The process of systematization of concepts consists in the assertion of identity between separate concepts and groups of concepts in one or more respects, in which precisely the various objects of concepts can be expressed by one and the same general judgment. This transfer of judgment from one object to another, or from one concept to another, constitutes a process of deductive reasoning, the sole significance of which is precisely that it organizes certain connections of representations or concepts by establishing or denying the relation of identity between them. It is true that such an understanding of deduction is far from being justified by certain forms of syllogistic thinking, but in judging these forms it must be borne in mind that they are expressions of a very complex formation of the deductive process of thought, and therefore in themselves they still require an explanation of their possibility. When, for example, the conclusion is drawn that all men are mortal, and that Caius is a man and therefore mortal, then thought obviously operates in this construction with propositions which could appear only in the preliminary processes of other inferences and with other elements. In order to affirm the thesis about the mortality of people, it is necessary to affirm the identity in the individual representations of individual people, i.e. it is necessary to form a concept of man; and in order to affirm the humanity of Caius, it is necessary to affirm the identity in the content of the idea of him and in the content of the concept of man. Only by the force of this identity can the subject of the first premise be thought of in the form of an indefinite number of individual representations, each of which can be combined with the representation of Kai in the general concept of man. Consequently, for all these ideas, whatever their number, the concept of man will be common, i.e. in its content it will be completely identical with the content of the subject of the first premise and, as identical, can always replace it. Consequently, instead of the proposition that all men are mortal, an identical proposition can always be posed: man is mortal, and in the conception of man all men are thought not with the exception of Caius, but together with him. Consequently, the conclusion is not something new in comparison with its foundation, but only a simple translation of the general proposition into a particular one. The new does not actually consist in the conclusion, but only in the products of identification that substantiate this conclusion, in the formation of a general concept of man and in the subsuming of a single idea under this general concept, while the conclusion is a simple exposition of the concept in relation to the idea reduced to it, and consequently not as separate from it and alien to it, but as one which is already contained in it and through it is expressed in all those judgments. the sum of which forms the content of this concept.

In view of the fact that the process of identification expresses the whole essence of deductive inference, it is not difficult to find this process even in constructions in which the act of identification is directly negated and the conclusion is made only by the force of this negation. Let us assume, for example, the following construction: true Christians live and act according to the spirit of the faith of Christ; some people who consider themselves Christians do not live and act according to the spirit of the faith of Christ; Consequently, some people who consider themselves Christians are not true Christians. The process of this inference obviously consists in establishing the relation of the predicates of the two premisses, but the real basis of this inference lies not in this relation, but behind it. From the proposition that one magnitude is not equal to another, it does not in the least follow that it is not equal to a third, unless it is established or assumed beforehand that the second and third magnitudes are equal to each other. Consequently, the negation of the predicate of the first premise in its application to the subject of the second premise does not in the least extend this negation to the subject of the first premise in relation to the subject of the second premise, unless it is established or assumed beforehand that the subject of the first premise fully covers its predicate, and vice versa, that the predicate of this premise fully covers its subject. i.e., unless it is established or assumed in advance that the subject and the predicate of the first premise are identical concepts. In this case, the negation of the predicate eo ipso is also the negation of the subject of the first premise in its relation to the subject of the second premise. Consequently, the essential character of deductive reasoning appears here no less sharply than in the first example, i.e., the determination of the correlation of two concepts through the medium of a third under the point of view of the principle of identity. If, however, this is the whole essence of deduction, then it goes without saying that every deductive inference, both in content and in its formal consistency, must be determined not by the scope of the concepts and not by their quality, but solely by the possibility or impossibility of the said correlation.

