It is here that Kant takes issue with Hume.  A survey of our knowledge makes clear, he thinks, that we are in the possession of a great deal of information that is not of the unsatisfactory kind that, according to Hume, all our knowledge of things must be.  There, for example, are all the truths of mathematics.  When we enunciate a truth regarding the relations of the lines and angles of a triangle, we are not merely unfolding in the predicate of our proposition what was implicitly contained in the subject.  There are propositions that do no more than this; they are analytical, i.e. they merely analyze the subject.  Thus, when we say:  Man is a rational animal, we may merely be defining the word “man”—­unpacking it, so to speak.  But a synthetic judgment is one in which the predicate is not contained in the subject; it adds to one’s information.  The mathematical truths are of this character.  So also is the truth that everything that happens must have a cause.

Do we connect things with one another in this way merely because we have had experience that they are thus connected?  Is it because they are given to us connected in this way?  That cannot be the case, Kant argues, for what is taken up as mere experienced act cannot be known as universally and necessarily true.  We perceive that these things must be so connected.  How shall we explain this necessity?

We can only explain it, said Kant, in this way:  We must assume that what is given us from without is merely the raw material of sensation, the matter of our experience; and that the ordering of this matter, the arranging it into a world of phenomena, the furnishing of form, is the work of the mind.  Thus, we must think of space, time, causality, and of all other relations which obtain between the elements of our experience, as due to the nature of the mind.  It perceives the world of phenomena that it does, because it constructs that world.  Its knowledge of things is stable and dependable because it cannot know any phenomenon which does not conform to its laws.  The water poured into a cup must take the shape of the cup; and the raw materials poured into a mind must take the form of an orderly world, spread out in space and time.

Kant thought that with this turn he had placed human knowledge upon a satisfactory basis, and had, at the same time, indicated the limitations of human knowledge.  If the world we perceive is a world which we make; if the forms of thought furnished by the mind have no other function than the ordering of the materials furnished by sense; then what can we say of that which may be beyond phenomena?  What of noumena?

It seems clear that, on Kant’s principles, we ought not to be able to say anything whatever of noumena.  To say that such may exist appears absurd.  All conceivable connection between them and existing things as we know them is cut off.  We cannot think of a noumenon as a substance, for the notions of substance and quality have been declared to be only a scheme for the ordering of phenomena.  Nor can we think of one as a cause of the sensations that we unite into a world, for just the same reason.  We are shut up logically to the world of phenomena, and that world of phenomena is, after all, the successor of the world of ideas advocated by Berkeley.