(_Translated from the German by Dr. R. M. Yerkes, Harvard University_)

[Wilhelm Ostwald, Professor of Physical Chemistry, University of Leipzig, since 1887. b. September 2, 1853, Riga, Russia. Grad. Candidate Chemistry, 1877; Master Chemistry, 1878; Doctor Chemistry, Dorpat. Dr. Hon. Halle and Cambridge; Privy Councilor; a.s.sistant, Dorpat, 1875-81; Regular Professor, Riga 1881-87. Member various learned and scientific societies. Author of _Manual of General Chemistry_; _Electro Chemistry_; _Foundation of Inorganic Chemistry_; _Lectures on Philosophy of Nature_; _Artist"s Letters_; _Essays and Lectures_; and many other noted works and papers on Chemistry and Philosophy.]

One of the few points on which the philosophy of to-day is united is the knowledge that the only thing completely certain and undoubted for each one is the content of his own consciousness; and here the certainty is to be ascribed not to the content of consciousness in general, but only to the momentary content.

This momentary content we divide into two large groups, which we refer to the inner and outer world. If we call any kind of content of consciousness an experience, then we ascribe to the outer world such experiences as arise without the activity of our will and cannot be called forth by its activity alone. Such experiences never arise without the activity of certain parts of our body, which we call sense organs.

In other words, the outer world is that which reaches our consciousness through the senses.

On the other hand, we ascribe to our inner world all experiences which arise without the immediate a.s.sistance of a sense organ. Here, first of all, belong all experiences which we call remembering and thinking. An exact and complete differentiation of the two territories is not intended here, for our purpose does not demand that this task be undertaken. For this purpose the general orientation in which every one recognizes familiar facts of his consciousness is sufficient.

Each experience has the characteristic of uniqueness. None of us doubts that the expression of the poet "Everything is only repeated in life" is really just the opposite of the truth, and that in fact nothing is repeated in life. But to express such a judgment we must be in position to compare different experiences with each other, and this possibility rests upon a fundamental phenomenon of our consciousness, memory. Memory alone enables us to put various experiences in relation to each other, so that the question as to their likeness or difference can be asked.

We find the simpler relations here in the inner experiences. A certain thought, such as twice two is four, I can bring up in my consciousness as often as I wish, and in addition to the content of the thought I experience the further consciousness that I have already had this thought before, that it is familiar to me.

A similar but somewhat more complex phenomenon appears in the experiences in which the outer world takes part. After I have eaten an apple, I can repeat the experience in two ways. First, as an inner experience, I can remember that I have eaten the apple and by an effort of my will I can re-create in myself, although with diminished strength and intensity, a part of the former experience--the part which belonged to my inner world. Another part, the sense impression which belonged to that experience, I cannot re-create by an effort of my will, but I must again eat an apple in order to have a similar experience of this sort.

This is a complete repet.i.tion of the experience to which the external world also contributes. Such a repet.i.tion does not depend altogether on my own powers, for it is necessary that I have an apple, that is, that certain conditions which are independent of me and belong to the outer world be fulfilled.

Whether the outer world takes part in the repet.i.tion of an experience or not has no influence upon the possibility of the content of consciousness which we call memory. From this it follows that this content depends upon the inner experience alone, and that we remember an external event only by means of its inner const.i.tuents. The mere repet.i.tion of corresponding sense impressions is not sufficient for this, for we can see the same person repeatedly without recognizing him, if the inner accompanying phenomena were so insignificant, as a result of lack of interest, that their repet.i.tion does not produce the content of consciousness known as memory. If we see him quite frequently, the frequent repet.i.tion of the external impression finally causes the memory of the corresponding inner experience.

From this it results that for the "memory"-reaction a certain intensity of the inner experience is necessary. This threshold can be attained either at once or by continued repet.i.tion. The repet.i.tions are the more effective the more rapidly they follow each other. From this we may conclude that the memory-value of an experience, or its capacity for calling forth the "memory"-reaction by repet.i.tion, decreases with the lapse of time. Further, we must consider the fact mentioned above, that an experience is never exactly repeated, and that therefore the "memory"-reaction occurs even where there is only resemblance or partial agreement in place of complete agreement. Here, too, there are different degrees; memory takes place more easily the more perfectly the two experiences agree, and _vice versa_.

