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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.
| 4533 | Logic and maths refer to fictitious entities which we have created [Nietzsche] |
| 6104 | Numbers are classes of classes, and hence fictions of fictions [Russell] |
| 18159 | Higher cardinalities in sets are just fairy stories [Bostock] |
| 18155 | A fairy tale may give predictions, but only a true theory can give explanations [Bostock] |
| 8714 | Fictionalists say 2+2=4 is true in the way that 'Oliver Twist lived in London' is true [Field,H] |
| 18214 | Mathematics is only empirical as regards which theory is useful [Field,H] |
| 18216 | Abstractions can form useful counterparts to concrete statements [Field,H] |
| 18210 | Why regard standard mathematics as truths, rather than as interesting fictions? [Field,H] |
| 10579 | Putting numbers in quantifiable position (rather than many quantifiers) makes expression easier [Yablo] |
| 8862 | Platonic objects are really created as existential metaphors [Yablo] |
| 22298 | Why is fictional arithmetic applicable to the real world? [Potter] |