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Single Idea 17935

[from 'Introduction to the Philosophy of Mathematics' by Mark Colyvan, in 14. Science / D. Explanation / 2. Types of Explanation / m. Explanation by proof ]

Full Idea

It might be argued that any proof by induction is revealing the explanation of the theorem, namely, that it holds by virtue of the structure of the natural numbers.

Gist of Idea

If inductive proofs hold because of the structure of natural numbers, they may explain theorems

Source

Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 5.2.1)

Book Reference

Colyvan,Mark: 'An Introduction to the Philosophy of Mathematics' [CUP 2012], p.82


A Reaction

This is because induction characterises the natural numbers, in the Peano Axioms.