If we look at these phenomena from the physiological side, we may say we have two kinds of apparatus or organs, one of which does not depend upon our will, whereas the other does. The former are the sense organs. The latter const.i.tutes the organ of thought. Only the activities of the latter const.i.tute our experiences or the content of our consciousness.

The activities of the former may call forth the corresponding processes of the latter, but this is not always necessary. Our sense organs can be influenced without our "noticing" it, that is, without the thinking apparatus being involved. An especially important reaction of the thinking apparatus is memory, that is, the consciousness that an experience which we have just had possesses more or less agreement with former experiences. With reference to the organ of thought, it is the expression of the general physiological fact that every process influences the organ in such a way that it has a different relation to the repet.i.tion of this process, from the first time, and moreover that the repet.i.tion is rendered easier. This influence decreases with time.

It is chiefly upon these phenomena that experience rests. Experience results from the fact that all events consist of a complete series of simultaneous and successive components. When a connection between some of those parts has become familiar to us by the repet.i.tion of similar occurrences (for instance, the succession of day and night), we do not feel such an occurrence as something completely new, but as something partially familiar, and the single parts or phases of it do not surprise us, but rather we antic.i.p.ate their coming or expect them. From expectation to prediction is only a short step, and so experience enables us to prophesy the future from the past and present.

Now this is also the road to science: for science is nothing but systematized experience, that is, experience reduced to its simplest and clearest forms. Its purposes to predict from a part of a phenomenon which is known another part which is not yet known. Here it may be a question of spatial as well as of temporal phenomena. Thus the scientific zoologist knows how to "determine," that is, to tell, from the skull of an animal, the nature of the other parts of the animal to which the skull belongs; likewise the astronomer is able to indicate the future, situation of a planet from a few observations of its present situation; and the more exact the first observations were, the more distant the future for which he can predict. All such scientific predictions are limited, therefore, with reference to their number and their accuracy. If the skull shown to the zoologist is that of a chicken, then he will probably be able to indicate the general characteristics of chickens, and also perhaps whether the chicken had a top-knot or not; but not its color, and only uncertainly its age and its size. Both facts, the possibility of prediction and its limitation in content and amount, are an expression for the two fundamental facts, that among our experiences there is similarity, but not complete agreement.

The foregoing considerations deserve to be discussed and extended in several directions. First, the objection will be made that a chicken or a planet is not an experience; we call them rather by the most general name of thing. But our knowledge of the chicken begins with the experiencing of certain visual impressions, to which are added, perhaps, certain impressions of hearing and touch. The sight impressions (to discuss these first) by no means completely agree. We see the chicken large or small, according to the distance; and according to its position and movement its outline is very different. As we have seen, however, these differences are continually grading into one other and do not reach beyond certain limits; we neglect to observe them and rest contented with the fact that certain other peculiarities (legs, wings, eyes, bill, comb, etc.) remain and do not change. The constant properties we group together as a thing, and the changing ones we call the states of this thing. Among the changing properties, we distinguish further those which depend upon us (for example, the distance) and those upon which we have no immediate influence (for instance, the position or motion): the first is called the subjective changeable part of our experience, while the second is called the objective mutability of the thing.

This omission of both the subjectively and objectively changeable portion of the experience in connection with the retention of the constant portion and the gathering together of the latter into a unity is one of the most important operations which we perform with our experiences. We call it the process of abstraction, and its product, the permanent unity, we call a concept. Plainly this procedure contains arbitrary as well as necessary factors. Arbitrary or accidental is the circ.u.mstance that quite different phases of a given experience come to consciousness according to our attention, the amount of practice we have had, indeed according to our whole intellectual nature. We may overlook constant factors and attend to changeable ones. The objective factors, however, become necessary as soon as we have noticed them; after we have seen that the chicken is black, it is not in our power to see it red.

