event reaches our consciousness, we are prepared also for the other parts that experience teaches are connected with it. This makes it possible for us to foresee future events. What signifi- cance the foreseeing of future events has for the preservation and the development of the individual as well as the si>ecies can only be indicated here. To give one instance, it is our ability to foretell the coming of winter with the impossibility of obtaining food directly during the winter that causes us to re- frain from at once using up all the food we have and to preserve it for the day of need. The ability to foretell, therefore, becomes the foundation of the whole structure of economic life. The Aim of Science 13 2, Science. The prophecy of future events based upon the knowledge of the details of recurring events is called science in its most general sense. Here, as in most cases in which language became fixed long before men had a clear knowledge of the things designated, the name of the thing is easily as- sociated with false ideas arising either from errors that had been overcome or from other, still more ac- cidental, causes. Thus, the mere knowledge of past events is also called science without any thought of its use for prophesying future events. Yet a mo- ment's reflection teaches that mere knowledge of the past which is not meant to, or cannot, serve as a basis for shaping the future is utterly aimless knowl- edge, and must take its place with other aimless activities called play. There are all sorts of plays re- quiring great acumen and patient application, as for example the game of chess; and no one has the right to prevent any individual from pursuing such games. But the player for his part must not de- mand special regard for his activity. By using his energies for his personal pleasure and not for a so- cial purpose, that is, for a general human purpose, he loses every claim to the social encouragement of his activity, and must be content if only his in- dividual rights are respected; and that, too, only so long as the social interests do not suffer by it. 3. The Aim of Science. These views are deliber- ately opposed to a very widespread idea that science should be cultivated " for its own sake," and not for 14 General Theory of Knowledge the sake of the benefits it actually brings or may be made to bring. We reply that there is nothing at all which is done merely " for its own sake." Every- thing, without exception, is done for human pur- poses. These purposes range from momentary per- sonal satisfaction to the most comprehensive social services involving disregard of one's own person. But in all our actions we never get beyond the sphere of the human. If, therefore, the phrase " for its own sake " means anything, it means that science should be followed for the sake of the immediate pleasure it affords, that is to say, as play (as we have just characterized it), and in the " for-its-own-sake " demand there is hidden a misunderstood idealism, which, on closer inspection, resolves itself into its very opposite, the degradation of science. The element of truth hidden in that misunderstood phrase is, that in a higher state of culture it is found better to disregard the immediate technical applica- tion in the pursuit of science, and to aim only for the greatest possible perfection and depth in the solution of its individual problems. Whether this is the cor- rect method of procedure and when it is so, is solely a question of the general state of culture. In the early stages of human civilization such a demand is utterly meaningless, and all science is necessarily and naturally confined to immediate life. But the wider and more complex human relations become, the wider and surer must the ability to predict future events become. Then it is the function of prophesy- The Science of Concepts 15 ing science to have answers ready for questions which as yet have not become pressing, but which with further development may sooner or later be- come so. In the net-like interlacing of the sciences, that is, of the various fields of knowledge, described in the introduction, we must always reckon with the fact that our anticipation of what kind of knowledge we shall next need must always remain very incomplete. It is possible to foresee future needs in general out- line with more or less certainty, but it is impossible to be prepared for particular individual cases which lie on the border line of such anticipation, and which may sometimes become of the utmost importance and urgency. Therefore it is one of the most important functions of science to achieve as perfect an elabora- tion as possible of all the relations conceivable, and in this practical necessity lies the foundation of the general or theoretical elaboration of science. The Science of Concepts. Here the question im- mediately arises : how can we secure such perfection? 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 sciences, a knowledge of which is presupposed for the pursuit of the other sciences. Since its foundation by the Greek philoso- pher Aristotle it has borne the name of logic, which name, etymologically speaking, hints suspiciously at the word, and the word, as is known, steps in where ideas are wanting. Here, however, we have to deal 1 6 General Theory of Knowledge with the very science of ideas, to which language bears the relation only of a means — and often an in- adequate means — to an end. We have already seen how, through the physiologic fact of memory, ex- periences are found in our consciousness which are similar, that is, partially coinciding with one another. These coinciding parts are those concerning which we can make predictions, for the very reason that they coincide in every single instance, and they alone, therefore, constitute that part of our experience which bears results and hence has significance. 