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Full Idea
Fictionalists struggle to explain why arithmetic is applicable to the real world in a way that other stories are not.
Gist of Idea
Why is fictional arithmetic applicable to the real world?
Source
Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 21 'Math')
Book Ref
Potter,Michael: 'The Rise of Anaytic Philosophy 1879-1930' [Routledge 2020], p.143
A Reaction
We know why some novels are realistic and others just the opposite. If a novel aimed to 'model' the real world it would be even closer to it. Fictionalists must explain why some fictions are useful.
| 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] |