### Single Idea 13509

#### [catalogued under 6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite]

Full Idea

Mathematical induction is a way to establish truths about the infinity of natural numbers by a finite proof.

Gist of Idea

We can establish truths about infinite numbers by means of induction

Source

William D. Hart (The Evolution of Logic [2010], 5)

Book Reference

Hart,W.D.: 'The Evolution of Logic' [CUP 2010], p.144

A Reaction

If there are truths about infinities, it is very tempting to infer that the infinities must therefore 'exist'. A nice, and large, question in philosophy is whether there can be truths without corresponding implications of existence.