It is true that logical science still indicates the fundamental rule of deductive reasoning in the well-known scholastic formula, "e mere negativis et e mere particularibus nihil sequitur," but this indication is in fact only a great misunderstanding. A conclusion can be drawn both from particular premises and from negative premises, as long as there are conditions for the possibility of affirming or denying the identity between these concepts. To clarify this point, we will take an example from the Logic of Prof. Vladislavlev: "No science should borrow its material from second sources; fairy tales cannot be called science; no conclusion is drawn from this." But we think that the learned author, who is absolutely convinced of the justice of his "fundamental rule" (e mere negativis...), did not try to draw any conclusion from this, and yet this conclusion follows, and moreover in the most natural way: "Fairy tales can also take their material from second sources." For by denying the identity between the subject of the first proposition and the subject of the second proposition, I thereby also deny the predicate of the first proposition in its relation to the subject of the second proposition, i.e., by denying the scientific character of fairy tales, I can no longer transfer to them the obligatory attribute of scientific thinking, I cannot say of them that they should not take their material from the second sources. It is, of course, true that the negation of one predicate does not provide any basis for the direct affirmation of its opposite predicate, because such a statement requires a positive reason; but it is also true that this negation determines the possibility of an opposite affirmation. A conclusion can be drawn precisely from this foundation and within its limits, i.e. a conclusion can only be made in the form of a simple expression of this possibility. The only question is whether such a conclusion will always be consistent and what exactly determines its consistency? That in a whole mass of cases such a conclusion will be untenable is beyond doubt, and that its inconsistency will be determined by the real impossibility of combining the negation of the predicate of the first premise with the negation of the subject in their relation to the subject of the second premise. But if it is certain that in one mass of cases the conclusion will be untenable, while in another mass of cases it will be valid, then it is self-evident that there must be some grounds or conditions for its validity, i.e., there must be such grounds or conditions by the force of which the logical possibility of transferring the negation from the subject to the predicate of the first premise passes into necessity. And this necessity coincides with the real necessity of such a translation. For example, let's assume the following construction: a birch cannot grow without roots, an oak is not a birch, therefore, an oak can grow without roots. The investigation is clearly ridiculous, because it clearly contradicts reality. And it is not difficult to guess the reasons for this absurdity, if only we compare this construction with the construction given from the Logic of Prof. Vladislavlev. We shall then observe that there are two fundamental differences in the relations between the elements of the two constructions. The first concerns the relationship between the subjects of both premisses, the second the relationship between the subject and the predicate of the first premise. Science and the fairy tale are thought of as opposites, and therefore the relation aimed at uniting the second premise with the first is necessarily the negation of the predicate of the first premise on the part of the subject of the second. In the second construction, however, the subjects of both premises (birch and oak) are formed from homogeneous concepts, and therefore there can be no opposition between them, and consequently no mutual negation. From this it is self-evident that the second premise in this construction can be directed not at negation, but only at distinguishing its subject from the subject of the first premise. Once this distinction has been established, identity is, of course, denied, but since concepts are homogeneous, it cannot be denied unconditionally, but necessarily under certain conditions, i.e., in some definite relations. Yet these conditions or relations are not expressed at all in the second premise, and therefore the conclusion from this is quite impossible. It may well be that the difference between the subjects of the two premisses is expressed by the predicate of the first premise, but it is very possible that it is also expressed by some other premise, which are completely unindicated in either premise. In this case it is expressed by other attributes, and not by a predicate, and therefore the expression of the subject's negation of the second premise of the subject of the first premise in this very predicate turns out to be absurd.

