The Indispensability of Mathematics
The Quine-Putnam indispensability argument in the philosophy of mathematics urges us to place mathematical entities on the same ontological footing as other theoretical entities essential to our best scientific theories. Recently, the argument has come under serious scrutiny, with many influential philosophers unconvinced of its cogency. This book not only outlines the indispensability argument in considerable detail but also defends it against various challenges.
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abstract accept account of mathematics appeal argue Armstrong axioms Azzouni Balaguer believe Benacerraf best explanation best scientific theories causal contact causal criterion causal explanation causally active entities causally idle chapter Cheyne and Pigden claim complex numbers confirmational holism consider contingent continuity thesis continuum mathematics contrastive empiricism depend discussion dispensable Eleatic Principle empirical science entity in question epistemic equation example existence fact false Field’s program Hale and Wright Hartry Field hypotheses indispensabilist indispensability argument indispensability theory latter least Maddy Maddy's Maddy’s mathematical entities mathematical objects mathematical realism mathematical theory Michael Resnik natural numbers Newtonian nominalistic non-causal ontological commitments Penelope Maddy philosophies of mathematics philosophy physical theories Platonism Platonist position posteriori predictions priori problem Quine Quine's Quine/Putnam indispensability argument Quinean naturalism reason relevant Resnik role scientists seems semantic semantic holism set theory Sober space-time special relativity suggests theorem theoretical entities thesis true truth