Applied mathematics, existential commitment and the Quine-Putnam indispensability thesis

Philosophia Mathematica 5 (3):193-209 (1997)
Abstract
The ramifications are explored of taking physical theories to commit their advocates only to ‘physically real’ entities, where ‘physically real’ means ‘causally efficacious’ (e.g., actual particles moving through space, such as dust motes), the ‘physically significant’ (e.g., centers of mass), and the merely mathematical—despite the fact that, in ordinary physical theory, all three sorts of posits are quantified over. It's argued that when such theories are regimented, existential quantification, even when interpreted ‘objectually’ (that is, in terms of satisfaction via variables, rather than by substitution-instances) need not imply any ontological commitments.
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Zoltán Gendler Szabó (2003). Believing in Things. Philosophy and Phenomenological Research 66 (3):584–611.
Jody Azzouni (2009). Empty de Re Attitudes About Numbers. Philosophia Mathematica 17 (2):163-188.
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