Modal dimensionalism (MD) is realism about spaces, times and worlds—metaphysical indices that make objects spatial, temporal and modal, respectively, and that play the role of alethic relativizers, i.e. items to which matters of truth are relativized. This paper examines several arguments against MD and shows that MD offers a feasible way to understand modal discourse.
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Unless stated otherwise, MR refers to Lewis (1986) as the orthodox version of modal realism.
Unless stated otherwise, MD refers to Yagisawa (2010) as the orthodox version of modal dimensionalism.
For Yagisawa, reality is fundamental and monadic, whereas existence is domain relative.
Taking the analogy seriously, Yagisawa introduces a new word, mau, combining the temporal ‘now’ with its (m)odal counterpart (cf. Yagisawa 2002, p. 29).
I will postpone the discussion about the metaphysics of logical spaces to section 9.
For the difference between rigid and non-rigid uses of the actuality tense, see Yagisawa (2010, pp. 76–77).
Yagisawa (2015, p. 322, fn. 9) thinks that to forbid predication of modal properties of world stages is a radical alternative, although I am not entirely clear on why this ought to be viewed as radical.
For the distinction between ordinary and extraordinary modalizing, see Divers (1999).
Cf. Cowling (2011, pp. 383–384).
Cf. Lewis (1986, pp. 12–13).
The validity of logic is just one part of the problem. The second is about how to build a semantics on amodalism. For a way to meet the worry, see Cowling (2011, pp. 486–491).
Two remarks are in order. MD, even if it postulates possible and impossible individuals, is not a priori committed to primitive modality. Although there is a difference between possibility and impossibility, the difference can be handled non-modally. One way to do this is to analyse any kind of possibility as a restricted modality, while those very restrictions (usually laws) are to be understood non-modally. So, extended modal realism, even if hard to swallow in principle, can be squared with Lewisian reductive ambitions. Second, extended modal realism does not aim to violate our everyday reasoning about actual and possible things. Impossible worlds do not actually exist. They do not exist possibly either, if ‘existing possibly’ means being restricted to a particular domain. As Yagisawa puts it, ‘[i]t is certainly impossible for impossibilia to exist under any possible conditions or circumstances. But that does not mean that impossibilia do not exist under any conditions or circumstances whatever. They exist under impossible conditions or circumstances’ (Yagisawa 1988, pp. 202–203). It is therefore not the case that MD automatically fails the non-reductive test, and indeed much more should be said about its commons-sense test failure. Nonetheless, it still holds that problems regarding representation of logical, metaphysical and mathematical phenomena present strong reason to reject the project. I think, however, that although controversial, extended modal realism might find some resources parallel to or parasitic upon competitive accounts.
Moreover, the argument runs regardless of whether we take ‘is real’ or ‘exists’ to be primitive (see Jago 2012).
See footnote 3.
For Yagisawa’s response, see Yagisawa (2011, p. 310).
Cf. Jago, Advanced modalizing problems, Mind, forthcoming.
There is yet another option available to MD. I have already pointed out that modal indices, unlike Lewis’s worlds, are not concrete. This feature puts it somewhere between MR and modal ersatzism. A version of the latter represents modality not genuinely but, to use Lewis’s label, by magic. But as I argued in Vacek (2015), there are ways to meet the challenge from magic. If my responses work, I do not detect a serious reason not to apply them to MD as well.
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I thank the anonymous referees for their helpful comments. I also thank John Divers, Fredrik Haraldsen, Daniel Nolan, Marián Zouhar and especially Takashi Yagisawa for discussions and comments. My work on this paper was supported by research grant Vega No. 2/0049/16, Fictionalism in Philosophy and Science.
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Vacek, M. Extended Modal Dimensionalism. Acta Anal 32, 13–28 (2017). https://doi.org/10.1007/s12136-016-0297-9
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