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6. Mathematics / C. Sources of Mathematics / 9. Fictional Mathematics

[mathematics is purely invented, and is not true]

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