That I reject the whole doctrine of the categories, and reckon it among the groundless assumptions with which Kant burdened the theory of knowledge, results from the criticism given above; and also from the proof of the contradictions in the Transcendental Logic, which had their ground in the confusion of perception and abstract knowledge; also further from the proof of the want of a distinct and definite conception of the nature of the understanding and of the reason, instead of which we found in Kant's writings only incoherent, inconsistent, insufficient, and incorrect utterances with regard to these two faculties of the mind. Finally, it results from the explanations which I myself have given of these faculties of the mind in the first book and its Supplements, and more fully in the essay on the principle of sufficient reason, § 21, 26, and 34,—explanations which are very definite and distinct, which clearly follow from the consideration of the nature of our knowledge, and which completely agree with the conceptions of those two faculties of knowledge that appear in the language and writings of all ages and all nations, but were not brought to distinctness. Their defence against the very different exposition of Kant has, for the most part, been given already along with the exposure of the errors of that exposition. Since, however, the table of judgments, which Kant makes the foundation of his theory of thinking, and indeed of his whole philosophy, has, in itself, as a whole, its correctness, it is still incumbent upon me to show how these universal forms of all judgment arise in our faculty of knowledge, and to reconcile them with my exposition of it. In this discussion I shall always attach to the concepts understanding and reason the sense given them in my explanation, which I therefore assume the reader is familiar with.

An essential difference between Kant's method and that which I follow lies in this, that he starts from indirect, reflected knowledge, while I start from direct or intuitive knowledge. He may be compared to a man who measures the height of a tower by its shadow, while I am like him who applies the measuring-rule directly to the tower itself. Therefore, for him philosophy is a science of conceptions, but for me it is a science in conceptions, drawn from knowledge of perception, the one source of all evidence, and comprehended and made permanent in general conceptions. He passes over this whole world of perception which surrounds us, so multifarious and rich in significance, and confines himself to the forms of abstract thinking; and, although he never expressly says so, this procedure is founded on the assumption that reflection is the ectype of all perception, that, therefore, all that is essential in perception must be expressed in reflection, and expressed in very contracted forms and outlines, which are thus easily surveyed. According to this, what is essential and conformable to law in abstract knowledge would, as it were, place in our hands all the threads by which the varied puppet-show of the world of perception is set in motion before our eyes. If Kant had only distinctly expressed this first principle of his method, and then followed it consistently, he would at least have been obliged to separate clearly the intuitive from the abstract, and we would not have had to contend with inextricable contradictions and confusions. But from the way in which he solves his problem we see that that fundamental principle of his method was only very indistinctly present to his mind, and thus we have still to arrive at it by conjecture even after a thorough study of his philosophy.

1. The so-called Quantity of judgments springs from the nature of concepts as such. It thus has its ground in the reason alone, and has absolutely no direct connection with the understanding and with knowledge of perception. It is indeed, as is explained at length in the first book, essential to concepts, as such, that they should have an extent, a sphere, and the wider, less determined concept includes the narrower and more determined. The latter can therefore be separated from the former, and this may happen in two ways,—either the narrower concept may be indicated as an indefinite part of the wider concept in general, or it may be defined and completely separated by means of the addition of a special name. The judgment which carries out this operation is in the first case called a particular, and in the second case an universal judgment. For example, one and the same part of the sphere of the concept tree may be isolated through a particular and through an universal judgment, thus—“Some trees bear gall-nuts,” or “All oaks bear gall-nuts.” One sees that the difference of the two operations is very slight; indeed, that the possibility of it depends upon the richness of the language. Nevertheless, Kant has explained this difference as disclosing two fundamentally different actions, functions, categories of the pure understanding which determines experience a priori through them.

After all that has been said there is no need of further polemic here.

To the affirmative and negative Kant adds the infinite judgment, making use of a crotchet of the old scholastics, an ingeniously invented stop-gap, which does not even require to be explained, a blind window, such as many others he made for the sake of his architectonic symmetry.

3. Under the very wide conception of Relation Kant has brought three entirely different properties of judgments, which we must, therefore, examine singly, in order to recognise their origin.

