To FOM or not to FOM, that is the question

(FOM is the ongoing exchange of electronic letters about foundations and philosophy of mathematics which is owned by Stephen G. Simpson, simpson@math.psu.edu). Untill about 1914 many outstanding mathematicians (Cantor, Hilbert, Poincare, Zermelo and others) wrote about the philosophy of mathematics. Later few wrote about it and the spirit of rationalism of the XIX-th Century seems to have been almost dislodged by mysticism; viz. the philosophical positions of Godel, Kreisel and many other philosophers of mathematics and philosophers of language. The purpose of this communication is to recall that the work of Skolem and Hilbert has definitely removed the need for any mystical (Platonic) assumptions in the ontology of mathematics. (This will constitute an answer to a number of letters which have appeared in FOM.) I will also argue that rationalists should resist being saddled with the term formalism and some other names used by their opponents since those names suggest a distorted view of rationalism.