4. Concrete and Abstract. Such coinciding or re- peated parts of similar experiences we call, as al- ready stated, concepts. But here, too, attention must immediately be drawn to a linguistic imperfection, 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 coincid- ing experiences; in other words, all the similar ex- periences. Thus, horse means, on the one hand, quite a definite thing which for the moment forms an object of our experience, and, on the other, the totality of all possible similar objects which have been present in our former experiences, and which we shall meet in our future experiences. It is true that these two sorts of contents of consciousness bear- ing the same name are distinguished also as concrete and abstract, and there is an inclination to attribute " reality " only to the first, while the other, as " mere The Subjective Part 17 entities in thought," are relegated to a lesser degree of reality. As a matter of fact, the difference, though important, is of quite another kind. It is the difference between the momentary experience, as op- posed to the totality of the corresponding memories and expectations. Hence not so much a difference in reality as in presence. However, our observations have already made it apparent that presence alone never yields knowledge. A necessary part of knowledge is the memory of former similar experi- ences. For without such memory and the corre- sponding comparison, it is quite impossible for us to get at those things which agree and which, therefore, may be predicted; and we should stand before every one of our experiences with the helplessness of a new-born babe.* 5. The Subjective Part, 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 us. Since the formation of con- cepts depends upon memories, and these may refer, according to the individual, to very different parts of the same experience of different individuals, con- cepts always possess an element dependent upon the * Sometimes on suddenly awaking from a profound sleep a person finds himself for the moment deprived of his personal stock of memories, unable to recall where and in what cir- cumstances he is. No one who has experienced such a condi- tion can ever forget the terrifying sense of helplessness it brings. 1 8 General Theory of Knowledge individual, or a subjective element. This, however, does not consist in the addition by the individual of new parts not found in the experience, but, on the contrary, in the different choice out of what is found in the experience. If every individual absorbed all parts of the experience, the individual, or subjective, dififerences would disappear. And since scientific experience endeavors to make the absorption of ex- periences as complete as possible, it aims nearer and nearer to this ideal by seeking to equalize the sub- jective deficiency of the individual memoi"y through the collocation of as many and as various memories as possible, thus filling in the subjective gaps in ex- perience as far as possible and rendering them harmless. 6. Empirical Concepts. First and uncondition- ally those concepts possess reality which always and without exception are based on experienced facts. But we can easily make manifold arbitrary combina- tions of concepts from different experiences, since our memory freely places them at our disposal, and from such a combination we can form a new concept. Of course it is not necessary that our arbitrary com- bination should also be found in our past or future experiences. On the contrary, we may rather ex- pect that there could be many more arbitrary com- binations not to be found in experience than com- binations later " confirmed " by experience. The former are purposeless because unreal, the latter, on the contrary, are of the utmost consequence because Simple and Complex Concepts 19 upon them is based the real aim of knowledge, pre- diction. The former are those which have brought the very " reahty " of the concepts into ill repute, while the latter show that the formation and the mutual reaction of the concepts practically constitute the entire content of all science. It is of the great- est importance, therefore, to distinguish between the two kinds of concept combinations, and the study of this differentiation forms the content of that most general of all the sciences which we have character- ized as logic, or, better, the science of concepts. 7. Simple and Complex Concepts. The forma- tion of concepts consists, as we have seen, in the selection of those parts of different but similar experiences which coincide with one an- other and in the elimination of those that are dif- ferent in kind. The results of such a procedure may vary greatly according to the number and the dif- ference of the experiences placed in relation with one another. If, for example, we compare only a few experiences, and if, moreover, these experiences are very similar to one another, then the resulting concepts will contain very many parts that agree. But at the same time they will have the peculiarity of not being applicable to other experiences, since these are without some of the coinciding parts of that narrower circle. Thus, for example, the con- cept which a rustic chained to the soil all his life has of human work does not apply to the work of the city man. A concept will embrace a larger num- 20 General Theory of Knowledge ber of individual cases in proportion as it contains fewer different parts. And by systematically fol- lowing out this thought we arrive at the conclusion that the concepts that are simple and have no dif- ferent parts at all find the widest application or are the most general. The elimination cf the non-coinciding parts from the concept-forming experience is called abstraction. Obviously abstraction must be carried the farther the more numerous and the more varied the experi- ences from which the concepts are abstracted, and the simplest concepts are the most abstract. By looking back over the ground just traversed, the less abstract ideas may also be regarded as the more complex in contradistinction to the simpler ones. Only we must guard against the error of literal in- terpretation