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Single Idea 18159

[filed under theme 6. Mathematics / C. Sources of Mathematics / 9. Fictional Mathematics ]

Full Idea

In its higher reaches, which posit sets of huge cardinalities, set theory is just a fairy story.

Gist of Idea

Higher cardinalities in sets are just fairy stories

Source

David Bostock (Philosophy of Mathematics [2009], 9.5.iii)

Book Ref

Bostock,David: 'Philosophy of Mathematics: An Introduction' [Wiley-Blackwell 2009], p.303


A Reaction

You can't say the higher reaches are fairy stories but the lower reaches aren't, if the higher is directly derived from the lower. The empty set and the singleton are fairy stories too. Bostock says the axiom of infinity triggers the fairy stories.