PART I

GENERAL THEORY OF KNOWLEDGE

=1. 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 individual experiences. The only connection between them is that they follow each other consecutively. Of these experiences, all of which at first are different from one another, certain parts come to be distinguished by the fact that they are repeated more frequently, and therefore receive a special character, that of _being familiar_. The familiarity is due to our _recalling_ a former similar experience; in other words, to our feeling that there is a relation between the present experience and certain former experiences. The cause of this phenomenon, which is at the basis of all mental life, is a quality common to all living things, and manifesting 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 beings, from the preservation of the species to the highest intellectual accomplishments, are conditioned by this special peculiarity. Suffice it to say that because of this quality all those processes which are repeated frequently in any given living organism, assume spontaneously, that is, from physiologic reasons, 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 permanent part in the sum-total of his experiences. Each time a complex event, like the change of seasons, for example, which we know from experience 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 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 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 refrain 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.

=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 associated with false ideas arising either from errors that had been overcome or from other, still more accidental, causes. Thus, the mere knowledge of _past_ events is also called science without any thought of its use for prophesying future events. Yet a moment'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 knowledge, and must take its place with other aimless activities called _play_. There are all sorts of plays requiring 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 demand special regard for his activity. By using his energies for his personal pleasure and not for a social 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 individual 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 deliberately opposed to a very widespread idea that science should be cultivated "for its own sake," and not for 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." Everything, without exception, is done for human purposes. These purposes range from momentary personal 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 application 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 correct 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 prophesying science to have answers ready for questions which as yet have not become pressing, but which with further development may sooner or later become 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 outline 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 elaboration 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 immediately 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 philosopher 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 with the very science of ideas, to which language bears the relation only of a means--and often an inadequate means--to an end. We have already seen how, through the physiologic fact of _memory_, experiences 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 repeated parts of similar experiences we call, as already 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 coinciding experiences; in other words, all the similar experiences. 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 bearing 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 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 opposed 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 experiences. For without such memory and the corresponding 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.[A]

[A] 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 circumstances he is. No one who has experienced such a condition can ever forget the terrifying sense of helplessness it brings.

=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 concepts depends upon memories, and these may refer, according to the individual, to very different parts of the same experience of different individuals, concepts always possess an element dependent upon the 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, differences would disappear. And since scientific experience endeavors to make the absorption of experiences as complete as possible, 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 possible, thus filling in the subjective gaps in experience as far as possible and rendering them harmless.

=6. Empirical Concepts.= First and unconditionally those concepts possess reality which always and without exception are based on _experienced_ facts. But we can easily make manifold arbitrary combinations 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 combination should also be found in our past or future experiences. On the contrary, we may rather expect that there could be many more arbitrary combinations not to be found in experience than combinations later "confirmed" by experience. The former are purposeless because unreal, the latter, on the contrary, are of the utmost consequence because upon them is based the real aim of knowledge, prediction. The former are those which have brought the very "reality" 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 greatest 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 characterized as logic, or, better, the science of concepts.

=7. Simple and Complex Concepts.= The formation of concepts consists, as we have seen, 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 kind. The results of such a procedure may vary greatly according to the number and the difference 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 concept 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 number of individual cases in proportion as it contains fewer different parts. 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 general.

The elimination of 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 experiences 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 interpretation 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 between substances, namely, between elements and compounds. From the chaos of all objects of experimentation (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 constituted that they can each be reduced to a limited number of simple substances. The simple substances, 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 chemistry reached its present state of clearness concerning the concept of the elements.

Nevertheless since then the relation has been completely reversed. While the study of the chemical elements has in the meantime undergone great development, so that not only have the elements of all the substances coming under the observation of the chemist been discovered, but, inversely, many compound substances have been constructed from their elements, not even an approach to such a development 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 utmost, 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 recognized. 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 beyond this general recognition no great step forward has been made. Not even a provisional table of the elementary concepts has been propounded and applied 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 simplest or truly elementary concepts have already been worked out. It must be left to later investigators to find these, 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 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 repeated experience. On analysis it is found to contain a vast number of other concepts, such as quadruped, vertebrate animal, warm-blooded, hairiness, and so on. Horse, then, is obviously a _complex empirical concept_.