and not suppose that the less simple concepts have really been compounded of the simpler ones. In point of origin they actually existed first, since the experience contains the ensemble of all the parts, those which have been retained as well as those which have been eliminated. It is only later, by a characteristic mental operation, after we have analyzed the more complex concept, that is, after we have disclosed the simpler concepts existing in it, that we can compound it again; in other words, execute its synthesis. These relations bear a striking resemblance to the relations known from chemistry to exist be- tween substances, namely, between elements and Simple and Complex Concepts 21 compounds. From the chaos of all objects of ex- perimentation (chemistry purposely limits itself to ponderable bodies) the pure substances are sifted out — an operation corresponding to the formation of concepts. The pure substances prove to be either simple. or compound, and the compounds are so con- stituted that they can each be reduced to a limited number of simple substances. The simple sub- stances, or elements, retain this quality of simplicity only until they are recalled ; that is, until it has been proved that they, too, can be resolved into still simpler elements. The same is true of the simple concepts. They can claim simplicity only until their complex nature is demonstrated. With all these similarities we must be extremely careful never to forget the differences existing alongside the agreements. So hereafter we shall make no further use of the chemical simile. 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 study. It is quite certain, however, that side by side with the given similarities there are also radical differences. Moreover, the notion of simple and complex concepts or " ideas " had been elaborated by John Locke long before chem- istry reached its present state of clearness concern- ing the concept of the elements. Nevertheless since then the relation has been com- pletely reversed. While the study of the chemical 22 General Theory of Knowledge elements has in the meantime undergone great de- velopment, so that not only have the elements of all the substances coming under the observation of the chemist been discovered, but, inversely, many com- pound substances have been constructed from their elements, not even an approach to such a develop- ment is apparent in the study of concepts. On the contrary, 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 century. This is due above all to the opinion of the most influential philosophers, that Aristotle's logic, or science of concepts, is absolutely true as well as exhaustive and complete, so that, at the ut- most, what is left for later generations to do is only to make a change in the form in which the matter is presented. It is true that in more recent times the grave error of this view is beginning to be recog- nized. We realize that Aristotle's logic embraces but a very small part of the entire field, though in this part he displays the greatest genius. But be- yond this general recognition no great step forward has been made. Not even a provisional table of the elementary concepts has been propounded and ap- plied since Locke. 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 concepts, but not in the sense that the Simple and Complex Concepts 23 simplest or truly elementary concepts have already been worked out. It must be left to later in- vestigators to find these, and it may be expected that the reduction of some concepts until then considered elementary into still simpler ones w^ill take place chiefly in times of great intellectual progress. Complex concepts can, in the first place, be formed from experience, for in an empirical concept we meet with several conceptual component parts which can be separated from one another by a process of abstraction, but are always found together in the given experiences. For example, the concept horse has originated from a very frequent, similarly re- peated experience. On analysis it is found to con- tain a vast number of other concepts, such as quadruped, vertebrate animal, warm-blooded, hairi- ness, and so on. Horse, then, is obviously a com- plex empirical concept. On the other hand, we can combine as many sim- ple concepts as we please, even if we did not find them combined in experience, for in reality there is nothing to hinder us from uniting all the concepts provided by memory into any combinations we please. In this way we obtain complex arbitrary concepts. The task of science can now be even more sharply defined than before by the fact that it per- mits the construction of arbitrary concepts which in circumstances to be foreseen become empirical con- cepts. This is another expression for prediction, 24 General Theory of Knowledge which we recognized as the characteristic of science. It goes deeper than the previous definition, because here the means for its realization are given. 8. The Conclusion. First let us consider the sci- entific import of the complex empirical concepts. It consists in the fact that they accustom us to the coexistence of the corresponding elements of a con- cept. So that when, in a new experience, we meet with some of these elements together, we immedi- ately suppose that we shall find in the same experi- ence the other elements also which have not yet been ascertained. Such a supposition is called a conclu- sion. A conclusion always exceeds the present ex- perience by predicting an expected experience. Therefore, the form of a conclusion is the universal form of scientific predication. A conclusion must contain at least two concepts, the one which is experienced, and the one which, on the basis of this experience, is expected. Every complex empirical concept makes such a conclusion possible after it has been separated into simpler con- cepts. And the simplest case is naturally the one in which there are only two parts, or in which only two parts are taken into consideration. To