Kant's Theory of Knowledge

by H. A. Prichard

The 'Copernican' revolution was brought about by consideration of the facts of mathematics. Kant accepted as an absolute starting-point the existence in mathematics of true universal and necessary judgements. He then asked, 'What follows as to the nature of the objects known in mathematics from the fact that we really know them?' Further, in his answer he accepted a distinction which he never examined or even questioned, viz. the distinction between things in themselves and phenomena.[19] This distinction assumed, Kant inferred from the truth of mathematics that things in space and time are only phenomena. According to him mathematicians are able to make the true judgements that they do make only because they deal with phenomena. Thus Kant in no way sought to prove the truth of mathematics. On the contrary, he argued from the truth of mathematics to the nature of the world which we thereby know. The phenomenal character of the world being thus established, he was able to reverse the argument and to regard the phenomenal character of the world as explaining the validity of mathematical judgements. They are valid, because they relate to phenomena. And the consideration which led Kant to take mathematics as his starting-point seems to have been the self-evidence of mathematical judgements. As we directly apprehend their necessity, they admit of no reasonable doubt.

On the other hand, the general principles underlying physics, e. g. that every change must have a cause, or that in all change the quantum of matter is constant, appeared to Kant in a different light. Though certainly not based on experience, they did not seem to him self-evident.[21] Hence,[22] in the case of these principles, he sought to give what he did not seek to give in the case of mathematical judgements, viz. a proof of their truth.[23] The nerve of the proof lies in the contention that these principles are involved not merely in any general judgement in physics, e. g. 'All bodies are heavy,' but even in any singular judgement, e. g. 'This body is heavy,' and that the validity of singular judgements is universally conceded. Thus here the fact upon which he takes his stand is not the admitted truth of the universal judgements under consideration, but the admitted truth of any singular judgement in physics. His treatment, then, of the universal judgements of mathematics and that of the principles underlying physics are distinguished by the fact that, while he accepts the former as needing no proof, he seeks to prove the latter from the admitted validity of singular judgements in physics. At the same time the acceptance of mathematical judgements and the proof of the a priori principles of physics have for Kant a common presupposition which distinguishes mathematics and physics from metaphysics. Like universal judgements in mathematics, singular judgements in physics, and therefore the principles which they presuppose, are true only if the objects to which they relate are phenomena. Both in mathematics and physics, therefore, it is a condition of a priori knowledge that it relates to phenomena and not to things in themselves. But, just for this reason, metaphysics is in a different position; since God, freedom, and immortality can never be objects of experience, a priori knowledge in metaphysics, and therefore metaphysics itself, is impossible. Thus for Kant the very condition, the realization of which justifies the acceptance of mathematical judgements and enables us to prove the principles of physics, involves the impossibility of metaphysics.

Further, the distinction drawn between a priori judgements in mathematics and in physics is largely responsible for the difficulty of understanding what Kant means by a priori. His unfortunate tendency to explain the term negatively could be remedied if it could be held either that the term refers solely to mathematical judgements or that he considers the truth of the law of causality to be apprehended in the same way that we see that two and two are four. For an a priori judgement could then be defined as one in which the mind, on the presentation of an individual in perception or imagination, and in virtue of its capacity of thinking, apprehends the necessity of a specific relation. But this definition is precluded by Kant's view that the law of causality and similar principles, though a priori, are not self-evident.

FOOTNOTES

[1] Locke's Essay, i, 1, §§ 2, 4.

[2] Caird, i, 10.

[3] B. 19, M. 12.

[4] Kant is careful to exclude from the class of a priori judgements proper what may be called relatively a priori judgements, viz. judgements which, though not independent of all experience, are independent of experience of the facts to which they relate. "Thus one would say of a man who undermined the foundations of his house that he might have known a priori that it would fall down, i. e. that he did not need to wait for the experience of its actual falling down. But still he could not know this wholly a priori, for he had first to learn through experience that bodies are heavy and consequently fall, if their supports are taken away." (B. 2, M. 2.)

[5] It may be noted that in this passage (Introduction, §§ 1 and 2) Kant is inconsistent in his use of the term 'pure'. Pure knowledge is introduced as a species of a priori knowledge: "A priori knowledge, if nothing empirical is mixed with it, is called pure". (B. 3, M. 2, 17.) And in accordance with this, the proposition 'every change has a cause' is said to be a priori but impure, because the conception of change can only be derived from experience. Yet immediately afterwards, pure, being opposed in general to empirical, can only mean a priori. Again, in the phrase 'pure a priori' (B. 4 fin., M. 3 med.), the context shows that 'pure' adds nothing to 'a priori', and the proposition 'every change must have a cause' is expressly given as an instance of pure a priori knowledge. The inconsistency of this treatment of the causal rule is explained by the fact that in the former passage he is thinking of the conception of change as empirical, while in the latter he is thinking of the judgement as not empirical. At bottom in this passage 'pure' simply means a priori.

[6] In reality, these tests come to the same thing, for necessity means the necessity of connexion between the subject and predicate of a judgement, and since empirical universality, to which strict universality is opposed, means numerical universality, as illustrated by the proposition 'All bodies are heavy', the only meaning left for strict universality is that of a universality reached not through an enumeration of instances, but through the apprehension of a necessity of connexion.