On the other hand, we can combine as many simple 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 _permits the construction of arbitrary concepts which in circumstances to be foreseen become empirical concepts_. This is another expression for _prediction_, 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 scientific import of the complex empirical concepts. It consists in the fact that they accustom us to the coexistence of the corresponding elements of a concept. So that when, in a new experience, we meet with some of these elements together, we immediately suppose that we shall find in the same experience the other elements also which have not yet been ascertained. Such a supposition is called a _conclusion_. A conclusion always exceeds the present experience 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 concepts. 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 reply 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 never experienced unless the other part is also experienced, then there is the _greatest_ probability 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 making 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 conclusion. In experiences that occur but rarely the probability is that so far we have experienced only certain 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 constant 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 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 conclusions will have the greater probability the more generally and the oftener the corresponding experiences have occurred and are occurring. Such concepts as are found consistently in many experiences otherwise different are called _general_ concepts, and therefore the probability of the conclusions described will be the greater the more _general_ the concepts to which they refer. This obtains to such a degree that we feel that certain very general conclusions 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 statement, 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 combinations of concepts at will, we have not the least difficulty, as everybody knows, in thinking any sort 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 represent 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 expectation, which implies its justification, is due to the recollection of the coincidence of the two concepts in former experiences, and the probability depends, in the manner described above, upon the number of valid cases. 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 untrue, that is, to abandon the expectation of B from A. For we know that our experience is always _incomplete_, that in certain circumstances we fail to notice existing factors, 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 occurrence of such disappointments, we will look elsewhere for relations between these and other elements of experience, in order that thereafter we may foresee such cases also and include them in our anticipations.

=9. The Natural Laws.= The facts just described have very frequently found expression in the doctrine of the _laws 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 different one. The laws of nature do not decree what shall happen, but _inform us 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 constructing those relations in which the desired results appear. If we cannot do so either because of ignorance or because of inaccessibility to the required relations, then we have no prospect of fashioning 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 simpler concepts are found in complex concepts. The complex concept _water_ contains the simpler ones _liquid_, a certain _density_, _transparency_, _colorlessness_,[B] 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.

[B] More precisely, a very pale blue.

Now what predictions do those natural laws enable 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 confirmed 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 particular 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 for science to make regular and generally valid progress through the labors of the most various investigators who work independently of one another, and often know nothing of one another.

Of course, it must not be forgotten that such conclusions 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 characteristics were absent, or the accepted characterization of the concept required an improvement (limitation or extension). In other words, one way or another, 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 adjustment 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 exception; in other words, that absolutely every part of an experience can be demonstrated as conditioned by natural law. Evidently such an assertion far exceeds the demonstrable. And even the usual conclusion cannot be applied here, that because it has happened so in the past it will happen so in the future also. 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 entirely. I will mention only the uncertainty in predicting the weather for only one day ahead. Moreover, when we consider 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 explained 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 express 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 perfection of this work.

=10. The Law of Causation.= By reason of its frequency and importance the mental process above described has been subjected to the most diverse investigations, and that most general form of the scientific 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 physiological organization of man, _memory in the most general sense_--the easier execution of such processes as have already repeatedly taken place in the organism, 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 recurring parts of experience step into the foreground, and on account of their paramount practical importance for the security of life, it may well be said in the sense of the theory of evolution and adaptation, 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 entire organization which he inherits from his parents had already been formed under such an influence. But that there can be forms or existence _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.[C]

[C] It cannot be objected that inorganic nature also is known to be subject to the law of causation. The causal mode of regarding inorganic phenomena is a distinctly human one, and nothing justifies the assertion that the same phenomena cannot be viewed in an entirely different manner.

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 effect does not exist in nature at all, but has been introduced 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, arrange 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 formally, 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 various experiences in the shape of natural laws. Consequently we must recognize that in addition to the _subjective_ factor in the formation of our knowledge 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 independent 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 consisted of such pebbles of equal size. But it would be equally false to assert that it was the sieves that _made_ the pebbles equal.

=11. 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 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 ourselves have not the power to change (as, for example, 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 eliminated without the disappearance of B, and then we must proceed in such a way as to form a corresponding 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 possible in order to determine what constant elements are found in the concept B, and to form from these 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 _existing_ concepts which had been formed for quite a different 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 reason also it is often necessary to determine empirically in what way the concept is to be definitely established.

