Abstract
The Quine-Putnam indispensability argument urges us to place mathematical entities on the same ontological footing as (other) theoretical entities of empirical science. Recently this argument has attracted much criticism, and in this paper I address one criticism due to Elliott Sober. Sober argues that mathematical theories cannot share the empirical support accrued by our best scientific theories, since mathematical propositions are not being tested in the same way as the clearly empirical propositions of science. In this paper I defend the Quine-Putnam argument against Sober's objections.
Similar content being viewed by others
REFERENCES
Colyvan, M.: forthcoming, ‘Confirmation Theory and Indispensability’, Philosophical Studies.
Field, H.: 1980, Science Without Numbers, Blackwell, Oxford.
Hellman, G.: 1992, ‘The Boxer and His Fists: The Constructivist in the Arena of Quantum Physics’, Proceedings of the Aristotelian Society, Supplement LXVI, 61-77.
Hellman, G.: forthcoming, ‘Some Ins and Outs of Indispensability: A Modal-Structural Perspective’, in A. Cantini, E. Casari and P. Minari (eds.), Logic in Florence, Kluwer, Dordrecht.
Maddy, P.: 1992, ‘Indispensability and Practice’, Journal of Philosophy 89, 275-289.
Maddy, P.: 1995, ‘Naturalism and Ontology’, Philosophia Mathematica (3), 3, 248-270.
Musgrave, A.: 1986, ‘Arithmetical Platonism: Is Wright Wrong or Must Field Yield?’, in M. Fricke (ed.), Essays in Honour of Bob Durrant, Otago University Philosophy Department, Dunedin, N.Z., 90-110.
Parsons, C.: 1996, ‘Mathematical Intuition’, reprinted in W. D. Hart (ed.), The Philosophy of Mathematics, Oxford University Press, Oxford, pp. 95–113.
Putnam, H.: 1979, ‘Philosophy of Logic’, reprinted in Mathematics Matter and Method: Philosophical Papers Vol. I, second edition, Cambridge University Press, Cambridge, pp. 323–357.
Quine, W. V.: 1980, ‘On What There Is’, reprinted in From a Logical Point of View, second edition, Harvard University Press, Cambridge, MA, 1–19.
Quine, W. V.: 1992, The Pursuit of Truth, revised edition, Harvard University Press, Cambridge, MA.
Resnik, M.: 1997, Mathematics as a Science of Patterns, Clarendon Press, Oxford.
Roseveare, N. T.: 1983, Mercury's Perihelion from Le Verrier to Einstein, Clarendon Press, Oxford.
Sober, E.: 1993, ‘Mathematics and Indispensability’, Philosophical Review 102, 35-57.
van Fraassen, B.: 1980, The Scientific Image, Clarendon Press, Oxford.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Colyvan, M. Contrastive Empiricism and Indispensability. Erkenntnis 51, 323–332 (1999). https://doi.org/10.1023/A:1005427803093
Issue Date:
DOI: https://doi.org/10.1023/A:1005427803093