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

by Norman Kemp Smith

But though the unique character of mathematical knowledge thus forced itself upon the attention of all the Cartesian thinkers, and in the above manner led even the most level-headed of Descartes’ successors to dream strange dreams, no real attempt was made (save in the neglected writings of Leibniz) to examine, in a sober spirit, the grounds and conditions of its possibility. In the English School, Locke’s eulogy of abstract ideas served only to drive his immediate successors to an opposite extreme. Both Berkeley and Hume attempted to explain away, in an impossible manner, those fundamental differences, which, beyond all questioning, profoundly differentiate mathematical from empirical judgments.[1768] It is not surprising that Kant, who had no direct acquaintance with Hume’s Treatise, should have asserted that had Hume realised the bearing of his main teaching upon the theory of mathematical science, he would have hesitated to draw his sceptical conclusions. Such, however, was not the case. Hume’s theory of mathematical reasoning undoubtedly forms the least satisfactory part of his philosophy. He did, however, perceive the general bearing of his central teaching. It was in large degree his ignorance of the mathematical disciplines that concealed from him the thorough unsatisfactoriness of his general position, and which prevented him from formulating the logical problem in its full scope—the problem, namely, how judgments which make additions to our previous knowledge, and yet do not rest upon mere sensation, are possible. He treated it only as it presents itself in those judgments which involve the concept of causality.[1769] But this analysis of causal judgments awoke Kant from his dogmatic slumber, and so ultimately led to the raising of the logical problem in its widest form:—how synthetic a priori judgments, whether mathematical, physical, or metaphysical, are possible.

Hume discussed the causal problem both in regard to the general principle of causality and in its bearing upon our particular judgments of causal relation. The problems concerned in these two discussions are essentially distinct. The first involves immensely wider issues, and so far as can be judged from the existing circumstantial evidence,[1770] it was this first discussion, not as has been so often assumed by Kant’s commentators the second and more limited problem, which exercised so profound an influence upon Kant at the turning-point of his speculations. In stating it, it will be best to take Hume’s own words.

“To begin with the first question concerning the necessity of a cause: ‘Tis a general maxim in philosophy, that whatever begins to exist, must have a cause of existence. This is commonly taken for granted in all reasonings, without any proof given or demanded. ‘Tis supposed to be founded on intuition, and to be one of those maxims, which though they may be deny’d with the lips, ‘tis impossible for men in their hearts really to doubt of. But if we examine this maxim by the idea of knowledge above explain’d we shall discover in it no mark of any such intuitive certainty; but on the contrary shall find, that ‘tis of a nature quite foreign to that species of conviction.”[1771]

The principle that every event must have a cause, is neither intuitively nor demonstratively certain. So far from there existing a necessary connection between the idea of an event as something happening in time and the idea of a cause, no connection of any kind is discoverable by us. We can conceive an object to be non-existent at this moment, and existent the next, without requiring to conjoin with it the altogether different idea of a productive source.

This had been implicitly recognised by those few philosophers who had attempted to give demonstrations of the principle. By so doing, however, they only reinforce Hume’s contention that it possesses no rational basis. When Hobbes argues that as all the points of time and place in which we can suppose an object to begin to exist, are in themselves equal, there must be some cause determining an event to happen at one moment rather than at another, he is assuming the very principle which he professes to prove. There is no greater difficulty in supposing the time and place to be fixed without a cause, than in supposing the existence to be so determined. If the denial of a cause is not intuitively absurd in the one case, it cannot be so in the other. If the first demands a proof, so likewise must the second. Similarly with the arguments advanced by Locke and Clarke. Locke argues that if anything is produced without a cause, it is produced by nothing, and that that is impossible, since nothing can never be a cause any more than it can be something, or equal to two right angles. Clarke’s contention that if anything were without a cause, it would produce itself, i.e. exist before it existed, is of the same character. These arguments assume the only point which is in question.

“When we exclude all causes we really do exclude them, and neither suppose nothing nor the object itself to be the causes of the existence, and consequently can draw no argument from the absurdity of these suppositions to prove the absurdity of that exclusion.”[1772]

The remaining argument, that every effect must have a cause, since this is implied in the very idea of an effect, is “still more frivolous.”

“Every effect necessarily presupposes a cause; effect being a relative term, of which cause is the correlative. But this does not prove that every being must be preceded by a cause; no more than it follows, because every husband must have a wife, that therefore every man must be married.”[1773]

The far-reaching conclusion, that the principle of causality has no possible rational basis, Hume extends and reinforces through his other doctrines, viz. that synthetic reason[1774] is merely generalised belief, and that belief is in all cases due to the ultimate instincts and propensities which de facto constitute our human nature. The synthetic principles which lie at the basis of our experience are non-rational in character. Each is due to a ‘blind and powerful instinct,’ which, demanding no evidence, and ignoring theoretical inconsistency for the sake of practical convenience, necessitates belief.

“Nature by an absolute and uncontrollable necessity has determined us to judge as well as to breathe and feel.”[1775] “All these operations are a species of natural instincts, which no reasoning or process of the thought and understanding is able either to produce or to prevent.”[1776]