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]