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 example, 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 candle, "Fire burns!" 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 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 absorption of heat. 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 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 concept 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 temporary rule require a limitation, while an unforeseen freedom requires an extension, of the accepted concept.

=12. Induction.= The form of conclusion previously 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 experiential 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, conclusions 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 cannot be so used.

To return to the inductive method--it is to be noted that _Aristotle_, who was the first to describe it, 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 _individual thing_ is so. While the incomplete induction merely says: since _many_ things of a certain kind are so, _presumably_ all things of this kind are so. One instantly perceives that the two conclusions are essentially 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 question 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 conclusion is _superfluous_, as it merely repeats knowledge 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 affirms something that has not yet been tested, and therefore involves as a condition an _extension_ of our knowledge, sometimes an extremely important extension. To be sure, it must give up the claim to unqualified or absolute validity, but, to compensate, it acquires the irreplaceable advantage of lending itself to practical application. Indeed, in accordance with the scientific practice justified by experience, described on p. 29, the scientific inductive conclusion 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 correct. 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 excluded. To wit, the discussion that has been carried on for centuries, and is not yet ended, over Euclid'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 procedure 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 incomplete 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 foreseen either, but which, according to the probability of the thesis and the correctness of the application are also probably correct. However, the investigator, 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 established by induction and in its confirmation by experience. This conduces to the growth of science, not in breadth, but in profundity. I again resort to the comparison I have frequently 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 inachievable. It is a regular, important, 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 instances. Now, if an especially gifted and far-seeing investigator 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 conditions 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 as follows. The investigator notices certain agreements 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 experimentation 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 principle 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 impel the author of the principle to carry out whatever readjustments may have become necessary. Upon the scientific imagination of the discoverer depends 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 deductive part of the work begins, and the consequent test of the proposition has the most essential influence on the value of the result.

It is immediately evident that this _deductive_ part is of all the more weight, the more _general_ the concepts 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 independent 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 question: _How are a priori judgments possible?_ We have seen that it is not always a question of _a priori_ judgments, but also of inductive conclusions 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. Accordingly 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 experience 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 the broadest assertions qualified by numerous "ifs" and "buts."

If, in spite of this, we arrange a very great part of our life and activity according to the prophecies we make in regard to numerous details in life, basing them upon natural laws, the question arises, how we get over the difficulty, or, rather, the impossibility just referred to.

The answer is, that we repeatedly so find or can form our experiences that certain natural relations _preponderatingly_ determine the experience, while the other parts that remain undetermined fall into the background. _The prophecy will cover so considerable a part of the experience that we can forego previous knowledge of the rest._ We can foretell enough to render a practical construction of life possible, and increasing experience, whether the personal experience of the individual or the general experience of science, constantly enlarges this controllable part of future experiences.

The procedure of science is similar to that of practical life, though freer. Whenever an investigator seeks to test a natural law of the form: if A is so, then B is so, he endeavors to choose or formulate the experiences in such a way that the fewest possible extraneous elements are present, and that those that are unavoidable should exert the least possible influence upon the relation in question. He never succeeds completely. In order, nevertheless, to reach a conclusion as to the form the relation will take without extraneous influences, the following general method is applied.

A series of instances are investigated which are so adjusted that the influence of the extraneous elements grows less and less. Then the relation investigated approaches a limit which is never quite reached, but to which it draws nearer and nearer, the less the influence of the extraneous elements. And the conclusion is drawn that if it were possible to exclude the extraneous elements entirely, the limit of the relation would be reached.

A case in which none of the extraneous elements of experience operate is called an _ideal case_, and the inference from a series of values leading to the limit-value is an _extrapolation_. _Such extrapolations to the ideal case_ are a quite natural procedure in science, and a very large part of natural laws, especially all quantitative laws, that is, such as express a relation between measurable values, have precise validity only in ideal cases.

We here confront the fact that many natural laws, and among them the most important, are expressed as, and taken to be, conditions _which never occur in reality_. This seemingly absurd procedure is, as a matter of fact, the best fitted for scientific purposes, since ideal cases are to be distinguished by this, _that with them the natural laws take on the simplest forms_. This is the result of the fact that in ideal cases we intentionally and arbitrarily overlook every complication of the determining factors, and in describing ideal cases we describe the simplest conceivable form of the class of experiences in question. 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 result. Just as we can represent the unlimited multitude of finite numbers by the figures up to ten, so we can represent an unlimited quantity of complicated events by a finite number of natural laws, and so reach a highly serviceable approximation to reality.

