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Full Idea
A common view is that although a fairy tale may provide very useful predictions, it cannot provide explanations for why things happen as they do. In order to do that a theory must also be true (or, at least, an approximation to the truth).
Gist of Idea
A fairy tale may give predictions, but only a true theory can give explanations
Source
David Bostock (Philosophy of Mathematics [2009], 9.B.5)
Book Ref
Bostock,David: 'Philosophy of Mathematics: An Introduction' [Wiley-Blackwell 2009], p.290
A Reaction
Of course, fictionalism offers an explanation of mathematics as a whole, but not of the details (except as the implications of the initial fictional assumptions).
| 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] |