So much being admitted, we have to recognise a fundamental division of judgments into two classes, analytic and synthetic. Judgments in which the predicate adds nothing to the subject are analytic. When we affirm all matter to be extended, that is an instance of the former, for here we are only making more explicit what was already contained in the notion of matter. On the other hand, when we affirm that all matter is heavy, that is an {89} instance of the latter or synthetic class, for we can think of matter without thinking that it has weight. Furthermore, this is not only a synthetic judgment, but it is a synthetic judgment _à posteriori_; for the law of universal gravitation is known only by experience. But there are also synthetic judgments _à priori_; for, as we have just seen, the fundamental truths of arithmetic and geometry belong to this class, as do also by consequence all the propositions logically deduced from these--that is to say, the whole of mathematical science. 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 {90} 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.