what extent such a conclusion is valid, that is to say, to what extent the experience produces the anticipated concept, obviously depends upon the re- ply to a very definite fundamental question. If in experience the union of the two parts of the concept occurs invariably, so that one part of the concept is The Conclusion 25 never experienced unless the other part is also ex- perienced, then there is the greatest probabil- ity that the expected experience will also have the same character, and that the conclusion will prove valid or true. To be sure, there is no way of mak- ing certain that the coincident occurrence of the two concepts, which experience has shown to be without exception hitherto, will continue to be so also in the future. For our only means of penetrating into the future consists in applying that conclusion from previous experiences to future experiences, and it can therefore by no means claim absolute validity. There are, however, different degrees of certainty, or, rather, probability, attaching to such a conclu- sion. In experiences that occur but rarely the prob- ability is that so far we have experienced only cer- tain combinations of simple concepts, while others, though occurring, have not yet entered within the limited circle of our experience. In such a case a conclusion of the kind mentioned above may be right, but there is also some probability of its being false. On the other hand, in experiences which happen extremely frequently and in the most diverse circumstances, and in which we always find the con- stant and unexceptional combination, the probability is very strong that we shall find the combination in future experiences also, and the probability of the conclusion approaches practical certainty. Of course, we can never quite exclude the possibility that new relations never as yet experienced might 26 General Theory of Knowledge enter, by which the conclusion which hitherto has always been true would now become false, whether because the expectation entertained prove invalid in single instances or in all cases. It follows from this that in general, our con- clusions will have the greater probability the more generally and the oftener the corresponding experi- ences have occurred and are occurring. Such con- cepts as are found consistently in many experiences otherwise different are called general concepts, and therefore the probability of the conclusions de- scribed will be the greater the more general the con- cepts to which they refer. This obtains to such a degree that we feel that certain very general con- clusions must be true always and without exception, and it is " unthinkable " to us that they can ever in any circumstances prove not valid. Such a state- ment, however, is never anything else than a hidden appeal to experience. For the mere putting of the question, whether the conclusion can also be false, demonstrates that the opposite of what has proved to be the experience so far can be conceived, 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 that, as has been premised, there are no such memories because the experiences did not exist. But since, on the other hand, there is no hindrance to thinking any combina- tions of concepts at will, we have not the least dif- ficulty, as everybody knows, in thinking any sort The Conclusion T] of " nonsense " whatsoever. Only it is impossible to reproduce such combinations from memory. The scientific conclusion, therefore, first takes the form : if A is, then B is also. Here A and B rep- resent the two simple concepts which are known from experience to be found together in the more complex concept C. The word " is " signifies here some empirical reality corresponding to the concepts. The conclusion may therefore also be expressed, somewhat more circumstantially and more precisely, in this form: if A is experienced, the experience of B is also expected. The evoking of this expecta- tion, which implies its justification, is due to the recollection of the coincidence of the two concepts in former experiences, and the probabihty depends, in the manner described above, upon the number of valid cases. Here it must be observed that even in- dividual cases in which our expectations have been deceived do not for the most part lead us to regard the conclusion as generally untrue, that is, to aban- don the expectation of B from A. For we know that our experience is always incomplete, that in certain circumstances we fail to notice existing fac- tors, and that, therefore, our failure to find that relation valid which, on other occasions, has been found to be valid, may be attributed to subjective causes. In case, however, of the repeated occur- rence of such disappointments, we will look else- where for relations between these and other ele- ments of experience, in order that thereafter we may 28 General Theory of Knowledge foresee such cases also and include them in our an- ticipations. 9. The Natural Laws. The facts just described have very frequently found expression in the doctrine of the laius of nature, in connection With which we have often, as in the man-made social or political laws, conceived of a lawmaker, who, for some reasons, or perhaps arbitrarily, has ordained that things should be as they are and not otherwise. But the intellectual history of the origin of the laws of nature shows that here the process is quite a dif- ferent one. The laws of nature do not decree what shall happen, but inform its what has happened and what is wont to happen. The knowledge of these laws, therefore, makes it possible for us, as I have emphasized again and again, to foresee the future in a certain degree and, in some measure, also to determine it. We determine the future by con- structing those relations in which the desired re- sults appear. If we cannot do so either because of ignorance or because of inaccessibility to the re- quired relations, then we have no prospect of fash- ioning the future according to our desires. The wider our knowledge of the natural