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

Philosophia Mathematica 5 (3):193-209 (1997)
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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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Jody Azzouni
Tufts University

Citations of this work

There is No Easy Road to Nominalism.M. Colyvan - 2010 - Mind 119 (474):285-306.
Abstract objects.Gideon Rosen - 2008 - Stanford Encyclopedia of Philosophy.
Can the Eleatic Principle be Justified?Mark Colyvan - 1998 - Canadian Journal of Philosophy 28 (3):313-335.
Believing in things.Zoltán Gendler Szabó - 2003 - Philosophy and Phenomenological Research 66 (3):584–611.

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References found in this work

Representing and Intervening.Ian Hacking - 1983 - British Journal for the Philosophy of Science 35 (4):381-390.
Representing and Intervening.Ian Hacking - 1987 - Revue de Métaphysique et de Morale 92 (2):279-279.
Indispensability and Practice.Penelope Maddy - 1992 - Journal of Philosophy 89 (6):275.
Mathematics and indispensability.Elliott Sober - 1993 - Philosophical Review 102 (1):35-57.

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