more from Immanuel Kant

Single Idea 8737

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers]

Full Idea

Kant suggested that arithmetic has no axioms.

Gist of Idea

Kant suggested that arithmetic has no axioms


report of Immanuel Kant (Critique of Pure Reason [1781], B204-6/A164) by Stewart Shapiro - Thinking About Mathematics 4.2

Book Reference

Shapiro,Stewart: 'Thinking About Mathematics' [OUP 2000], p.87

A Reaction

A hundred years later a queue was forming to spell out the axioms of arithmetic. The definitions of 0 and 1 always look to me more like logicians' tricks than profound truths. Some notions of successor and induction do, however, seem needed.