laws, that is, of the actual behavior of things, the more likely and more numerous the possibilities for fashioning the future according to our desires. In this way science can be conceived of as the study of how to become happy. For he is happy whose desires are fulfilled. In this conception the natural laws indicate what The Natural Laws 29 simpler concepts are found in complex concepts. The complex concept water contains the simpler ones liquid, a certain density, transparency, color-' lessness* and many others. The sentences, water is a liquid, water has a density of one, water is transparent, water is colorless, or, pale blue, etc., are so many natural laws. Now what predictions do those natural laws en- able us to make? They enable us to predict that when we have recognized a given body as water by virtue of the above properties, we are justified in expecting to find in the same body all the other known properties of water. And so far experience has invariably con- firmed such expectations. Furthermore, we may expect that if in a given specimen of water we discover a relation which up to that time was unknown, we shall find this relation also in all the other specimens of water even though they were not tested for that par- ticular relation. It is obvious how enormously this facilitates the progress of science. 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 test. As a matter of fact, this is the general method that science pursues. It is this that makes it possible * More precisely, a very pale blue. 30 General Theory of Knowledge for science to make regular and generally valid progress through the labors of the most various in- vestigators who work independently of one another, and often know nothing of one another. Of course, it must not be forgotten that such con- clusions are always obtained in accordance with the following formula; things have been so until now, therefore we expect that they will be so in the future. In every such case, therefore, there is the possibility of error. Thus far, whenever an expectation was not realized, it was almost always possible to find an " explanation " for the error. Either the inclusion of the special case in the general concept proved to be inadmissible because some of its other character- istics were absent, or the accepted characterization of the concept required an improvement (limitation or extension). In other words, one way or an- other, there was a discrepancy between the concept and the experience, and, as a rule, sooner or later it becomes possible for us to arrive at a better adjust- ment between them. This general truth has often been interpreted to mean that in the end such an adjustment must of necessity always be possible to reach, without ex- ception; in other words, that absolutely every part of an experience can be demonstrated as condi- tioned by natural law. Evidently such an asser- tion far exceeds the demonstrable. And even the usual conclusion cannot be applied here, that be- cause it has happened so in the past it will happen The Law of Causation 31 so in the future also. For the part of our experi- ences that we can grasp by natural laws is in- finitesimally small in comparison with that in which our knowledge still fails us entirely. I will men- tion only the uncertainty in predicting the weather for only one day ahead. Moreover, when we con- sider that until now only the easiest problems had been solved, and naturally so, because they were most accessible to the means at hand, then we can readily see that experience offers no basis whatever for such a conclusion. We must not say, therefore, that because we have been able so far to explain all experiences by natural laws it will be so in the future likewise. For we are far from being able to explain all experiences. In fact, it is only a very small part that we have begun to investigate. We are as little justified in saying that we have ex- plained all the problems of our experience that have been subjected to scientific investigation. We have by no means explained all of them. Every science, even mathematics, teems with unsolved problems. So we must resign ourselves to the present status of human knowledge and ability, and may at best ex- press the hope founded upon previous experience, 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 perfec- tion of this work. 10. The Law of Causation. By reason of its fre- quency and importance the mental process above de- 32 General Theory of Knowledge scribed has been subjected to the most diverse in- vestigations, and that most general form of the sci- entific conclusion (which we apply in ordinary life even much more frequently than in science) has been raised, under the name of the law of causation, to a principle anteceding all experience and to the very condition making experience possible. Of this so much is true, that through the peculiar physi- ological organization of man, memory in the most general sense — the easier execution of such processes as have already repeatedly taken place in the organ- ism, as against entirely new kinds of processes — the formation of concepts (of the recurring parts in the constantly changing variety of processes), is especially stimulated and facilitated. By it the re- curring parts of experience step into the foreground, and on account of their paramount practical im- portance for the security of life, it may well be said in the sense of the theory of evolution and adapta- tion, that the entire structure and mode of life of the organism, especially of the human organism, nay, perhaps life itself, is indissolubly bound up with that foresight and, therefore, with the law of causation also. Of course, there is nothing in the way of calling such a relation an a priori relation, if it is so desired. As far as the individual is concerned it no doubt antedates all his experience, since the en- tire organization which he inherits from his par- ents had already been formed under such an in- fluence. But that there can be forms or existence The Law of Causation 33 without such an attribute is shown by the whole world of the inorganic, in which, as far as our knowledge goes, there is no evidence of either memory or foresight, but only of an immediate passive participation in the processes of the world around them.