more from Bernard Bolzano

### Single Idea 9185

#### [catalogued under 12. Knowledge Sources / E. Direct Knowledge / 2. Intuition]

Full Idea

Bolzano was determined to expel Kantian intuition from analysis, and to prove from first principles anything that could be proved, no matter how obvious it might seem when thought of in geometrical terms.

Clarification

'Analysis', in mathematics, is the theory of real numbers

Gist of Idea

Bolzano wanted to avoid Kantian intuitions, and prove everything that could be proved

Source

report of Bernard Bolzano (Theory of Science (Wissenschaftslehre, 4 vols) [1837]) by Michael Dummett - The Philosophy of Mathematics 2.3

Book Reference

'Philosophy 2: further through the subject', ed/tr. Grayling,A.C. [OUP 1998], p.129

A Reaction

This is characteristic of the Enlightenment Project, well after the Enlightenment. It is a step towards Frege's attack on 'psychologism' in mathematics. The problem is that it led us into a spurious platonism. We live in troubled times.