(b.) The form of the categorical judgment is nothing but the form of judgment in general, in its strictest sense. For, strictly speaking, judging merely means thinking, the combination of, or the impossibility of combining, the spheres of the concepts. Therefore the hypothetical and the disjunctive combination are properly no special forms of the judgment; for they are only applied to already completed judgments, in which the combination of the concepts remains unchanged the categorical. But they again connect these judgments, for the hypothetical form expresses their dependence upon each other, and the disjunctive their incompatibility. Mere concepts, however, have only one class of relations to each other, those which are expressed in the categorical judgment. The fuller determination, or the sub-species of this relation, are the intersection and the complete separateness of the concept-spheres, i.e., thus affirmation and negation; out of which Kant has made special categories, under quite a different title, that of quality. Intersection and separateness have again sub-species, according as the spheres lie within each other entirely, or only in part, a determination which constitutes the quantity of the judgments; out of which Kant has again made a quite special class of categories. Thus he separates what is very closely related, and even identical, the easily surveyed modifications of the one possible relation of mere concepts to each other, and, on the other hand, unites what is very different under this title of relation.

Aristotle also denies reciprocity in the strict sense; for he remarks that two things may certainly be reciprocal causes of each other, but only if this is understood in a different sense of each of them; for example, that one acts upon the other as the motive, but the latter acts upon the former as the cause of its movement. We find in two passages the same words: Physic., lib. ii. c. 3, and Metaph., lib. v. c. 2. Εστι δε τινα και αλληλων αιτια; οἱον το πονειν αιτιον της ευεξιας, και αὑτη του πονειν; αλλ᾽ ου τον αυτον τροπον, αλλα το μεν ὡς τελος, το δε ὡς αρχη κινησεως. (Sunt præterea quæ sibi sunt mutuo causæ, ut exercitium bonæ habitudinis, et hæc exercitii: at non eodem modo, sed hæc ut finis, aliud ut principium motus.) If, besides this, he had accepted a reciprocity proper, he would have introduced it here, for in both passages he is concerned with enumerating all the possible kinds of causes. In the Analyt. post., lib. ii. c. 11, he speaks of a circle of causes and effects, but not of reciprocity.

4. The categories of Modality have this advantage over all others, that what is expressed through each of them really corresponds to the form of judgment from which it is derived; which with the other categories is scarcely ever the case, because for the most part they are deduced from the forms of judgment with the most capricious violence.

I hold that to be necessary and to be the consequent of a given reason are absolutely interchangeable notions, and completely identical. We can never know, nor even think, anything as necessary, except so far as we regard it as the consequent of a given reason; and the conception of necessity contains absolutely nothing more than this dependence, this being established through something else, and this inevitable following from it. Thus it arises and exists simply and solely through the application of the principle of sufficient reason. Therefore, there is, according to the different forms of this principle, a physical necessity (the effect from the cause), a logical (through the ground of knowing, in analytical judgments, syllogisms, &c.), a mathematical (according to the ground of being in time and space), and finally a practical necessity, by which we intend to signify not determination through a pretended categorical imperative, but the necessary occurrence of an action according to the motives presented, in the case of a given empirical character. But everything necessary is only so relatively, that is, under the presupposition of the reason from which it follows; therefore absolute necessity is a contradiction. With regard to the rest, I refer to § 49 of the essay on the principle of sufficient reason.

From this exposition, which requires no proof because it rests directly upon the knowledge of the principle of sufficient reason and upon the development of the conceptions of the necessary, the actual, and the possible, it is sufficiently evident how entirely groundless is Kant's assumption of three special functions of the understanding for these three conceptions, and that here again he has allowed himself to be disturbed by no reflection in the carrying out of his architectonic symmetry.

I take this opportunity of adding a few further remarks on these conceptions of modality. Since all necessity rests upon the principle of sufficient reason, and is on this account relative, all apodictic judgments are originally, and according to their ultimate significance, hypothetical. They become categorical only through the addition of an assertatory minor, thus in the conclusion. If this minor is still undecided, and this indecision is expressed, this gives the problematical judgment.

Maj. All houses (consequently also my house) can be destroyed by fire.

Min. My house is on fire.

Concl. My house is being destroyed by fire.

After this exposition, which presupposes the recollection of what was said both in the essay on the principle of sufficient reason and in the first book of the present work, there will, it is hoped, be no further doubt as to the true and very heterogeneous source of those forms which the table of judgments lays before us, nor as to the inadmissibility and utter groundlessness of the assumption of twelve special functions of the understanding for the explanation of them. The latter point is also supported by a number of special circumstances very easily noted. Thus, for example, it requires great love of symmetry and much trust in a clue derived from it, to lead one to assume that an affirmative, a categorical, and an assertatory judgment are three such different things that they justify the assumption of an entirely special function of the understanding for each of them.