Thus geometry deals with absolutely straight lines, absolutely flat surfaces, and perfect spheres, though such have never been observed, and the results of geometry come the closer to truth, the more nearly the real lines, surfaces, and spheres correspond to the ideal demands. Similarly, in physics, there are no ideal gases or mirrors, or in chemistry ideally pure substances, though the expressed simple laws in these sciences are valid for only such bodies. The non-ideal bodies of these sciences, which reality presents in various degrees of approximation, correspond the more closely to these laws, the slighter the deviation of the real from the ideal. And the same method is applied in the so-called mental sciences, psychology and sociology, in which the "normal eye" and a "state with an entirely closed door" are examples of such idealized limit-concepts.

=15. The Determinateness of Things.= A very widespread view and a very grave one, because of its erroneous results, is _that by the natural laws things are unequivocally and unalterably determined down to the very minutest detail_. This is called _determinism_, and is regarded as an inevitable consequence of every natural scientific generalization. But an accurate investigation of actual relations produces something rather different.

The most general formulation of the natural law: _if A is experienced, then we expect B_, necessarily refers in the first place only to certain _parts_ of the thing experienced. For perfect similarity in two experiences is excluded by the mere fact that we ourselves change unceasingly and one-sidedly. Consequently, no matter how accurate the repetition of a former experience may be, our very participation in it, an element bound to enter, causes it to be different. Therefore we deal with only a _partial_ repetition of any experience, and the common part is all the smaller a fraction of the entire experience, the more _general_ the concept corresponding to this part. But the most general and most important natural laws apply to such very general ideas, and accordingly they determine only a small part of the whole result. Other parts are determined by other laws, but we can never point out an experience that has been determined completely and unequivocally by natural laws known to us. For example, we know that when we throw a stone, it will describe an approximate parabolic curve in falling to the ground. But if we should attempt to determine its course accurately, we should have to take into consideration the resistance of the air, the rotatory motion of the stone upon being thrown, the movement of the earth, and numerous other circumstances, the exact determination of which is a matter beyond the power of all sciences. Nothing but an _approximate_ determination of the stone's course is possible, and every step forward toward accuracy and absoluteness would require scientific advances which it would probably take centuries to accomplish.

Science, therefore, can by no means determine the exact linear course that the stone will take in its fall. It can merely establish a certain broader path within which the stone's movement will remain. And the path is the wider the smaller the progress science has made in the branch in question. The same conditions prevail in the case of every other prediction based upon natural laws. Natural laws merely provide a certain frame within which the thing will remain. But which of the infinitely numerous possibilities within this frame will become reality can never be absolutely determined by human powers.

The belief that it is possible has been evoked merely by a far-reaching method of abstraction on the part of science. By assuming in place of the stone "a non-extended point of mass" and by disregarding all the other factors which in some way (whether known or unknown) exercise an influence on the stone's movement, we can effect an apparently perfect solution of the problem. But the solution is not valid for real experience, merely for an ideal case, which bears only a more or less profound similarity to the real. It is only such an ideal world, that is, a world arbitrarily removed from its actual complexity, that has the quality of absolute determinateness which we are wont to ascribe to the real world.

We might point to the method of abstraction generally adopted in science and to the extrapolation to ideal cases which has just been explained, and regard the assertion of the absolute determinateness of events in the world as a justified extrapolation to the ideal case. In other words, we might say that we know all the natural laws and how to apply them perfectly to the individual instances. In controversion of this it must be said that the ulterior justification of such ideal extrapolation is not yet feasible. The justification lies in the demonstration that the real cases approximate the ideal the more closely the more we actualize our presumptions. But in this case this is not feasible, since, for the greater part of our experiences, we do not even know the approximate or ideal natural laws by the help of which we can construct such ideal cases. For instance, the whole province of organic life is at present essentially like an unknown land, in which there are only a few widely separated paths ending in _culs-de-sac_.

