more from Bernard Bolzano

Single Idea 9830

[catalogued under 6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics]

Full Idea

Bolzano began the process of eliminating intuition from analysis, by proving something apparently obvious (that as continuous function must be zero at some point). Proof reveals on what a theorem rests, and that it is not intuition.

Gist of Idea

Bolzano began the elimination of intuition, by proving something which seemed obvious


report of Bernard Bolzano (Theory of Science (Wissenschaftslehre, 4 vols) [1837]) by Michael Dummett - Frege philosophy of mathematics Ch.6

Book Reference

Dummett,Michael: 'Frege: philosophy of mathematics' [Duckworth 1991], p.67

A Reaction

Kant was the target of Bolzano's attack. Two responses might be to say that many other basic ideas are intuited but impossible to prove, or to say that proof itself depends on intuition, if you dig deep enough.