Accordingly, in general, our knowledge of that which agrees must be less than it actually could be, since we have not been able to observe every agreement, and our concept is always poorer in const.i.tuents at any given time than it might be. To seek out such elements of concepts as have been overlooked, and to prove that they are necessary factors of the corresponding experiences, is one of the never-ending tasks of science.

The other case, namely, that elements have been received in the concept which do not prove to be constant, also happens, and leads to another task. One can then leave that element out of the concept, if further experiences show that the other elements are found in them, or one can form a new concept which contains the former elements, leaving out those that have been recognized as unessential. For a long time the white color belonged to the concept swan. When the Dutch black swans became known, it was possible either to drop the element white from the concept swan (as actually happened), or to make a new concept for the bird which is similar to the swan but black. Which choice is made in a given case is largely arbitrary, and is determined by considerations of expediency.

Into the formation of concepts, therefore, two factors are operative, an objective empirical factor, and a subjective or purposive factor. The fitness of a concept is seen in relation to its purpose, which we shall now consider.

The purpose of a concept is its use for prediction. The old logic set up the syllogism as the type of thought-activity, and its simplest example is the well-known

All men are mortal, Caius is a man, Therefore Caius is mortal.

In general, the scheme runs

To the concept M belongs the element B, C belongs under the concept M, Therefore the element B is found in C.

One can say that this method of reasoning is in regular use even to this day. It must be added, however, that this use is of a quite different nature from that of the ancients. Whereas formerly the setting up of the first proposition or the major premise was considered the most important thing, and the establishment of the second proposition or minor premise was thought to be a rather trifling matter, now the relation is reversed. The major premise contains the description of a concept, the minor makes the a.s.sertion that a certain thing belongs under this concept. What right exists for such an a.s.sertion? The most palpable reply would be, since all the elements of the concept M (including B) are found in C, C belongs under the concept M. Such a conclusion would indeed be binding, but at the same time quite worthless, for it only repeats the minor premise. Actually the method of reasoning is essentially different, for the minor premise is not obtained by showing that all the elements of the concept M are found in C, but only some of them. The conclusion is not necessary, but only probable, and the whole process of reasoning runs: Certain elements are frequently found together, therefore they are united in the concept M. Certain of these elements are recognized in the thing C, therefore probably the other elements of the concept M will be found in C.

The old logic, also, was familiar with this kind of conclusion. It was branded, however, as the worst of all, by the name of incomplete induction, since the absolute certainty demanded of the syllogism did not belong to its results. One must admit, however, that the whole of modern science makes use of no other form of reasoning than incomplete induction, for it alone admits of a prediction, that is, an indication of relations which have not been immediately observed.

How does science get along with the defective certainty of this process of reasoning? The answer is, that the probability of the conclusion can run through all degrees from mere conjecture to the maximum probability, which is practically indistinguishable from certainty. The probability is the greater the more frequently an incomplete induction of this kind has proven correct in later experience. Accordingly we have at our command a number of expressions which in their simplest and most general form have the appearance: If an element A is met within a thing, then the element B is also found in it (in spatial or temporal relationship).

If the relation is temporal, this general statement is known by some such name as the law of causality. If it is spatial, one talks of the idea (in the Platonic sense), or the type of the thing, of substance, etc.

From the considerations here presented we get an easy answer to many questions which are frequently discussed in very different senses.

First, the question concerning the general validity of the law of causality. All attempts to prove such a validity have failed, and there has remained only the indication that without this law we should feel an unbearable uncertainty in reference to the world. From this, however, we see very plainly that here it is merely a question of expediency. From the continuous flux of our experiences we hunt out those groups which can always be found again, in order to be able to conclude that if the element A is given, the element B will be present. We do not find this relationship as "given," but we put it into our experiences, in that we consider the parts which correspond to the relationship as belonging together.

