Mathematics & the Nature of Reality
Mathematical Fictionalism
Agrees with skeptics that abstract mathematical objects like numbers don’t literally exist, but holds mathematics is still worth using — the way a novel’s characters don’t exist but the story is still worth telling — because it is a useful, convenient fiction rather than a body of literal truths.
Proponents
Hartry Field
Evidence For
Sidesteps Benacerraf's epistemological problem entirely by denying there are any abstract objects out there to have mysterious knowledge of in the first place; Field attempted to show physics itself could in principle be reformulated without quantifying over numbers.
Evidence Against
The project of fully 'nominalizing' — rewriting — all of physics without any reference to numbers has never been completed for anything beyond toy examples, and doesn't explain why the useful fiction happens to be so reliably predictive.
Transmissions
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