Nov 26, 2012
Hilbert's Program 1_Documented by Marsigit
Hilbert had an anti-Kantian reaction now called formalism. The program is implemented in two steps:
1) Divide all of the mathematical sciences into two broad classes: The real part (or conceptual part) of mathematics and the ideal part of mathematics. The real part included only the parts of mathematics which don't take us into the infinitary realm. It involved no ontological or epistemological questions. Logic, and number theory are part of real mathematics. The ideal part of mathematics included everything else-- all the parts of mathematics that would have been discarded without Hilbert's second motive. This includes geometry, set theory, and analysis. Hilbert had the basic idea that any branch of mathematics can be formalized (meaning it can be expressed in a formal language and can be axiomatized to give a formal system.