Mathematical Fictionalism
Mathematics can function as a useful fiction without its apparent objects literally existing.
What it claims
Mathematical fictionalism can read mathematical discourse literally as apparently quantifying over numbers while denying that such objects exist. The relevant existential claims are then not literally true, even though claims can be true within the mathematical fiction. It challenges the indispensability argument's inference from scientific success to mathematical ontology.
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Key thinkers
Hartry Field · Stephen Yablo · Mary Leng · Mark Balaguer