Up to this point Kant would have carried the whole Cartesian school, and, more generally, all the modern Platonists, along with him; while he would have given the English empiricists and their French disciples a rather hard nut to crack. For they would have had to choose between admitting that mathematics was a mass of identical propositions or explaining, in the face of Hume's criticism, what claims to absolute certainty its truths, any more than the Law of Causation, possess. Now, the great philosophical genius of Kant is shown by nothing more than by this, that he did not stop here. Recognising to the same extent as Locke and Hume that all knowledge comes from experience—at any rate, in the sense of not coming by supernatural communication, as Malebranche and Berkeley thought—he puts the famous question, How are synthetic judgments à priori possible? Or, as it might be paradoxically expressed, How come we to know with the most certainty the things that we have not been taught by experience? The answer is, that we know them by the most intimate experience of all—the underlying consciousness that we have made them what they are. Our minds are no mere passive recipients, in which a mass of sensations, poured in from some external
source, are then arranged after an order equally originated from without; there is a principle of spontaneity in our own subjectivity by which the objective order of nature is created. What Kant calls the Matter of knowledge is given from without, the Form from within. And this process begins with the imposition of the two great fundamental Forms, Space and Time, on the raw material of sensation by our minds.
By space and time Kant does not mean the abstract ideas of coexistence and succession; nor does he call them, as some critics used incorrectly to suppose, forms of thought, but forms of intuition. We do not build them up with the help of muscular or other feelings, but are conscious of them in a way not admitting of any further analysis. The parts of space, no doubt, are coexistent, but they are also connected and continuous; more than this, positions in space do not admit of mutual substitution; the right hand and left hand glove are perfectly symmetrical, but the one cannot be superimposed on the other. Besides, all particular spaces are contained in universal space, not as particular conceptions are contained in a general conception, but as parts of that which extends to infinity, and where each has an individual place of its own, repeating all the characters of space in general except its illimitable extension. And the same is true of time, with this further distinction from abstract succession, that succession may be reversed; whereas the order of past, present, and future is irreversibly maintained.
The contemporary school of Reid in Scotland, and the subsequent Eclectic school of Victor Cousin in France, would agree with Kant in maintaining that sensuous experience will not account for our knowledge of space and time. But they would protest, in the name
of common sense, against the reduction of these apparently fundamental elements to purely subjective forms. They would ask, with the German critic Trendelenburg, Why cannot space and time be known intuitively and yet really exist? Kant furnishes no direct answer to the question, but he has suggested one in another connection. Mathematical truth is concerned with spatial and temporal relations, and for that truth to be above suspicion and exception we must assume that the objects with which it deals are wholly within our grasp—that our knowledge of them is exhaustive. But there could be no such assurance on the supposition that, besides the space and time of our sensuous experience, another space and time existed independently of our consciousness as attributes of things in themselves—possibly differing in important respects from ours—as, for example, a finite, or a non-continuous, or a four-dimensional space, and a time with a circular instead of a progressive movement.
This easy assumption that reality accommodates itself to our intellectual convenience, instead of our being obliged to accommodate our theories of knowledge to reality, runs through and vitiates the whole of Kant's philosophy. But, taking the narrower ground of logical consistency, one hardly sees how his principles can hold together. We are told that the subjectivity of space and time is not presented as a plausible hypothesis, but as a certain and indubitable truth, for in no other way can mathematical certainty be explained. The claim is questionable, but let it be granted. Immediately a fresh difficulty starts up. What is the source of our certainty that space and time are subjective forms of intuition? If the answer is, because that assumption guarantees the certainty of mathematics, then Kant is
reasoning in a circle. If he appeals—as in consistency he ought—to another order of subjectivity as the sanction of his first transcendental argument, such reasoning involves the regress to infinity.
Again, on Kant's theory, time is the form of intuition for the inner sense. So when we become conscious of mental events we know them only as phenomena; we remain ignorant of what mind is in itself. But before the publication in 1770 of Kant's inaugural dissertation on The Sensible and the Intelligible World every one, plain men and philosophers alike, believed that the consciousness of our successive thoughts and feelings was the very type of reality itself; and they held this belief with a higher degree of assurance than that given to the axioms of geometry. By what right, then, are we asked to give up the greater for the less, to surrender our self-assurance as a ransom for Euclid's Elements or even for Newton's Principia?
Once more, surely mathematics is concerned not with space and time as such, but with their artificial delimitations as points, lines, figures, numbers, moments, etc. And it may be granted that these are purely subjective in the sense of being imposed by our imagination (with the aid of sensible signs) on the external world. What if this subjectivity were the true source of that peculiar certainty belonging to synthetic judgments à priori? True, Kant counts in our judgments about the infinity and eternity of space and time with other accepted characteristics of theirs as intuitive certainties. But there are thinkers who find the negation of such properties not inconceivable, so that they cannot be adduced as evidence of a priority, still less of subjectivity.
Eleven years after the inaugural dissertation Kant