The Philosophy of Immanuel Kant

by A. D. Lindsay

CHAPTER II

KANT'S STATEMENT OF THE PROBLEM. SYNTHETIC
A PRIORI JUDGMENTS

In the preface to the second edition of the Critique of Pure Reason Kant finds the necessity of criticism in the contrast between certain rational sciences and metaphysics. Mathematics and physics, he observes, are obviously certain sciences. They are not empirical, they make steady progress, the results they have reached are secure and unanimously accepted, and have a certainty which no mere empirical investigation could attain. Metaphysics, on the other hand, though as ancient an inquiry, seems incapable of any settled results. Its history is a record, not of steady progress, but of bewildering marches and countermarches. The confident conclusions of one philosopher are as confidently denied by another, and the endless indecisive conflict produces in the minds of most men the conviction that in philosophy one doctrine is as good as another, and therefore none are worth very much. In the sphere where reason might be expected to be most at home, reason is impotent; yet the achievements of reason in those other spheres of the a priori sciences should preserve us from any general scepticism of the powers of reason. The task of criticism will be to examine the part played by reason in science, and to ask how far its failure in metaphysics is due to mistakes in method, and how far to the different nature of the objects of the a priori sciences and of metaphysics. Kant points out that it was some time before either mathematics or physics followed the secure path of a science. The contrast between the haphazard and empirical observations of the Babylonians or Egyptians and the science of the Greeks was due to the discovery of a new method. The discovery by Galileo and Torricelli of modern physics came about by a similar revolution in method. The Critique, therefore, is to be a treatise on method. It will examine the method of reason in the sciences, and ask what conclusions can be drawn as to the proper method of metaphysics.

In the Prolegomena, a work in which he summarises the results of the first Critique, Kant describes the Critique as an answer to three questions: How is mathematics possible? How is pure science of nature or physics possible? and, How is metaphysics possible? Something of the nature of his answer to the third, and for him the most important, question, may be gathered from the fact that he explains that the third question should not be put in the form, How is metaphysics as a science possible? That question can only be answered by saying that it is not possible. But it is still allowable and necessary to ask, How is metaphysics possible as a natural disposition of the mind? For the main result of his inquiries into the place of reason in the sciences is to show that reason is successful in the sciences only because of the presence of certain conditions which are wanting in metaphysics. At first sight we might think it natural that the objects of metaphysics which Kant enumerates as God, Freedom, and Immortality should be understood by reason, and find it more difficult to explain how reason should apply to the world of ordinary experience. The knowledge of everyday things is thought of as empirical, a matter of observation; while we are inclined to think that, if there is rational knowledge, it is knowledge of something else, of the mere agreement or disagreement of ideas (as Hume thought), or of the essences of things, known independently and apart from perception, as Plato thought. Kant argues that the combination of a priori reasoning and empirical observation, which earlier thinkers had found so puzzling in the exact sciences, exhibits the only possible use of reason, that reason, divorced from and with no reference to the world of experience, is barren, and that consequently metaphysics, if that be taken to mean a rational knowledge of objects which are outside of our experience, does not exist. We are left with metaphysics as a natural disposition; for Kant holds that the questions which metaphysics seeks to answer arise from the nature of reason and its relation to experience, though their answer is to be sought not in knowledge but in action.

This last point must be elucidated later. In the meantime we must see how this inquiry into the nature of reason crystalises itself into a seemingly abstract and trivial question: How are synthetic a priori judgments possible? It is baffling at first to find an inquiry of the scope we have indicated suddenly take such a narrow form, but a little consideration will show the importance of the question. Knowledge may be regarded as either analysis or synthesis, as a puzzling out or unravelling of what we somehow know already, or as a putting together of what had previously been known or observed separately. The rationalist school, whom we described in the last chapter, were inclined to regard all knowledge as analytical. They thought of progress in knowledge as an advance from obscure to clear apprehension, and as a thinking out or making clear of something which had always been known somehow. Mathematics, the typical form of knowledge for the rationalists, had been thought of as the analysis of what was implied or given in the definitions. The conception of analytic a priori knowledge was thus familiar and simple. On the other hand, the empiricists had thought of knowledge as primarily synthesis--or, as they called it, association--a connecting together of ideas in their nature separate. Knowledge of a thing was thought of as the observing together of several ideas. Judgments about objects were regarded as judgments about the co-existence of separate ideas, ideas which were not thought of as being bound by any logical necessity. We do not understand why a substance with the specific gravity of gold should be yellow; we only observe the co-existence of certain qualities. The judgment, then, gold is yellow, is synthetic; it is an assertion of the co-existence of separate qualities. It is also empirical; it does not express a reasoned insight into the necessary connection of gold and yellow. It seems rather a record of observation. Synthetic knowledge, then, was thought of as in its nature empirical and a posteriori. Hume, who thought of all knowledge of the world in experience as synthetic, denied to such knowledge any necessity or certainty.

