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Full Idea
The fictionalist can say that the sense in which '2+2=4' is true is pretty much the same as the sense in which 'Oliver Twist lived in London' is true. They are true 'according to a well-known story', or 'according to standard mathematics'.
Gist of Idea
Fictionalists say 2+2=4 is true in the way that 'Oliver Twist lived in London' is true
Source
Hartry Field (Realism, Mathematics and Modality [1989], 1.1.1), quoted by Michèle Friend - Introducing the Philosophy of Mathematics 6.3
Book Ref
Field,Hartry: 'Realism, Mathematics and Modality' [Blackwell 1989], p.3
A Reaction
The roots of this idea are in Carnap. Fictionalism strikes me as brilliant, but poisonous in large doses. Novels can aspire to artistic truth, or to documentary truth. We invent a fiction, and nudge it slowly towards reality.
| 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] |