more from Gottlob Frege

Single Idea 9631

[catalogued under 6. Mathematics / C. Sources of Mathematics / 7. Formalism]

Full Idea

Early formalism (Thomae etc) was crushed by Frege: first, mathematics must be about classes of symbols (abstract types), not the symbols themselves (the tokens); second, games may be meaningless, but meta-games are not.

Gist of Idea

Formalism fails to recognise types of symbols, and also meta-games

Source

report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by James Robert Brown - Philosophy of Mathematics Ch.5

Book Reference

Brown,James Robert: 'Philosophy of Mathematics' [Routledge 2002], p.64


A Reaction

Brown goes on to show how Hilbert revived the formalist project. A really austere formalist view of mathematics clearly seems to be missing something basic, either in physical nature, or in the world of ideas.