Abstract
In this paper I argue, that if it is metaphysically possible for it to have been the case that nothing existed, then it follows that the right modal logic cannot extend D, ruling out popular modal logics S4 and S5. I provisionally defend the claim that it is possible for nothing to have existed. I then consider the various ways of resisting the conclusion that the right modal logic is weaker than D.
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Notes
See Baldwin (1996), van Inwagen (1996), Bricker (2001), Rodriguez-Pereyra (2004), Coggins (2010). Bricker and Rodriguez-Pereyra are concerned to argue that modal realism is in fact compatible with the version of metaphysical nihilism restricted to concreta, though Rodriguez-Pereyra acknowledges that it is not compatible with the more radical nihilism considered here.
Cf. Salmon (1989) on this and some related issues.
In this example, tense is important; there is a still a possible world in which I had instead baked bread in the first place. But this is more of a backward-looking metaphysical possibility rather than the practical possibility in question.
Accordingly, “possibly φ” might be false in a world w either because in w there are no states of affairs that include φ or because none of the states of affairs that include φ are possible. The argument below turns on this fact.
Cf. Numeroff (1991).
K itself is the result of adding to classical logic the axiom schema □(φ→ψ)→( □φ→□ψ) and the rule of necessitation: if φ has been proved from no assumptions, then infer □φ.
Yli-Vakurri and Hawthorne (2020: 560). This quotation shows that I do not have an idiosyncratic take on the literature in claiming that S5 is widely accepted as the right modal logic.
The subtraction argument was subsequently tweaked by Rodriguez-Pereyra (1997), criticized by Paseau (2002) and (2006), and defended by Efird and Stoneham (2005) and Rodriguez-Pereyra (2013). Cameron (2006) is a more neutral examination of the subtraction argument, criticizing the assumptions of both the argument itself as well as various counterarguments, leading to the conclusion that “we have seen no good reason to accept either nihilistic thesis, or to reject them” (218).
Balaguer (2016) suggests a fourfold taxonomy including alongside Platonism and Aristotelianism (which he calls immanent realism), conceptualism—which holds that abstracta are mental objects—and nominalism. The conceptualist will be subject to a similar argument for nihilism as the Aristotelian. The nominalist can grant the possibility of nihilism but will avoid my main argument by objecting to the use of possible worlds in the first place.
Or something along those lines. The devil lies in the details, of course.
As Cowling (2017: 83) puts it, “since [Aristotelian] universals are located where and only where they are instantiated, such views typically hold that properties like mass exist in only some worlds, namely those worlds where mass is instantiated.”
Cf. Rosen (2002: 292–5) on the question of whether Platonism without modal extremism is coherent.
In the taxonomy of Cowling (2017: 202–3), the denial of modal extremism I have in mind would be called serious mutabilism.
This and similar arguments are often produced to show that numbers must exist necessarily, e.g. Hale and Wright (1992). See Field (1993) for a forceful reply to Hale and Wright (1992) and Tennant (1997) for further critical discussion of the debate. Tennant in particular is sensitive to the role of a free logic.
This objection was raised by Damon Stanley.
I owe this point to an anonymous referee.
In general of course there will not be a unique state of affairs in which φ holds. There are various ways of interpreting the expression “the maximal state of affairs such that φ”, but the points I will make about substitutional quantification will not turn on these issues, so I will ignore the further complications that they entail.
References
Adams, R. M. (1974). Theories of Actuality. Noûs, 8, 211–231
Armstrong, D. M. (1989). A Combinatorial Theory of Possibility. Cambridge: Cambridge University Press
Balaguer, M. (2016). Platonism in Metaphysics. The Stanford Encyclopedia of Philosophy
Baldwin, T. (1996). There Might Be Nothing. Analysis, 56(4), 231–238
Brenner, A. (2020). Explaining Why There is Something Rather than Nothing. Erkenntnis. https://doi.org/10.1007/s10670-020-00277-6
Bricker, P. (2001). Island universes and the analysis of modality. In G. Preyer, & F. Siebelt (Eds.), Reality and Humean Supervenience. Lanham, MD: Rowman & Littlefield
Cameron, R. (2006). Much ado about nothing: a study of metaphysical nihilism. Erkenntnis, 64, 192–222
Coggins, G. (2010). Could There Have Been Nothing? Against Metaphysical Nihilism. New York: Palgrave-Macmillan
Cowling, S. (2017). Abstract Entities. New York: Routledge
Dummett, M. (1991). The Logical Basis of Metaphysics. Cambridge MA: Harvard University Press
Efird, D., & Stoneham, T. (2005). The Subtraction Argument for Metaphysical Nihilism. Journal of Philosophy, 102(6), 303–325
Field, H. (1993). The Conceptual Contingency of Mathematical Objects. Mind, 102, 285–299
Hale, R., & Wright, C. (1992). Nominalism and the Contingency of Abstract Objects. Journal of Phlosophy, 89, 111–135
Kripke, S. (1981). Naming and Necessity. Malden, MA: Blackwell
Lewis, D. (1968). Counterpart Theory and Quantified Modal Logic. Journal of Philosophy, 65(5), 113–126
Lewis, D. (1986). On the Plurality of Worlds. Malden, MA: Blackwell
Menzel, C. (1991). The True Modal Logic. Journal of Philosophical Logic, 20, 331–374
Nozick, R. (1981). Philosophical Explanations. Cambridge, MA: Belknap Press
Numeroff, L. (1991). If You Give a Moose a Muffin. New York: HarperCollins
Paseau, A. (2002). Why the subtraction argument does not add up. Analysis, 62, 72–75
Paseau, A. (2006). The subtraction argument(s). Dialectica, 60(2), 145–156
Plantinga, A. (1974). The Nature of Necessity. Oxford: Oxford University Press
Rodriguez-Pereyra, G. (1997). There might be nothing: the subtraction argument improved. Analysis, 57, 159–166
Rodriguez-Pereyra, G. (2004). Modal Realism and Metaphysical Nihilism. Mind, 113(452), 683–704
Rodriguez-Pereyra, G. (2013). The Subtraction Arguments for Metaphysical Nihilism: compared and defended. In Tyron, & Goldschmidt (Eds.), The Puzzle of Existence: Why is There Something Rather than Nothing? (pp. 197–214). Routledge
Rosen, G. (2002). A Study in Modal Deviance. In J. Hawthorne, & Tamar Gendler (Eds.), Conceivability and Possibility (pp. 283–307). Oxford: Oxford University Press
Salmon, N. (1989). The Logic of What Might Have Been. Philosophical Review, 98(1), 3–34
Tennant, N. (1997). On the Necessary Existence of Numbers. Nous, 31(3), 3–7
van Inwagen, P. (1986). Two Concepts of Possible Worlds. Midwest Studies in Philosophy, XI, 185–213
van Inwagen, P. (1996). Why is there anything at all? Proceedings of the Aristotelian Society Supplementary, 70, 95–120
Williamson, T. (2013). Modal Logic as Metaphysics. Oxford: Oxford University Press
Yablo, S. (2014). Aboutness. Princeton: Princeton University Press
Yli-Vakurri, J., & Hawthorne, J. (2020). The Necessity of Mathematics. Nous, 54(3), 549–577
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Brauer, E. Metaphysical Nihilism and Modal Logic. Philos Stud 179, 2751–2763 (2022). https://doi.org/10.1007/s11098-022-01793-7
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DOI: https://doi.org/10.1007/s11098-022-01793-7