https://orcid.org/0000-0002-4040-6203
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ABSTRACT
This paper argues that modal realism has a problem with mathematical impossibilities. Due to the peculiar way it treats both propositions and mathematical objects, modal realism cannot distinguish the content of different mathematically impossible beliefs. While one might be happy to identify all logically impossible beliefs, there are many different mathematically impossible beliefs, none of which is a belief in a logical contradiction. The fact that it cannot distinguish these beliefs speaks against adopting modal realism.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Notes
1 See, e.g. Yagisawa (Citation2009, ch. 8), Krakauer (Citation2013), Nolan (Citation2013) and Berto and Jago (Citation2019).
2 See also the account of objects that are ‘actual by courtesy’ in Lewis (Citation1986c, 95–96).
3 Such views are proposed in a number of places in the literature, including Lewis (Citation1986a, 15–16). See also Restall (Citation1997), Mares (Citation1997), Divers (Citation2002, 313, n. 19), and Kiourti (Citation2009, ch. III).
4 Berto (Citation2010, 485) gives the example of the belief that Charles is married and a bachelor. See also the discussion of ‘triangular’ and ‘trilateral’ in Kiourti (Citation2009, 82) and Vacek (Citation2013b, 295–296).
5 Earlier versions of this paper were presented at the University of Sydney and at the first South American Logic Meeting in Cusco, Peru. I received helpful feedback from my audiences on both occasions, and especially from Mark Colyvan, Kristie Miller, and David Braddon–Mitchell. Two referees for Inquiry made very helpful suggestions that improved the paper, but all remaining mistakes are my own. My work was supported by the Marion Hoeflich Memorial Endowment for Advances in Philosophy.