* Further, the circumstance that the causal relation is brought about by the peculiar manner in which we react upon our experiences, has sometimes been expressed in this way — the relation of cause and ef- fect does not exist in nature at all, but has been in- troduced by men. The element of truth in this is, that a quite differently organized being, it is to be supposed, would be able to, or would have to, ar- range its experiences according to quite different mutual relations. But since we have no experience of such a being, we have no possibility of forming a valid opinion of its behavior. On the other hand, we must recognize that it is possible, at least for- mally, to conceive also of kinds of experiences with no. coinciding parts, or a world in which there are no experiences at all with coinciding parts. In such, therefore, prediction is impossible. Such a world will not call forth, even in a being endowed with memory, a conception and generalization of the * It cannot be objected that inorganic nature also is known to be subject to the law of causation. The causal mode of re- garding inorganic phenomena is a distinctly human one, and nothing justifies the assertion that the same phenomena cannot be viewed in an entirely different manner. 34 General Theory of Knowledge various experiences in the shape of natural laws. Consequently we must recognize that in addition to the subjective factor in the formation of our knowl- edge of the world, or that factor which is dependent upon our physico-psychical structure, there is also the objective character of the world with which we must decidedly reckon, or that character which is in- dependent of us; and that in so far the natural laws contain also objective parts. To represent the relation clearly to our minds by a figure, we may compare the world to a heap of gravel and man to a pair of sieves, one coarser than the other. As gravel passes through the double sieve pebbles of apparently equal size accumulate between the sieves, the larger ones being excluded by the first sieve and the smaller ones allowed to pass by the second. It would be an error to assert that all the gravel con- sisted of such pebbles of equal size. But it would be equally false to assert that it was the sieves that made the pebbles equal. II. The Purification of the Causal Relation. If by experience we have found a proposition of the content. If A is, then B is also, the two concepts A and B generally consist of several elements which we will designate as a, a', a", a"', etc., and as b, b', b", b"'. Now the question arises, whether or not all these elements are essential for the relation in question. It is quite possible, in fact, even highly probable, that at first only a special instance of the existing phenomena was found, that is, that the Purification of the Causal Relation 35 concept A, which has been found to be connected with the concept B, contains other determining parts which are not at all requisite to the appearance of B. The general method of convincing oneself of this is by eliminating one by one the component parts of the concept A, namely, a, a', a", etc., and then seeing whether B still appears. It is not always easy to carry out this process of elimination. Our greater or less ability to conduct such investigations depends upon whether we deal with things that are merely the objects of our observation, and which we our- selves have not the power to change (as, for ex- ample, astronomical phenomena), or with things which are the objects of our experimentation, and which we can influence. In the latter case one or another factor is usually found which can be elim- inated without the disappearance of B, and then we must proceed in such a way as to form a correspond- ing new concept A' from the factors recognized as necessary (which new concept will be more general than the former A), and to express the given proposition in the improved form: If A' is, then B is also. Quite similar is the case with the other member of this relation. It often happens that when a, or a", a"' is found, somewhat different things appear, which do not fit the concept as first constructed. Then we must multiply the experiences as much as pos- sible in order to determine what constant elements are found in the concept B, and to form from these 36 General Theory of Knowledge constant elements the corresponding concept B'. The improved proposition will then read : if A' is, then B' is also. This entire process may be called the purification of the causal relation. By this term we express the general fact that in first forming such a regular connection, the proper concepts are very seldom brought into relation with one another at once. The cause of it is that at first we make use of exist- ing concepts which had been formed for quite a dif- ferent purpose. It must therefore be regarded as a special piece of good fortune if these old concepts should at once prove suited to the new purpose. Furthermore, the existing concepts are as a rule so vaguely characterized by their names, which we must employ to express the new relation, that for this rea- son also it is often necessary to determine empirically in what way the concept is to be definitely estab- lished. The various sciences are constantly occupied with this work of the mutual adaptation of the concepts that enter into a causal relation. By way of ex- ample, we may take the " self-understood " proposi- tion which we use when we call out to a careless child when it sticks its finger into the flame of a candle, " Fire bums ! " We discover that there are self-luminous bodies which produce no increase of temperature, and therefore no sensation of pain. We discover that there are processes