Hume, however, had noticed that the principle of causation, the judgment that every event has a cause, is both a priori and synthetic. It is not, he held, derived from experience; rather it is a principle which guides our investigation of experience. It is not got from analysis of the notion of causation, nor is it simply concerned with the agreement or disagreement of our ideas. It asserts the necessary connection of two perfectly separate existing things. Hume himself, as we saw, tried to explain away these uncomfortable facts. He was too wedded to his belief that all knowledge was derived from passively received impressions to face them rightly. Kant, coming to the problem with different prepossessions, with the belief that most knowledge was analytic, was impressed with Hume's proof that the principle of causation could not be derived from analysis. The very basis of all science of nature, then, contradicted the belief that knowledge was analytical. Kant was also, with Hume, convinced that the principle of causation was not derived from experience, for he saw that experience assumed it. At the same time, he was not prepared, like Hume, to explain it away. Further, he saw that the problem raised by the principle of causation was a wide one. For other judgments, he held, are both synthetic and a priori, among them mathematical judgments. As we shall see afterwards, Kant proved the impossibility of arriving at knowledge of God or the soul by mere analysis of concepts. The judgments of metaphysics, about God or the soul, are also synthetic. But the validity of the judgments of metaphysics is under dispute. If we examine the synthetic a priori judgments of mathematics and of science whose validity is certain, we may then discover whether such judgments in metaphysics can or can not have similar certainty. We may thus see that the problem of the possibility of synthetic a priori judgments is a restatement in logical terms of the problem of the relation between the a priori sciences and metaphysics.

Something more must be said of the importance of synthetic a priori judgments in Kant's account of knowledge. Their existence, we have seen, exposes the shortcomings of both rationalism, which allowed only for analytic a priori judgments, and empiricism, which allowed only of synthetic a posteriori judgments. Both these theories tended to regard knowledge as an analysis or description of what was present to the mind, and differed really only in their view of what was present. For, though the empiricist thought of empirical knowledge as synthesis, the synthesis was not ascribed to the mind, but to associating ideas; the mind only observed, and knowledge was merely the apprehension of objects by the senses. We see what is before our eyes, and notice the differences and similarities in what is before us. The rationalist conceived of thought as simply apprehending the nature of the real, freed from the illusions of sense perception. The mathematician has before his thought the nature of a triangle, and sees intellectually what that nature implies. We may try to mediate between the two by saying that while all knowing is observing, some is observing of objects of thought and some of objects of sense, the one being called understanding, the other perception. In most scientific judgments, however, we are not simply observing objects either of thought or of sense. Scientific judgments are more than descriptions of what is present to the mind or to the senses; they are essentially anticipations. They go beyond what is immediately given. This is shown by the fact that it is the characteristic of a scientific proposition that it can be verified. If we understand it rightly, we see that it implies that, under such-and-such conditions, such-and-such things will be experienced. Hence the importance of experiment to science. A scientific proposition is, of course, grounded on observation of perceived fact and understanding of universal connection, but it is an assertion of something beyond that.

If, then, all scientific judgments are synthetic, and if both rationalism and empiricism failed to account for the manner in which such judgments go beyond what is immediately given to the mind, ought we not to say that the real problem for Kant is to show not merely how synthetic a priori judgments are possible, but how any synthetic judgments are possible? This seems at first sight plausible, but the suggestion must be rejected; for, when Kant asks how a judgment is possible, he is not asking how we come to make it, but how we know that it is valid. Now, if we consider any empirical judgment about the facts of nature, we must recognise that Locke and Hume were right in denying certainty to such judgments. In all general statements about concrete facts we to a certain extent go beyond our evidence. Empirical scientific statements are not theoretically certain. They may, of course, be certain enough for all practical purposes. They are reasonable expectations of what will happen, but reasonable expectation is a very different thing from the certainty of mathematical insight.

Now Kant maintained that, while such empirical judgments are not certain, they all imply the certainty of a number of general principles on which they depend. These general principles are the synthetic a priori judgments with which he is especially concerned. When we apply the principles of trigonometry to an engineering problem, we know that our measurements are only approximate, and that the result also will only be approximate; but the possibility of arriving at such approximate results depends on the absolute truth of the trigonometrical principles, and on the assumption that they express not simply the agreement or disagreement of ideas, but hold of the real. When we apply the rules of arithmetic to counting objects, there may be a certain arbitrariness in deciding on our unit. There is no such arbitrariness in the rule. All scientific judgments of causation are only approximately certain, but they all imply the certainty of the principle of causation, and are based on the assumption that such a principle is of universal application. This and the other principles assumed in our empirical judgments are, then, the synthetic judgments with which Kant is concerned. Now, it is of the nature of our empirical knowledge that it is fragmentary and not uniform, that we are concerned with an indefinite number of things whose connections we do not wholly understand, and which we cannot therefore anticipate. Yet we assume that all these objects will obey the rules of arithmetic and geometry, and will all be subject in their changes to the principle of causation. On such assumptions all the sciences of applied mathematics depend. How are they justifiable? That is Kant's question.

Kant, when he considers mathematics, is concerned with the assumptions of applied mathematics, of those sciences which, though mathematical, make statements about existing objects, and in which the old distinction between understanding and perception which was based on the difference in the objects of these two faculties breaks down. The sciences which Kant is investigating imply that principles which are clearly not derived from mere observation are yet the basis on which we order and arrange what we observe. Now, if we held that the objects of mathematics were independent entities quite separate from the things we perceive, it would be impossible to explain how we might assume that the things we perceive would be subject to the rules of mathematics. If, on the other hand, we held that in mathematics we were simply concerned with the various objects of the senses, it would be impossible to explain how mathematics can have a generality and necessity which no statements can have which rest on observation of the various things we see. The existence of applied mathematics implies firstly that understanding and perception are distinct, and that neither of them can be reduced to the other, for that would mean that we should have to give up either the element of observation and experiment or the element of necessity and a priority, and secondly, that understanding and perception are combined, and must be combined for any advance in science.