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Full Idea
Quantification over mathematical entities is indispensable for science..., therefore we should accept such quantification; but this commits us to accepting the existence of the mathematical entities in question.
Gist of Idea
We must quantify over numbers for science; but that commits us to their existence
Source
Hilary Putnam (The Philosophy of Logic [1971], p.57), quoted by Stephen Yablo - Apriority and Existence
Book Ref
'New Essays on the A Priori', ed/tr. Boghossian,P /Peacocke,C [OUP 2000], p.197
A Reaction
I'm not surprised that Hartry Field launched his Fictionalist view of mathematics in response to such a counterintuitive claim. I take it we use numbers to slice up reality the way we use latitude to slice up the globe. No commitment to lines!
18199 | Indispensability strongly supports predicative sets, and somewhat supports impredicative sets [Putnam] |
18200 | Very large sets should be studied in an 'if-then' spirit [Putnam] |
8857 | We must quantify over numbers for science; but that commits us to their existence [Putnam] |