The very same thing may be said of spatial complexes. Such factors as are always, or at any rate often, found together are taken by us as "belonging together," and out of them a concept is formed which embraces these factors. A question as to the why has here, as with the temporal complexes, no definite meaning. There are countless things that happen together once to which we pay no attention because they happen only once or but seldom. The knowledge of the fact that such a single concurrence exists amounts to nothing, since from the presence of one factor it does not lead to a conclusion as to the presence of another, and therefore does not make possible prediction. Of all the possible, and even actual combinations, only those interest us which are repeated, and this arbitrary but expedient selection produces the impression that the world consists only of combinations that can be repeated; that, in other words, the law of causality or of the type is a general one. However general or limited application those laws have, is more a question of our skill in finding the constant combinations among those that are present than a question of objective natural fact.

Thus we see the development and pursuit of all sciences going on in such a way that on the one hand more and more constant combinations are discovered, and on the other hand more inclusive relations of this kind are found out, by means of which elements are united with each other which before no one had even tried to bring together. So sciences are increasing both in the sense of an increasing complication and in an increasing unification.

If we consider from this standpoint the development and procedure of the various sciences, we find a rational division of the sum total of science in the question as to the scope and multiplicity of the combinations or groups treated of in them. These two properties are in a certain sense ant.i.thetical. The simpler a complex is, that is, the fewer elements brought together in it, the more frequently it is met with, and _vice versa_. One can therefore arrange all the sciences in such a way that one begins with the least multiplicity and the greatest scope, and ends with the greatest multiplicity and the least scope. The first science will be the most general, and will therefore contain the most general and therefore the most barren concepts; the last will contain the most specific and therefore the richest.

What are these limiting concepts? The most general is the concept of _thing_, that is, any piece of experience, seized arbitrarily from the flux of our experiences, which can be repeated. The most specific and richest is the concept of _human intercourse_. Between the science of things and the science of human intercourse, all the other sciences are found arranged in regular gradation. If one follows out the scheme the following outline results:

1. Theory of order. } 2. Theory of numbers, or arithmetic. } Mathematics.

3. Theory of time. } 4. Theory of s.p.a.ce, or geometry. } 5. Mechanics. } 6. Physics. } Energetics.

7. Chemistry. } 8. Physiology. } 9. Psychology. } Biology.

10. Sociology. }

This table is arbitrary in so far as the grades a.s.sumed can be increased or diminished according to need. For example, mechanics and physics could be taken together; or between physics and chemistry, physical chemistry could be inserted. Likewise between physiology and psychology, anthropology might find a place; or the first five sciences might be united under mathematics. How one makes these divisions is entirely a practical question, which will be answered at any time in accordance with the purposes of division; and dispute concerning the matter is almost useless.

I should like, however, to call attention to the three great groups of mathematics, energetics, and biology (in the wider sense). They represent the decisive regulative thought which humanity has evolved, contributed up to this time, toward the scientific mastery of its experiences. Arrangement is the fundamental thought of mathematics. From mechanics to chemistry the concept of energy is the most important; and for the last three sciences it is the concept of life. Mathematics, energetics, and biology, therefore, embrace the totality of the sciences.

Before we enter upon the closer consideration of these sciences, it will be well to antic.i.p.ate another objection which can be raised on the basis of the following fact. Besides the sciences named (and those which lie between them) there are many others, as geology, history, medicine, philology, which we find difficulty in arranging in the above scheme, which must, however, be taken into consideration in some way or other.

They are often characterized by the fact that they stand in relation with several of the sciences named, but even more by the following circ.u.mstance. Their task is not, as is true of the pure sciences above named, the discovery of general relationships, but they relate rather to existing complex objects whose origin, scope, extent, etc., in short, whose temporal and spatial relationships they have to discover or to "explain." For this purpose they make use of relations which are placed at their disposal by the first-named pure sciences. These sciences, therefore, had better be called applied sciences. However, in this connection we should not think only or even chiefly of technical applications; rather the expression is used to indicate that the reciprocal relations of the parts of an object are to be called to mind by the application of the general rules found in pure science.

While in such a task the abstraction process of pure science is not applicable (for the omission of certain parts and the concentration upon others which is characteristic of these is excluded by the nature of the task), yet in a given case usually the necessity of bringing in various pure sciences for the purpose of explanation is evident.

Astronomy is one of these applied sciences. Primarily it rests upon mechanics, and in its instrumental portion, upon optics; in its present development on the spectroscopic side, however, it borrows considerably of chemistry. In like manner history is applied sociology and psychology. Medicine makes use of all the sciences before mentioned, up to psychology, etc.