=16. The Freedom of the Will.= This relation explains why, on the one hand, we assume a far-reaching determinateness for many things, that is, for all those accessible to scientific treatment and regulation, and why, on the other hand, we have the consciousness of acting _freely_, that is, of being able to control future events according to the relations they bear to our wishes. 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 consciousness_, and that we feel these processes (in themselves determined) as if we ourselves determined their course. Nor can we prove this idea to be false, that, since the number of factors which influence each experience is indefinitely great and their nature indefinitely complex, each event would appear to be determined in the eyes of an all-comprehensive intellect. But to our finite minds an undetermined residue necessarily remains in each experience, and to that extent the world must always remain in part practically undetermined to human beings. Thus, both views, that the world is not completely determined, and that it really is, though we can never recognize that it is, lead practically to the same result: _that we can and must assume in our practical attitude to the world that it is only partially determined_.

But if two different lines of thought in the whole world of experience everywhere lead to the same result, they cannot be materially, but merely formally or superficially, different. For those things are alike which cannot be distinguished. There is no other definition of alikeness. Thus, if we see that the age-long dispute between these two views always breaks out afresh without seeming to be able to reach an end, this is readily understood, from what has been said, since the very same essential arguments which can be adduced of _one_ view can be used as a prop for the _other_ view, because in their essential results the two are the same. 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 questions. Each time we encounter such problems, we must ask ourselves: what would be the difference empirically if the one or the other view were correct? In other words, we first assume the one to be correct, and develop the consequences accordingly. Then we assume the second to be correct and develop the consequences accordingly. If in the two cases the consequences differ in a certain definite point, we at least have the possibility of ascertaining the false view by investigating in favor of which case experience decides on this point. However, we may not conclude that by this the other view has been proved to be entirely correct. It likewise may be false, only with the peculiar quality that in the case in question it leads to the correct conclusions. That such a thing is possible, every one knows who has attentively observed his own experiences. How often we act correctly in actual practice, though we have started out on false premises! The explanation of this possibility resides in the highly composite nature of each experience and each assumption. It is quite possible--and, in fact, it is the general rule--that a certain view contains true elements, but _along with them false elements also_. In applications of the view where the true elements are the decisive factors, true results are obtained, despite the errors present. Likewise, false results will be achieved where the false elements are decisive, despite the true results that can be had, or have been had, elsewhere, by means of the true elements. Hence, in case of the "confirmation," we can only conclude that that portion of the view essential for the instance in question is correct.

One readily perceives that these observations find application in all provinces of science and life. There are no absolutely correct assertions, and even the falsest may in some respect be true. There are only greater and lesser probabilities, and every advance made by the human intellect tends to increase the degree of probability of experiential relations, or natural laws.

=17. The Classification of the Sciences.= From the preceding observations the means may be drawn for outlining a complete table of the sciences. However, we must not regard it complete in the sense that it gives every possible ramification and turn of each science, but that it sets up a frame inside of which at given points each science finds its place, so that, in the course of progressive enlargement, the frame need not be exceeded.

The basic thought upon which this classification rests is that of graded abstraction. We have seen (p. 19) that a concept is all the more general, that is, is applicable to all the more experiences, the fewer parts or elementary concepts it contains. So we shall begin the system of the sciences with the most general concepts, that is, the elementary concepts (or with what for the time being we shall have to consider elementary concepts), and, in grading the concept complexes according to their increasing diversity, set up a corresponding graded series of sciences. One thing more is to be noted here, that this graded series, on account of the very large number of new concepts entering, must produce a correspondingly great number of diverse sciences. For practical reasons groups of such grades have been combined temporarily. Thereby a rougher classification, though one easier to obtain a survey of, has been made. The most suitable and lasting scheme of this sort was originated by the French philosopher, _Auguste Comte_, since whom it has undergone a few changes.

