David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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Proceedings of the Aristotelian Society 110 (2pt2):133-181 (2010)
According to a tradition stemming from Quine and Putnam, we have the same broadly inductive reason for believing in numbers as we have for believing in electrons: certain theories that entail that there are numbers are better, qua explanations of our evidence, than any theories that do not. This paper investigates how modal theories of the form ‘Possibly, the concrete world is just as it in fact is and T’ and ‘Necessarily, if standard mathematics is true and the concrete world is just as it in fact is, then T’ bear on this claim. It concludes that, while analogies with theories that attempt to eliminate unobservable concrete entities provide good reason to regard theories of the former sort as explanatorily bad, this reason does not apply to theories of the latter sort
|Keywords||Nominalism Explanation Indispensability Numbers|
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References found in this work BETA
Saul A. Kripke (1980). Naming and Necessity. Harvard University Press.
Theodore Sider (2001). Four Dimensionalism: An Ontology of Persistence and Time. Oxford University Press.
David Lewis (1991). Parts of Classes. Blackwell.
David K. Lewis (1983). Philosophical Papers. Oxford University Press.
Saul Kripke (2010). Naming and Necessity. In Darragh Byrne & Max Kölbel (eds.), Philosophy. Routledge 431-433.
Citations of this work BETA
Cian Dorr (2011). Physical Geometry and Fundamental Metaphysics. Proceedings of the Aristotelian Society 111 (1pt1):135-159.
Christopher Pincock, Alan Baker, Alexander Paseau & Mary Leng (2012). Science and Mathematics: The Scope and Limits of Mathematical Fictionalism. [REVIEW] Metascience 21 (2):269-294.
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