Thence Socrates goes on to characterise intellectual cognition. What is it after all, to cognise? Undoubtedly we arrive at it by forming judgments. I form a judgment about some object; for instance, I say to myself, what is in front of me is a tree. How do I arrive at saying that? I can only do it if I already know what a tree is. I must remember my conception of a tree. A tree is a physical object. If I remember a tree, I therefore remember a physical object. I say of something that it is a tree, if it resembles other things which I have previously observed and which I know to be trees. Memory is the medium for this knowledge. It makes it possible for me to compare the various objects of sense. But this does not exhaust my knowledge. If I see two similar things, I form a judgment and say, these things are alike. Now, in reality, two things are never exactly alike. I can only find a likeness in certain respects. The idea of a perfect similarity therefore arises within me without having its correspondence in reality. And this idea helps me to form a judgment, as memory helps me to a judgment and to knowledge. Just as one tree reminds me of others, so am I reminded of the idea of similarity by looking at two things from a certain point of view. Thoughts and memories therefore arise within me which are not due to physical reality. All kinds of knowledge not borrowed from sense-reality are grounded on such thoughts. The whole of mathematics consists of them. He would be a bad geometrician who could only bring into mathematical relations what he can see with his eyes and touch with his hands. Thus we have thoughts which do not originate in perishable nature, but arise out of the spirit. And it is these that bear in them the mark of eternal truth. What mathematics teach will be eternally true, even if to-morrow the whole cosmic system should fall into ruins and an entirely new one arise. Conditions might prevail in another cosmic system, to which our present mathematical truths would not be applicable, but these would be none the less true in themselves.