Element contents
Indispensability
Published online by Cambridge University Press: 16 May 2023
Summary
Our best scientific theories explain a wide range of empirical phenomena, make accurate predictions, and are widely believed. Since many of these theories make ample use of mathematics, it is natural to see them as confirming its truth. Perhaps the use of mathematics in science even gives us reason to believe in the existence of abstract mathematical objects such as numbers and sets. These issues lie at the heart of the Indispensability Argument, to which this Element is devoted. The Element's first half traces the evolution of the Indispensability Argument from its origins in Quine and Putnam's works, taking in naturalism, confirmational holism, Field's program, and the use of idealisations in science along the way. Its second half examines the explanatory version of the Indispensability Argument, and focuses on several more recent versions of easy-road and hard-road fictionalism respectively.
- Type
- Element
- Information
- Online ISBN: 9781009099042Publisher: Cambridge University PressPrint publication: 08 June 2023
References
Azzouni, J. (1994), Metaphysical Myths, Mathematical Practice, Cambridge University Press.Google Scholar
Azzouni, J. (2000), “Stipulation, Logic, and Ontological Independence,” Philosophia Mathematica 8, 225–43.CrossRefGoogle Scholar
Baker, A. (2003), “Does the Existence of Mathematical Objects Make a Difference?” Australasian Journal of Philosophy 81, 246–4.Google Scholar
Baker, A. (2005), “Are There Genuine Mathematical Explanations of Physical Phenomena?” Mind 114, 223–8.Google Scholar
Baker, A. (2012), “Science and Mathematics: The Scope and Limits of Mathematical Fictionalism,” Book Symposium, Metascience, 21, 269–94.Google Scholar
Baker, A. (2016), “Parsimony and Inference to the Best Mathematical Explanation,” Synthese, 193, 333–50.CrossRefGoogle Scholar
Baker, A. (2017), “Mathematics and Explanatory Generality,” Philosophia Mathematica 25, 194–209.Google Scholar
Balaguer, M. (1998), Platonism and Anti-Platonism in Mathematics, Oxford University Press.Google Scholar
Bangu, S. (2012), The Applicability of Mathematics in Science: Indispensability and Ontology, Palgrave Macmillan.Google Scholar
Burgess, J. P. and Rosen, G. (1997), A Subject Without An Object, Oxford University Press.Google Scholar
Cheyne, C. (1998), “Existence Claims and Causality,” Australasian Journal of Philosophy 76, 34–47.Google Scholar
Colyvan, M. (2019), “Indispensability Arguments in the Philosophy of Mathematics,” in Zalta, E. and U. Nodelman (principal eds.) Stanford Encyclopedia of Philosophy, https://plato.stanford.edu/.Google Scholar
Craver, C. (2014), “The Ontic Conception of Explanation,” in Kaiser, M., Scholz, O. R., Plenge, D., and Huttemann, A. (eds.), Explanation in the Special Sciences, Springer, 27–52.Google Scholar
Daly, C. and Langford, S. (2009), “Mathematical Explanation and Indispensability Arguments,” Philosophical Quarterly 59, 641–58.Google Scholar
Franklin, J. (2014), An Aristotelian Realist Philosophy of Mathematics, Palgrave Macmillan.CrossRefGoogle Scholar
Goles, E., Schulz, O., and Markus, M. (2001), “Prime Number Selection of Cycles in a Predator-Prey Model,” Complexity 6, 33–8.CrossRefGoogle Scholar
Gould, S. (1977), “Of Bamboos, Cicadas, and the Economy of Adam Smith,” in Gould, S. (ed.) Ever Since Darwin: Reflections on Natural History, Norton.Google Scholar
Hellman, G. (1989), Mathematics Without Numbers: Towards a Modal-Structural Interpretation, Oxford University Press.Google Scholar
Hellman, G. and Shapiro, S. (2019), Mathematical Structuralism, Cambridge University Press.Google Scholar
Knowles, R. and Saatsi, J. (2019), “Mathematics and Explanatory Generality: Nothing but Cognitive Salience,” Erkenntnis, 86, 1119–37.Google Scholar
Leng, M. (2021), “Models, Structures, and the Explanatory Role of Mathematics in Empirical Science,” Synthese 199, 10415–40.Google Scholar
Liggins, D. (2008), “Quine, Putnam and the ‘Quine–Putnam’ Indispensability Argument,” Erkenntnis 68, 113–27.Google Scholar
