Full Idea
Kant suggested that arithmetic has no axioms.
Gist of Idea
Kant suggested that arithmetic has no axioms
Source
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.