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Single Idea 10236

[from 'Philosophy of Mathematics' by Stewart Shapiro, in 6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics ]

Full Idea

We cannot ground mathematics in any domain or theory that is more secure than mathematics itself.

Gist of Idea

There is no grounding for mathematics that is more secure than mathematics

Source

Stewart Shapiro (Philosophy of Mathematics [1997], 4.8)

Book Reference

Shapiro,Stewart: 'Philosophy of Mathematics:structure and ontology' [OUP 1997], p.135


A Reaction

This pronouncement comes after a hundred years of hard work, notably by Gödel, so we'd better believe it. It might explain why Putnam rejects the idea that mathematics needs 'foundations'. Personally I'm prepare to found it in countable objects.