Why inference to the best explanation doesn’t secure empirical grounds for mathematical platonism

Synthese 198 (1):1-13 (2018)
  Copy   BIBTEX

Abstract

Proponents of the explanatory indispensability argument for mathematical platonism maintain that claims about mathematical entities play an essential explanatory role in some of our best scientific explanations. They infer that the existence of mathematical entities is supported by way of inference to the best explanation from empirical phenomena and therefore that there are the same sort of empirical grounds for believing in mathematical entities as there are for believing in concrete unobservables such as quarks. I object that this inference depends on a false view of how abductive considerations mediate the transfer of empirical support. More specifically, I argue that even if inference to the best explanation is cogent, and claims about mathematical entities play an essential explanatory role in some of our best scientific explanations, it doesn’t follow that the empirical phenomena that license those explanations also provide empirical support for the claim that mathematical entities exist.

Similar books and articles

Mathematical Explanations Of Empirical Facts, And Mathematical Realism.Aidan Lyon - 2012 - Australasian Journal of Philosophy 90 (3):559-578.
Multiple realization and expressive power in mathematics and ethics.David Liggins - 2016 - In Uri D. Leibowitz & Neil Sinclair (eds.), Explanation in Ethics and Mathematics: Debunking and Dispensability. Oxford, England: Oxford University Press UK.
Mathematical platonism meets ontological pluralism?Matteo Plebani - 2017 - Inquiry: An Interdisciplinary Journal of Philosophy:1-19.
Mathematics and Program Explanations.Juha Saatsi - 2012 - Australasian Journal of Philosophy 90 (3):579-584.
Platonism and anti-Platonism in mathematics.Mark Balaguer - 1998 - New York: Oxford University Press.
Platonism, and Mind-Independent Existence.Tommaso Piazza - 2009 - Grazer Philosophische Studien 78 (1):159-183.

Analytics

Added to PP
2018-12-19

Downloads
472 (#42,326)

6 months
140 (#27,042)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Kenneth Boyce
University of Missouri, Columbia

References found in this work

Two Dogmas of Empiricism.W. Quine - 1951 - [Longmans, Green].
Two Dogmas of Empiricism.Willard V. O. Quine - 1951 - Philosophical Review 60 (1):20–43.
Inference to the Best Explanation.Peter Lipton - 1991 - London and New York: Routledge/Taylor and Francis Group.
Science Without Numbers: A Defence of Nominalism.Hartry H. Field - 1980 - Princeton, NJ, USA: Princeton University Press.
Two Dogmas of Empiricism.W. V. O. Quine - 2011 - In Robert B. Talisse & Scott F. Aikin (eds.), The Pragmatism Reader: From Peirce Through the Present. Princeton University Press. pp. 202-220.

View all 80 references / Add more references