of combustion that develop no light, but heat enough to burn one's Purification of the Causal Relation 37 fingers. And, finally, the scientific investigation of this proposition arrives at the general expression that, as a rule, chemical processes are accompanied by the development of heat, but that, conversely, such processes may also be accompanied by the ab- sorption of heat. In this way that casual sentence which we call out to the child develops into the ex- tensive science of thermo-chemistry when it is sub- jected to the continuous purification of the causal relation, which is the general task of science. It remains to be added that in this process of adapting concepts it is necessary also sometimes to follow the opposite course. This is the case when exceptions are noticed in a relation as expressed for the time being; when, therefore, the proposition if A is present, then B is present also, is in a great many instances valid, but occasionally fails. This is an indication that in the concept A an element is still lacking. This element, however, is present in the instances that tally, but absent in the negative cases, and its absence is not noticed because it is not contained in A. Then it is necessary to seek this part, and after it has been found, to embody it in the concept A, which thus passes into the new con- cept A'. This case is the obverse of the former one. Here the more suitable concept proves to be less general than the concept accepted temporarily, while in the first case the improved concept is more general. Hence we formulate the rule : exceptions to the 38 General Theory of Knowledge temporary rule require a limitation, while an un- foreseen freedom requires an extension, of the ac- cepted concept. 12. Induction. The form of conclusion previ- ously discussed, because it has been so, I expect it will continue to be so in the future, is the form through which each science has arisen and has won its real content, that is, its value for the judgment of the future. It is called inference by induction, and the sciences in which it is preponderatingly applied are called inductive sciences. They are also called ex- periential or empirical sciences. At the basis of this nomenclature is the notion that there are other sciences, the deductive or rational sciences, in which a reverse logical procedure is applied, whereby from general principles admitted to be valid in advance, according to an absolutely sure logical process, con- clusions of like absolute validity are drawn. At the present time people are beginning to recognize the fact that the deductive sciences must give up these claims one by one, and that they already have given them up to a certain extent ; partly because on closer study they prove to be inductive sciences, and partly because they must forego the title and rank of a science altogether. The latter alternative applies especially to those provinces of knowledge which have not been used in prophesying the future or can- not be so used. To return to the inductive method — it is to be noted that Aristotle, who was the first to describe it. Induction 39 proposed two kinds of induction, the complete and the incomplete. The' first has this form: since all things of a certain kind are so, each indizndual thing is so. While the incomplete induction merely says : since many things of a certain kind are so, pre- sumably all things of this kind are so. One in- stantly perceives that the two conclusions are es- sentially different. The first lays claim to afford an absolutely certain result. But it rests upon the assumption that all the things of the kind in ques- tion are known and have been tested as to their behavior. This hypothesis is generally impossible of fulfilment, since we can never prove that there are not more things of the same kind other than those known to us or tested by us. Moreover, the con- clusion is superfluous, as it merely repeats knowl- edge that we have already directly acquired, since we have tested all the things of the one kind, hence the special thing to which the predication refers. On the other hand, the incomplete induction af- firms something that has not yet been tested, and therefore involves as a condition an extension of our knowledge, sometimes an extremely important ex- tension. To be sure, it must give up the claim to unqualified or absolute validity, but, to compensate, it acquires the irreplaceable advantage of lending it- self to practical application. Indeed, in accordance with the scientific practice justified by experience, described on p. 29, the scientific inductive conclusion 40 General Theory of Knowledge assumes the form : because it has once been found to be so, it will always be so. From this appears the significance of this method for the enlargement of science, which, without it, would have had to proceed at an incomparably slower pace. 13. Deduction. In addition to the inductive method, science has (p. 38) another method, which, in a sense, should be the reverse of the inductive and is claimed to provide absolutely correct results. It is called the deductive method, 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 validity. As a matter of fact^ there is no science that does or could work in such a way. In the first place, we ask in vain, how can we arrive at such general, or absolutely valid, premises, since all knowledge is of empiric origin and is therefore equipped with the possibility of error as ineradicable evidence of this origin. In the next place, we cannot see how from principles at hand conclusions can be drawn the content of which exceeds that of these principles (and of the other means employed). In the third place, 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 cor- rect. In practice it has actually come to pass that in the so-called deductive sciences doubts and con- tradictions on the part of the various investigators Deduction 41 of the same question are by no means excluded. To wit, the discussion that has been carried on for