A Commentary to Kant's 'Critique of Pure Reason'

by Norman Kemp Smith

“It has been made a difficulty that my divisions in pure philosophy have almost always been threefold. But this lies in the nature of the case. If an a priori division is to be made, it must be either analytic, according to the principle of contradiction, and then it is always twofold (quodlibet ens est aut A aut non A); or else synthetic. And if in this latter case it is derived from a priori concepts (not as in mathematics from the a priori intuition corresponding to the concept) the division must necessarily be a trichotomy. For according to what is requisite for synthetic unity in general, there must be (1) a condition, (2) a conditioned, and (3) the concept which arises from the union of these two.”

The last stage, as expressed in the Critique, was, as we have already noted, merely an application of his earlier position that all thinking is judging. This appreciation of the inseparable connection of the categories with the act of judging is sound in principle, and is pregnant with many of the most valuable results of the Critical teaching. But these fruitful consequences follow only upon the lines developed in the transcendental deduction. They are bound up with Kant’s fundamental Copernican discovery that the categories are forms of synthesis, and accordingly express functions or relations. The categories can no longer be viewed, in the manner of the Dissertation,[703] as yielding concepts of objects. The view of the concept which we find in the Dissertation is, indeed, applied in the Critique to space and time—they are taken as in themselves intuitions, not as merely forms of intuition—but the categories are recognised as being of an altogether relational character. Though a priori, they are not, in and by themselves, complete objects of consciousness, and accordingly can reveal no object. They are functions, not contents. That, however, is to anticipate. We must first discharge, as briefly as possible, the ungrateful task of dwelling further upon the laboured, arbitrary, and self-contradictory character of the detailed working out of the metaphysical deduction. The deduction is given in Sections II. and III.

Section II. The Logical Function of the Understanding in Judgment.[704]—Kant’s introductory statement may here be noted. If, he says, we leave out of consideration the content of any judgment, and attend only to the mere form, we “find” that the function of thought in a judgment “can” be brought under four heads, each with three subdivisions. But Kant himself, in this same section, recognises in the frankest and most explicit manner, that the necessary distinctions are only to be obtained by taking account of the matter as well as of the form of judgments. And even after this contradiction is discounted, the term “find” may be allowed as legitimate only if the word “can” is correspondingly emphasised. The distinctions were not derived from any existing logic. They were reached only by the freest possible handling of the classifications currently employed. Examination of the table of judgments, and comparison of it with the table of categories, supply conclusive evidence that the former has been rearranged, in highly artificial fashion, so as to yield a more or less predetermined list of required categories.

1. Quantity.—Kant here frankly departs from the classification of judgments followed in formal logic; and the reason which he gives for so doing is in direct contradiction to his demand that only the form of judgment must be taken into account. The “quantity of knowledge” here referred to is determinable, not from the form, but only from the content of the judgment. Also, the statement that the singular judgment stands to the universal as unity to infinity (Unendlichkeit) is decidedly open to question. The universal is itself a form of unity, as Kant virtually admits in deriving, as he does, the category of unity from the universal judgment.

2. Quality.—Kant makes a similar modification in the logical treatment of quality, by distinguishing between affirmative and infinite judgments. The proposition, A is not-B, is to be viewed as neither affirmative nor negative. As the content of the predicate includes the infinite number of things that are not-B, the judgment is infinite. Kant, in a very artificial and somewhat arbitrary manner, contrives to define it as limitative in character, and so as sharing simultaneously in the nature both of affirmation and of negation. The way is thus prepared for the “discovery” of the category of limitation.

3. Relation.—Wolff, Baumgarten, Meier, Baumeister, Reimarus, and Lambert, with very minor differences, agree in the following division:[705]

Judgments–	Simple = Categorical
	Complex–	Copulative (i.e. categorical with morethan one subject or more than one predicate).
		Hypothetical.
		Disjunctive.

Kant omits the copulative judgment, and by ignoring the distinction between simple and complex judgments (which in Reimarus, and also less definitely in Wolff, is connected with the distinction between conditional and unconditional judgments) contrives to bring the remaining three types of judgment under the new heading of “relation.” They had never before been thus co-ordinated, and had never before been subsumed under this particular title. It is by no means clear why such distinctions as those between simple and complex, conditioned and unconditioned, should be ignored, and why the copulative judgment should not be recognised as well as the hypothetical. Kant’s criterion of importance and unimportance in the distinctions employed by the logicians of his day was wholly personal to himself; and, though hard to define, was certainly not dictated by any logic that is traceable to Aristotelian sources. His exposition is throughout controlled by foreknowledge of the particular categories which he desires to “discover.”

4. Modality.—Neither Wolff nor Reimarus gives any account of modality.[706] Baumgarten classifies judgments as pure or modal (existing in four forms, necessity, contingency, possibility, impossibility). Baumeister and Thomasius also recognise four forms of modality. Meier distinguishes between pure judgment (judicium purum) and impure judgment (judicium modale, modificatum, complexum qua copula), but does not classify the forms of modality. Lambert alone[707] classifies judgments as “possible, actual (wirklich), necessary, and their opposite.” But when Kant adopts this threefold division, the inclusion of actuality renders the general title “modality” inapplicable in its traditional sense. The expression of actuality in the assertoric judgment involves no adverbial modification of the predicate. Also, in its “affirmative” and “categorical” forms it has already been made to yield two other categories.

Kant speaks of the problematic, the assertoric, and the apodictic forms of judgment as representing the stages through which knowledge passes in the process of its development.