Abstract

The Ideal Nature of Mathematics In the form of images of the world, cartesian mathematics functions unconditionally. Every real number is a complex one. This applies to rationals and irrationals in mathematics. Mathematics takes authority from within itself, not from the world. Thus, it can make no claims on the world and its reality. Benacerraf makes good use of this as he encounters the problem not only of mathematics but of science in general. If we make a compromise between epistemology and semantics in the realm of mathematics, we shall only blur its ideal nature; we do not know what triggers it. Rayo responds to this challenge by admitting that semantics certainly cannot trespass such limits, whereas Linnebo reluctantly accepts the compromise as a possibility for safeguarding the ideal.