more from Michèle Friend

Single Idea 8716

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

Full Idea

There are not enough constraints in the Formalist view of mathematics, so there is no way to select a direction for trying to develop mathematics. There is no part of mathematics that is more important than another.

Gist of Idea

Formalism is unconstrained, so cannot indicate importance, or directions for research


Michèle Friend (Introducing the Philosophy of Mathematics [2007], 6.6)

Book Reference

Friend,Michèle: 'Introducing the Philosophy of Mathematics' [Acumen 2007], p.149

A Reaction

One might reply that an area of maths could be 'important' if lots of other areas depended on it, and big developments would ripple big changes through the interior of the subject. Formalism does, though, seem to reduce maths to a game.