Below is the table of the sciences, which I shall then proceed to explain:

I. _Formal Sciences._ Main concept: order Logic, or the science of the Manifold Mathematics, or the science of Quantity Geometry, or the science of Space Phoronomy, or the science of Motion

II. _Physical Sciences._ Main concept: energy Mechanics Physics Chemistry

III. _Biological Sciences._ Main concept: life Physiology Psychology Sociology

As is evident, we first have to deal with the three great groups of the formal, the physical, and the biological sciences. The formal sciences treat of characteristics belonging to all experiences, characteristics, consequently, that enter into every known phase of life, and so affect science in the broadest sense. In order immediately to overcome a widespread error, I emphasize the fact that these sciences are to be considered just as experiential or empirical as the sciences of the other two groups, as to which there is no doubt that they are empirical. But because the concepts dealt with by the first group are so extremely wide, and the experiences corresponding to them, therefore, are the most general of all experiences, we easily forget that we are dealing with experiences at all; and our very firmly rooted consciousness of the unqualified similarity of these experiences causes them to seem native qualities of the mind, or _a priori_ judgments. Nevertheless, mathematics has been proved to be an empirical science by the fact that in certain of its branches (the theory of numbers) laws are known which have been found empirically and the "deductive" proof of which we have as yet not succeeded in obtaining. The most general concept expressed and operative in these sciences is the concept of order, of _conjugacy_ or _function_, the content and significance of which will become clear later in a more thorough study of the special sciences.

In the second group, the physical sciences, the arbitrariness of the classification becomes very apparent, since these sciences are among the best known. We are perfectly justified in regarding mechanics as a part of physics; and in our day physical chemistry, which in the last twenty years suddenly developed into an extended and important special science, thrust itself between physics and chemistry.

The most general concept of the physical sciences is that of _energy_, which does not appear in the formal sciences. To be sure it is not a fundamental concept. On the contrary, its characteristic is undoubtedly that of compositeness, or, rather, complexity.

The third group comprehends all the relations of living beings. Their most general concept, accordingly, is that of _life_. By physiology is understood the entire science dealing with non-psychic life phenomena. It therefore embraces what is called, in the present often chance arrangement of scientific activities, botany, zoology, and physiology of the plants, animals, and man. Psychology is the science of mental phenomena. As such, it is not limited to man, even though for many reasons he claims by far the preponderating part of it for himself. Sociology is the science which deals with the peculiarities of the human race. It may therefore be called anthropology, but in a far wider sense than the word is now applied.

=18. The Applied Sciences.= 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 institutions. We look in vain not only for theology and jurisprudence, but also for astronomy, medicine, etc.

The explanation and justification of this is, that for purposes of systematization we must distinguish between _pure_ and _applied_ sciences. By virtue of their strictly conceptual exclusiveness the pure sciences constitute a regular hierarchy or graded series, so that all the concepts that have been used and dealt with in the preceding sciences are repeated in the following sciences, while certain characteristic new concepts enter in addition. Thus logic, the science of the manifold, exercises its dominion over all the other sciences, while the specific concepts of physics and chemistry have nothing to do with it, though they are of importance to all the biologic sciences. Through this graded addition of new (naturally empiric) concepts, the construction of the pure sciences proceeds in strict regularity, and their problems arise exclusively from the application of new concepts to all the earlier ones. In other words, their problems do not reach them accidentally from without, but result from the action and reaction of their concepts upon one another.

At the same time there are problems that each day sets before us without regard to system. These come from our endeavor to improve life and avert evil. In the problems of life we are confronted by the whole variety of possible concepts, and under the day's immediate compulsion we cannot wait, if we are sowing crops or helping a sick man, 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 energy. When other signs fail, we use the position of the stars for finding our way on the high seas. In this manner we turn the teaching of the stars, or astronomy, into an applied science, in which at first mechanics alone seemed to have a part. Later physics took a share in it, then optics took a particularly prominent share, and in recent times not only did chemistry find its way into astronomy, but the specifically biologic concept of evolution was applied in astronomy with success.

Thus, side by side with the pure sciences are the applied, which are to be distinguished from the pure sciences by the fact that they do not unfold their problems systematically, but are assigned them by the external circumstances of man's life. The pure sciences, therefore, almost always have a larger or smaller share in the tasks of the applied sciences. For instance, in building a bridge or railroad, physical problems have to be taken into consideration as well as sociologic problems (problems of trade), and a good physician should be a psychologist as well as a chemist.

But since all the individual questions arising in the applied sciences may be considered essentially as problems of one or other pure science, they need not be explicitly enumerated along with the pure sciences, especially since their development is greatly dependent upon temporary conditions and is therefore incapable of simple systematization.