Kant's Theory of Knowledge

by H. A. Prichard

While there is no difficulty in determining what Kant would have recognized as an a priori judgement, there is difficulty in determining what he meant by calling such a judgement a priori. The general account is given in the first two sections of the Introduction. An a priori judgement is introduced as something opposed to an a posteriori judgement, or a judgement which has its source in experience. Instances of the latter would be 'This body is heavy', and 'This body is hot'. The point of the word 'experience' is that there is direct apprehension of some individual, e. g. an individual body. To say that a judgement has its source in experience is of course to imply a distinction between the judgement and experience, and the word 'source' may be taken to mean that the judgement depends for its validity upon the experience of the individual thing to which the judgement relates. An a priori judgement, then, as first described, is simply a judgement which is not a posteriori. It is independent of all experience; in other words, its validity does not depend on the experience of individual things. It might be illustrated by the judgement that all three-sided figures must have three angles. So far, then, no positive meaning has been given to a priori.[4]

Kant then proceeds, not as we should expect, to state the positive meaning of a priori; but to give tests for what is a priori. Since a test implies a distinction between itself and what is tested, it is implied that the meaning of a priori is already known.[5]

The tests given are necessity and strict universality.[6] Since judgements which are necessary and strictly universal cannot be based on experience, their existence is said to indicate another source of knowledge. And Kant gives as illustrations, (1) any proposition in mathematics, and (2) the proposition 'Every change must have a cause'.

So far Kant has said nothing which determines the positive meaning of a priori. A clue is, however, to be found in two subsequent phrases. He says that we may content ourselves with having established as a fact the pure use of our faculty of knowledge.[7] And he adds that not only in judgements, but even in conceptions, is an a priori origin manifest.[8] The second statement seems to make the a priori character of a judgement consist in its origin. As this origin cannot be experience, it must, as the first statement implies, lie in our faculty of knowledge. Kant's point is that the existence of universal and necessary judgements shows that we must possess a faculty of knowledge capable of yielding knowledge without appeal to experience. The term a priori, then, has some reference to the existence of this faculty; in other words, it gives expression to a doctrine of 'innate ideas'. Perhaps, however, it is hardly fair to press the phrase 'test of a priori judgements'. If so, it may be said that on the whole, by a priori judgements Kant really means judgements which are universal and necessary, and that he regards them as implying a faculty which gives us knowledge without appeal to experience.

We may now turn to the term 'synthetic judgement'. Kant distinguishes analytic and synthetic judgements thus. In any judgement the predicate B either belongs to the subject A, as something contained (though covertly) in the conception A, or lies completely outside the conception A, although it stands in relation to it. In the former case the judgement is called analytic, in the latter synthetic.[9] 'All bodies are extended' is an analytic judgement; 'All bodies are heavy' is synthetic. It immediately follows that only synthetic judgements extend our knowledge; for in making an analytic judgement we are only clearing up our conception of the subject. This process yields no new knowledge, for it only gives us a clearer view of what we know already. Further, all judgements based on experience are synthetic, for it would be absurd to base an analytical judgement on experience, when to make the judgement we need not go beyond our own conceptions. On the other hand, a priori judgements are sometimes analytic and sometimes synthetic. For, besides analytical judgements, all judgements in mathematics and certain judgements which underlie physics are asserted independently of experience, and they are synthetic.

Here Kant is obviously right in vindicating the synthetic character of mathematical judgements. In the arithmetical judgement 7 + 5 = 12, the thought of certain units as a group of twelve is no mere repetition of the thought of them as a group of five added to a group of seven. Though the same units are referred to, they are regarded differently. Thus the thought of them as twelve means either that we think of them as formed by adding one unit to a group of eleven, or that we think of them as formed by adding two units to a group of ten, and so on. And the assertion is that the same units, which can be grouped in one way, can also be grouped in another. Similarly, Kant is right in pointing out that the geometrical judgement, 'A straight line between two points is the shortest,' is synthetic, on the ground that the conception of straightness is purely qualitative,[10] while the conception of shortest distance implies the thought of quantity.

