more from Stewart Shapiro

### Single Idea 8753

#### [catalogued under 6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism]

Full Idea

Critics commonly complain that the intuitionist restrictions cripple the mathematician. On the other hand, intuitionist mathematics allows for many potentially important distinctions not available in classical mathematics, and is often more subtle.

Gist of Idea

Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions

Source

Stewart Shapiro (Thinking About Mathematics [2000], 7.1)

Book Reference

Shapiro,Stewart: 'Thinking About Mathematics' [OUP 2000], p.174

A Reaction

The main way in which it cripples is its restriction on talk of infinity ('Cantor's heaven'), which was resented by Hilbert. Since high-level infinities are interesting, it would be odd if we were not allowed to discuss them.