Alas, the spheres of truth are less transparent than those of illusion.

The subject for which I am asking your attention deals with the foundations of mathematics. To understand the development of the opposing theories existing in this field one must first gain a clear understnding of the concept science for it is as a part of science that mathematics originally took its place in human thought.

...an incorrect theory, even if it cannot be inhibited by any contradiction that would refute it, is none the less incorrect, just as a criminal policy is none the less criminal even if it cannot be inhibited by any court that would curb it.

Mathematics is nothing more, nothing less, than the exact part of our thinking.

Oil is seldom found where it is most needed, and seldom most needed where it is found.

Beyond the natural numbers, addition, multiplication, and mathematical induction are intuitively clear.