It is important to get clearly in mind the nature of these sciences, since, on account of their compound nature, they resist arrangement amongst the pure sciences, while, on account of their practical significance, they still demand consideration. The latter fact gives them also a sort of arbitrary or accidental character, since their development is largely conditioned by the special needs of the time.

Their number, speaking in general, is very large, since each pure science may be turned into an applied science in various ways; and since in addition we have combinations of two, three, or more sciences.

Moreover, the method of procedure in the applied sciences is fundamentally different from that in the pure sciences. In the first it is a question of the greatest possible a.n.a.lysis of a single given complex into its scientifically comprehensible parts; while pure science, on the other hand, considers many complexes together in order to separate out from them their common element, but expressly disclaims the complete a.n.a.lysis of a single complex.

In scientific work, as it appears in practice, pure and applied science are by no means sharply separated. On the one hand the auxiliaries of investigations, such as apparatus, books, etc., demand of the pure investigator knowledge and application in applied science; and, on the other hand, the applied scientist is frequently unable to accomplish his task unless he himself becomes for the time being a pure investigator and ascertains or discovers the missing general relationships which he needs for his task. A separation and differentiation of the two forms of science was necessary, however, since the method and the aim of each present essential differences.

In order to consider the method of procedure of pure science more carefully, let us turn back to the table on pages 339, 340, and attend to the single sciences separately. The theory of arrangement was mentioned first, although this place is usually a.s.signed to mathematics.

However, mathematics has to do with the concepts of number and magnitude as fundamentals, while the theory of arrangement does not make use of these. Here the fundamental concept is rather the thing or object of which nothing more is demanded or considered than that it is a fragment of our experience which can be isolated and will remain so. It must not be an arbitrary combination; such a thing would have only momentary duration, and the task of science, to learn the unknown from the given, could not find application. Rather must this element have such a nature that it can be characterized and recognized again, that is, it must already have a conceptual nature. Therefore only parts of our experience which can be repeated (which alone can be objects of science) can be characterized as things or objects. But in saying this we have said all that was demanded of them. In other respects they may be just as different as is conceivable.

If the question is asked, What can be said scientifically about indefinite things of this sort? it is especially the relations of arrangement and a.s.sociation which yield an answer. If we call any definite combination of such things a group, we can arrange such a group in different ways, that is, we can determine for each thing the relation in which it is to stand to the neighboring thing. From every such arrangement result not only the relationships indicated, but a great number of new ones, and it appears that when the first relationships are given the others always follow in like manner. This, however, is the type of the scientific proposition or natural law (page 335). From the presence of certain relations of arrangement we can deduce the presence of others which we have not yet demonstrated.

To ill.u.s.trate this fact by an example, let us think of the things arranged in a simple row, while we choose one thing as a first member and a.s.sociate another with it as following it; with the latter another is a.s.sociated, etc. Thereby the position of each thing in the row is determined only in relation to the immediately preceding thing.

Nevertheless, the position of every member in the whole row, and therefore its relation to every other member, is determined by this.

This is seen in a number of special laws. If we differentiate former and latter members we can formulate the proposition, among others, if B is a later member with reference to A, and C with reference to B, then C is also a later member with reference to A.

The correctness and validity of this proposition seems to us beyond all doubt. But this is only a result of the fact that we are able to demonstrate it very easily in countless single cases, and have so demonstrated it. We know only cases which correspond to the proposition, and have never experienced a contradictory case. To call such a proposition, however, a necessity of thinking, does not appear to me correct. For the expression necessity of thinking can only rest upon the fact that every time the proposition is thought, that is, every time one remembers its demonstration, its confirmation always arises. But every sort of false proposition is also thinkable. An undeniable proof of this is the fact that so much which is false is actually thought. But to base the proof for the correctness of a proposition upon the impossibility of thinking its opposite is an impossible undertaking, because every sort of nonsense can be thought: where the proof was thought to have been given, there has always been a confusion of thought and intuition, proof or inspection.