Maddy, P. (1992), “Indispensability and Practice,” The Journal of Philosophy 89, 275–89.Google Scholar
Maddy, P. (forthcoming), “Reply to Paseau,” in Kennedy, J. (ed.), On the Philosophy of Penelope Maddy:Set-theoretic Foundations and Naturalistic Methodology, Springer.Google Scholar
Malament, D. (1982), “Review of Science Without Numbers,” Journal of Philosophy 79, 523–34.Google Scholar
Marcus, R. (2014), “How Not to Enhance the Indispensability Argument,” Philosophia Mathematica 22, 345–60.Google Scholar
Meyer, G. (2009), “Extending Hartry Field’s Instrumental Account of Applied Mathematics to Statistical Mechanics,” Philosophia Mathematica 17, 273–312.Google Scholar
Molinini, D. (2016), “Evidence, Explanation and Enhanced Indispensability,” Synthese 193, 403–22.Google Scholar
Morrison, J. (2010), “Just How Controversial is Evidential Holism?” Synthese 173, 335–52.Google Scholar
Paseau, A. C. (2005), “Naturalism in Mathematics and the Authority of Philosophy,” The British Journal for the Philosophy of Science 56, 399–418.CrossRefGoogle Scholar
Paseau, A. C. (2007), “Scientific Platonism,” in Leng, M., Paseau, A. C., and Potter, M. (eds.), Mathematical Knowledge, Oxford University Press, 123–49.Google Scholar
Paseau, A. C. (2012), “Practitioners First,” Book Symposium on Mathematics and Reality by Leng, Mary, Metascience 21, 282–8.Google Scholar
Paseau, A. C. (forthcoming a), “Trumping Naturalism Revisited,” in Kennedy, J. (ed.), On the Philosophy of Penelope Maddy:Set-theoretic Foundations and Naturalistic Methodology, Springer.Google Scholar
Pincock, C. (2012), Mathematics and Scientific Representation, Oxford University Press.Google Scholar
Planck, M. (1950), Scientific Autobiography and Other Papers (trans. F. Gaynor), Williams & Norgate.Google Scholar
Putnam, H. (1967), “Mathematics without Foundations,” The Journal of Philosophy 64, 5–22.Google Scholar
Putnam, H. (1971), Philosophy of Logic, Harper and Row, repr. in his Mathematics, Matter and Method: Philosophical Papers 1 (1979), Cambridge University Press, 323–57.Google Scholar
Putnam, H. (2012), Philosophy in an Age of Science, Caro, M. De and Macarthur, D. (eds.), Harvard University Press.Google Scholar
Quine, W. V. (1951), “Two Dogmas of Empiricism,” Philosophical Review 60, repr. in his Quintessence: Basic Readings from the Philosophy of W.V. Quine (2004), Gibson, R. F. Jr. (ed.), Harvard University Press, 31–53.Google Scholar
Quine, W. V. and Goodman, N. (1947), “Steps Towards a Constructive Nominalism,” Journal of Symbolic Logic 12, 105–22.Google Scholar
Resnik, M. (2005), “Quine and the Web of Belief,” in Shapiro, S. (ed.), The Oxford Handbook of Philosophy of Mathematics and Logic, Oxford University Press, 412–36.Google Scholar
Rizza, D. (2011), “Magicicada, Mathematical Explanation and Mathematical Realism,” Erkenntnis 74, 101–14.Google Scholar
Saatsi, J. (2011), “The Enhanced Indispensability Argument: Representational versus Explanatory Role of Mathematics in Science,” British Journal for the Philosophy of Science 62, 143–54.Google Scholar
Strevens, M. (2011), Depth: An Account of Scientific Explanation, Harvard University Press.Google Scholar
Tallant, J. (2013), “Optimus Prime: Paraphrasing Prime Number Talk,” Synthese 190, 2065–83.Google Scholar
Urquhart, A. (1990), “The Logic of Physical Theory,” in A. Irvine, D. (ed.), Physicalism in Mathematics, Kluwer.Google Scholar
Vineberg, S. (2018), “Mathematical Explanation and Indispensability,” Theoria 33, 233–47.Google Scholar
Woodward, J. (2003), Making Things Happen: A Theory of Causal Explanation, Oxford University Press.Google Scholar
Yablo, S. (1998), “Does Ontology Rest on a Mistake?” Proceedings of the Aristotelian Society 72, 229–61.Google Scholar
Yablo, S. (2000), “Apriority and Existence,” in Boghossian, P. and Peacocke, C. (eds.), New Essays on the A Priori, Oxford University Press, 197–228.Google Scholar
Yablo, S. (2005), “The Myth of the Seven,” in Kalderon, M. (ed.), Fictionalism in Metaphysics, Oxford University Press, 88–115.Google Scholar
- 9
- Cited by