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

by Norman Kemp Smith

CHAPTER I
THE DISCIPLINE[1685] OF PURE REASON

KANT is neither an intellectualist nor an anti-intellectualist. Reason, the proper duty of which is to prescribe a discipline to all other endeavours, itself requires discipline; and when it is employed in the metaphysical sphere, independently of experience, it demands not merely the correction of single errors, but the eradication of their causes through “a separate negative code,” such as a Critical philosophy can alone supply. In the Transcendental Doctrine of Elements this demand has been met as regards the materials or contents of the Critical system; we are now concerned only with its methods or formal conditions.[1686]

This distinction is highly artificial. As already indicated, it is determined by the requirements of Kant’s architectonic. The entire teaching of the Methodology has already been more or less exhaustively expounded in the earlier divisions of the Critique.

SECTION I
THE DISCIPLINE OF PURE REASON IN ITS DOGMATIC EMPLOYMENT

In dealing with the distinction between mathematical and philosophical knowledge, Kant is here returning to one of the main points of his Introduction to the Critique.[1687] His most exhaustive treatment of it is, however, to be found in a treatise which he wrote as early as 1764, his Enquiry into the Clearness of the Principles of Natural Theology and Morals. The continued influence of the teaching of that early work is obvious throughout this section, and largely accounts for the form in which certain of its tenets are propounded.

“...one can say with Bishop Warburton that nothing has been more injurious to philosophy than mathematics, that is, than the imitation of its method in a sphere where it is impossible of application....”[1688]

So far from being identical in general nature, mathematics and philosophy are, Kant declares, fundamentally opposed in all essential features. For it is in their methods, and not merely in their subject-matter, that the essential difference between them is to be found.[1689] Philosophical knowledge can be acquired only through concepts, mathematical knowledge is gained through the construction of concepts.[1690] The one is discursive merely; the other is intuitive. Philosophy can consider the particular only in the general; mathematics studies the general in the particular.[1691] Philosophical concepts, such as those of substance and causality, are, indeed, capable of application in transcendental synthesis, but in this employment they yield only empirical knowledge of the sensuously given; and from empirical concepts the universal and necessary judgments required for the possibility of metaphysical science can never be obtained.

The exactness of mathematics depends on definitions, axioms, and demonstrations, none of which are obtainable in philosophy. To take each in order.

I. Definitions.—To define in the manner prescribed by mathematics is to represent the complete concept of a thing. This is never possible in regard to empirical concepts. We are more certain of their denotation than of their connotation; and though they may be explained, they cannot be defined. Since new observations add or remove predicates, an empirical concept is always liable to modification.

“What useful purpose could be served by defining an empirical concept, such, for instance, as that of water? When we speak of water and its properties, we do not stop short at what is thought in the word water, but proceed to experiments. The word, with the few marks which are attached to it, is more properly to be regarded as merely a designation than as a conception. The so-called definition is nothing more than a determining of the word.”[1692]