Let us consider some examples of this. The science of geometry deals with the laws of space. But it takes {4} space just as it finds it in common experience. It takes space for granted. No geometrician asks what space is. This, then, will be a problem for philosophy. Moreover, geometry is founded upon certain fundamental propositions which, it asserts, being self-evident, require no investigation. These are called "axioms." That two straight lines cannot enclose a space, and that equals being added to equals the results are equal, are common examples. Into the ground of these axioms the geometrician does not enquire. That is the business of philosophy. Not that philosophers affect to doubt the truth of these axioms. But surely it is a very strange thing, and a fact quite worthy of study, that there are some statements of which we feel that we must give the most laborious proofs, and others in the case of which we feel no such necessity. How is it that some propositions can be self-evident and others must be proved? What is the ground of this distinction? And when one comes to think of it, it is a very extraordinary property of mind that it should be able to make the most universal and unconditional statements about things, without a jot of evidence or proof. When we say that two straight lines cannot enclose a space, we do not mean merely that this has been found true in regard to all the particular pairs of straight lines with which we have tried the experiment. We mean that it never can be and never has been otherwise. We mean that a million million years ago two straight lines did not enclose a space, and that it will be the same a million million years hence, and that it is just as true on those stars, if there are any, which are invisible even to the greatest telescopes. But we have no experience of what will {5} happen a million million years hence, or of what can take place among those remote stars. And yet we assert, with absolute confidence, that our axiom is and must be equally true everywhere and at all times. Moreover, we do not found this on probabilities gathered from experience. Nobody would make experiments or use telescopes to prove such axioms. How is it that they are thus self-evident, that the mind can make these definite and far-reaching assertions without any evidence at all? Geometricians do not consider these questions. They take the facts for granted. To solve these problems is for philosophy.