more from Stewart Shapiro

Single Idea 8752

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

Full Idea

The Deductivist version of formalism (sometimes called 'if-thenism') says that the practice of mathematics consists of determining logical consequences of otherwise uninterpreted axioms.

Gist of Idea

Deductivism says mathematics is logical consequences of uninterpreted axioms


Stewart Shapiro (Thinking About Mathematics [2000], 6.2)

Book Reference

Shapiro,Stewart: 'Thinking About Mathematics' [OUP 2000], p.149

A Reaction

[Hilbert is the source] More plausible than Term or Game Formalism (qv). It still leaves the question of why it seems applicable to nature, and why those particular axioms might be chosen. In some sense, though, it is obviously right.

Related Ideas

Idea 8749 Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro]

Idea 8750 Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro]

Idea 10061 The If-thenist view only seems to work for the axiomatised portions of mathematics [Musgrave]