more from Bernard Bolzano

### Single Idea 9618

#### [catalogued under 6. Mathematics / A. Nature of Mathematics / 2. Geometry]

Full Idea

Bolzano if the father of 'arithmetization', which sought to found all of analysis on the concepts of arithmetic and to eliminate geometrical notions entirely (with logicism taking it a step further, by reducing arithmetic to logic).

Gist of Idea

Bolzano wanted to reduce all of geometry to arithmetic

Source

report of Bernard Bolzano (Theory of Science (Wissenschaftslehre, 4 vols) [1837]) by James Robert Brown - Philosophy of Mathematics Ch. 3

Book Reference

Brown,James Robert: 'Philosophy of Mathematics' [Routledge 2002], p.28

A Reaction

Brown's book is a defence of geometrical diagrams against Bolzano's approach. Bolzano sounds like the modern heir of Pythagoras, if he thinks that space is essentially numerical.