Hence the question naturally arises: under what conditions can the negation of the identity between the two subjects be expressed through the negation of the predicate of one of the premisses in its relation to the subject of the other premise? The answer to this question is indicated by the second fundamental difference in the constructions we have cited. When it is said that science should not take its material from second sources, in this case an essential demand is made of science, i.e., a demand that is thought of in the very concept of science. Consequently, the subject and the predicate in this position are analytically connected, i.e. they are thought of and considered as identical expressions in the relation in which they are connected. Therefore, any negation of the subject of such a proposition is at the same time a negation of its connection with the predicate, not in relation to itself, but in relation to this connection with that element of the second premise by which the subject of the first premise is denied. That is, the predicate of the first premise cannot be connected with the subject of the second premise in the same way as it is connected with the subject of the first premise, because this subject is negated by the subject of the second premise, while the predicate of the first premise is identical with its subject. The second formation is completely unsuitable for such a case. The concept of the impossibility of growth without the intermediary of roots, while forming a predicate in this judgment about the birch, does not, however, in the least express the subject of this judgment in its particularity, does not in the least express what actually makes the birch a birch, and not some other kind of plant. As a consequence, the subject and the predicate of a given judgment cannot be thought of and considered as identical expressions, and therefore the negation of the subject of this judgment on the part of the subject of another judgment can in no case be transferred to a given connection between it and the predicate. In other words, the subjects of both premisses may not be identical, but the relation of the predicate of one of the premisses to both subjects may be the same, because the predicate itself is not identical with either subject. Consequently, it is possible to transfer the negation of the subject of the first premise to its connection with the predicate in relation to this relation to the subject of the second premise only on the condition that the predicate is the essential predicate of its subject, when it is the subject itself to its particularity. In this case, the negation of the subject consists precisely in the fact that its essential predicate is denied, i.e., the conclusion affirms the impossibility of connecting this predicate with the subject of the second premise by the same connection as it is connected with the subject of the first premise.

Consequently, the conclusion from these judgments can only be an expression of this negation: a person (not-not) can be mistaken, i.e. the conclusion affirms only the impossibility of identity in connection with both subjects.

Then the compared concepts would be identified in the conclusion. Suppose, for example, that a student who is beginning to study philosophy knows the general proposition that all preachers of pessimism do not recognize the good of life, but who exactly preached pessimism is not told to him. He studied the history of philosophy and found that Schopenhauer did not recognize the good of life. From this he draws the direct conclusion that Schopenhauer was a preacher of pessimism.

Obviously, this conclusion is determined by the identity of the connection of the predicate of the first premise with both subjects, and is substantiated by the identity of the content of this predicate with the content of its subject. The same predicate which is thought of in the first proposition is also affirmed in relation to the subject of the second premise. But this predicate is an identical expression of its subject: the preachers of pessimism are the very people who do not recognize the good of life, and vice versa – it is precisely those people who preach pessimism who do not recognize the good of life. Consequently, the predicate in this case expresses the only attribute of its subject and, consequently, it expresses in itself the entire content of its concept. Therefore, the connection of this predicate with the subject of the second premise eo ipso is the connection of this subject with the concept whose entire content is expressed by the predicate. The predicate, of course, is not identical with the subject of the second premise, but by the force of the very fact of its connection with this subject, it determines it in the relation in which it is identical with the subject of the first premise. Hence, the idea of Schopenhauer is not only the idea of a man who did not recognize the good of life. It also contains many other attributes which are not expressed by the predicate, but in the process of inference these attributes play no role at all, because the subject of the judgment cannot be thought of in any other respect than that which is determined by its predicate. In this case, therefore, the idea of Schopenhauer is only the idea of him as a man who did not recognize the good of life, and consequently in this respect the idea of Schopenhauer is identical with the concept of a preacher of pessimism, i.e., identical with the concept of the subject of the first premise.

Thus the general condition of the possibility of deductive inference is fully expressed by the logical law of the excluded middle: the concepts to be combined must stand in such a definite relation to the intermediate concept that their mutual connection through this concept is either affirmed or denied. In the absence of this condition, when the indefinite formulation of concepts in relation to the intermediate concept makes it impossible to say either yes or no about their connection, the conclusion is impossible.

IV. The Process of Cognition

1.

The Active Nature of Psychic Reality and the Process of Cognition: the Psychological Nature of Cognition and the Problem of Faith.

In the process of formation and unification of representations, all the content is created and all forms of visual connection between individual things and phenomena of objective reality are determined. In the process of development and organization of concepts, a classification of things and phenomena is created and all forms of their conceivable relations to each other are organized on the basis of their represented content. If we consider these processes only according to their own content, i.e., quite independently of all other states of consciousness, then their entire significance will obviously be expressed only by the organization of the chaotic world of consciousness, and therefore their entire application will be limited to the world of impressions given alone. The fact is that both of these processes are completely dependent on the formation of impressions, and this formation depends on the number of relations of the subject to the external world.