cen- turies, and is not yet ended, over Euchd's parallel theorem in geometry. If we ask whether, in the sense of the observations we have just made of the formation of scientific principles, there is anything at all like deduction, we can find a procedure which bears a certain resemblance with that impossible pro- cedure and which, as a matter of fact, is frequently and to very good purpose applied in science. It consists in the fact that general principles which have been acquired through the ordinary incom- plete induction are applied to special instances which, at the proposition of the principle, had not been taken into consideration, and whose connection with the general concept had not become directly evident. Through such application of general principles to cases that have not been regarded before, specific natural laws are obtained which had not been fore- seen either, but which, according to the probability of the thesis and the correctness of the applica- tion are also probably correct. However, the in- vestigator, bearing in mind the factor of uncertainty in these ratiocinations feels in each such instance the need for testing the results by experience, and he does not consider the deduction complete until he had found confirmation in experience. Deduction, therefore, actually consists in the searching out of particular instances of a principle 42 General Theory of Knowledge established by induction and in its confirmation by experience. This conduces to the growth of sci- ence, not in breadth, but in profundity. I again resort to the comparison I have frec[uently made of science with a very complex network. At first glance we cannot obtain a complete picture of all the meshes. So, 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 in- achievable. It is a regular, important, and neces- sary part of all scientific work to learn the extent of this range and investigate the specific forms which the law assumes in the remoter instances. Now, if an especially gifted and far-seeing in- vestigator has succeeded in stating in advance an especially general formulation of an inductive law, it is everywhere confirmed in the course of the trial applications, and the impression easily arises that confirmation is superfluous, since it results simply in what had already been " deduced." In point of fact, however, the reverse is not infrequently the case, that the principle is not confirmed, and condi- tions quite different from those anticipated are found. Such discoveries, then, as a rule, constitute the starting-point of important and far-reaching modifications of the original formulation of the law in question. As we see, deduction is a necessary complement of, in fact, a part of, the inductive process. The history of the origin of a natural law is in general Deduction 43 as follows. The investigator notices certain agree- ments in individual instances under his observation. He assumes that these agreements are general, and propounds a temporary natural law corresponding to them. Then he proceeds by further experimenta- tion to test the law in order to see whether he can find full confirmation of it by a number of other instances. If not, he tries other formulations of the law applicable to the contradictory instances, or exclusive of them, as not allied. Through such a process of adjustment he finally arrives at a prin- ciple that possesses a certain range of validity. He informs other scientists of the principle. These in their turn are impelled to test other instances known to them to which the principle can be applied. Any doubts or contradictions arising from this again im- pel the author of the principle to carry out what- ever readjustments may have become necessary. Upon the scientific imagination of the discoverer de- pends the range of instances sufficing for the formulation of the general inductive principle. It also frequently depends upon conscious operations of the mind dubbed " scientific instinct." But as soon as the principle has been propounded, even if only in the consciousness of the discoverer, the de- ductive part of the work begins, and the consequent test of the proposition has the most essential in- fluence on the value of the result. It is immediately evident that this deductive part is of all the more weight, the more general the con- 44 General Theory of Knowledge cepts in question are. If, in addition, the inductive laws posited soon prove to be of a comparatively high degree of perfection, we obtain the impression described above, that an unlimited number of inde- pendent results can be deduced from a premise. Kant was keenly alive to the peculiarity of such a view, which had been widely spread pre-eminently by Euclid's presentation of geometry, and he gave expression to his opinion of it in the famous ques- tion : How are a priori judgments possible f We have seen that it is not always a question of a priori judgments, but also of inductive conclu- sions applied and tested according to deductive methods. 14. Ideal Cases. Each experience may generally be considered under an indefinite number of various concepts, all of which may be abstracted from that experience by corresponding observations. Accord- ingly an indefinite number of natural laws would be required for prophesying that experience in all its parts. Likewise the indefinite number of premises must be known through the application of which those natural laws acquire a certain content. Thus it seems as if it were altogether impossible to apply natural laws for the determination of a single ex- perience to come, and in a certain sense this is true (p. 30). For example, when a child is born, we are quite incapable of foretelling the peculiar events that will occur in its life. Beyond the statement that it will live a while and then die, we can make only Ideal Cases 45 the broadest assertions qualified by numerous " ifs " and " buts." If, in spite of this, we arrange a very great part of our hfe and activity according to the prophecies we mal