It should now be an easy matter to understand the problem expressed by the question, 'How are a priori synthetic judgements possible?' Its substance may be stated thus. The existence of a posteriori synthetic judgements presents no difficulty. For experience is equivalent to perception, and, as we suppose, in perception we are confronted with reality, and apprehend it as it is. If I am asked, 'How do I know that my pen is black or my chair hard?' I answer that it is because I see or feel it to be so. In such cases, then, when my assertion is challenged, I appeal to my experience or perception of the reality to which the assertion relates. My appeal raises no difficulty because it conforms to the universal belief that if judgements are to rank as knowledge, they must be made to conform to the nature of things, and that the conformity is established by appeal to actual experience of the things. But do a priori synthetic judgements satisfy this condition? Apparently not. For when I assert that every straight line is the shortest way between its extremities, I have not had, and never can have, experience of all possible straight lines. How then can I be sure that all cases will conform to my judgement? In fact, how can I anticipate my experience at all? How can I make an assertion about any individual until I have had actual experience of it? In an a priori synthetic judgement the mind in some way, in virtue of its own powers and independently of experience, makes an assertion to which it claims that reality must conform. Yet why should reality conform? A priori judgements of the other kind, viz. analytic judgements, offer no difficulty, since they are at bottom tautologies, and consequently denial of them is self-contradictory and meaningless. But there is difficulty where a judgement asserts that a term B is connected with another term A, B being neither identical with nor a part of A. In this case there is no contradiction in asserting that A is not B, and it would seem that only experience can determine whether all A is or is not B. Otherwise we are presupposing that things must conform to our ideas about them. Now metaphysics claims to make a priori synthetic judgements, for it does not base its results on any appeal to experience. Hence, before we enter upon metaphysics, we really ought to investigate our right to make a priori synthetic judgements at all. Therein, in fact, lies the importance to metaphysics of the existence of such judgements in mathematics and physics. For it shows that the difficulty is not peculiar to metaphysics, but is a general one shared by other subjects; and the existence of such judgements in mathematics is specially important because there their validity or certainty has never been questioned.[11] The success of mathematics shows that at any rate under certain conditions a priori synthetic judgements are valid, and if we can determine these conditions, we shall be able to decide whether such judgements are possible in metaphysics. In this way we shall be able to settle a disputed case of their validity by examination of an undisputed case. The general problem, however, is simply to show what it is which makes a priori synthetic judgements as such possible; and there will be three cases, those of mathematics, of physics, and of metaphysics.

The outline of the solution of this problem is contained in the Preface to the Second Edition. There Kant urges that the key is to be found by consideration of mathematics and physics. If the question be raised as to what it is that has enabled these subjects to advance, in both cases the answer will be found to lie in a change of method. "Since the earliest times to which the history of human reason reaches, mathematics has, among that wonderful nation the Greeks, followed the safe road of a science. Still it is not to be supposed that it was as easy for this science to strike into, or rather to construct for itself, that royal road, as it was for logic, in which reason has only to do with itself. On the contrary, I believe that it must have remained long in the stage of groping (chiefly among the Egyptians), and that this change is to be ascribed to a revolution, due to the happy thought of one man, through whose experiment the path to be followed was rendered unmistakable for future generations, and the certain way of a science was entered upon and sketched out once for all.... A new light shone upon the first man (Thales, or whatever may have been his name) who demonstrated the properties of the isosceles triangle; for he found that he ought not to investigate that which he saw in the figure or even the mere conception of the same, and learn its properties from this, but that he ought to produce the figure by virtue of that which he himself had thought into it a priori in accordance with conceptions and had represented (by means of a construction), and that in order to know something with certainty a priori he must not attribute to the figure any property other than that which necessarily follows from that which he has himself introduced into the figure, in accordance with his conception."[12]

Here Kant's point is as follows. Geometry remained barren so long as men confined themselves either to the empirical study of individual figures, of which the properties were to be discovered by observation, or to the consideration of the mere conception of various kinds of figure, e. g. of an isosceles triangle. In order to advance, men had in some sense to produce the figure through their own activity, and in the act of constructing it to recognize that certain features were necessitated by those features which they had given to the figure in constructing it. Thus men had to make a triangle by drawing three straight lines so as to enclose a space, and then to recognize that three angles must have been made by the same process. In this way the mind discovered a general rule, which must apply to all cases, because the mind itself had determined the nature of the cases. A property B follows from a nature A; all instances of A must possess the property B, because they have solely that nature A which the mind has given them and whatever is involved in A. The mind's own rule holds good in all cases, because the mind has itself determined the nature of the cases.

Kant's statements about physics, though not the same, are analogous. Experiment, he holds, is only fruitful when reason does not follow nature in a passive spirit, but compels nature to answer its own questions. Thus, when Torricelli made an experiment to ascertain whether a certain column of air would sustain a given weight, he had previously calculated that the quantity of air was just sufficient to balance the weight, and the significance of the experiment lay in his expectation that nature would conform to his calculations and in the vindication of this expectation. Reason, Kant says, must approach nature not as a pupil but as a judge, and this attitude forms the condition of progress in physics.