Single Idea 9887

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

Full Idea

Frege's three main objections to radical formalism are that it cannot account for the application of mathematics, that it confuses a formal theory with its metatheory, and it cannot explain an infinite sequence.

Gist of Idea

Formalism misunderstands applications, metatheory, and infinity

Source

report of Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §86-137) by Michael Dummett - Frege philosophy of mathematics

Book Reference

Dummett,Michael: 'Frege: philosophy of mathematics' [Duckworth 1991], p.252


A Reaction

The application is because we don't design maths randomly, but to be useful. The third objection might be dealt with by potential infinities (from formal rules). The second objection sounds promising.

Related Idea

Idea 6425 Formalism can't apply numbers to reality, so it is an evasion [Russell]