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Metaphysical and absolute possibility

  • S.I. : New Directions in the Epistemology of Modality
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Abstract

It is widely alleged that metaphysical possibility is “absolute” possibility (Kripke in Naming and necessity, Harvard University Press, Cambridge, 1980; Lewis in On the plurality of worlds, Blackwell, Oxford, 1986; van Inwagen in Philos Stud 92:68–84, 1997; Rosen, in: Gendler and Hawthorne (eds) Conceivability and possibility, Clarendon, Oxford, 2002, p 16; Stalnaker, in: Stalnaker (ed) Ways a world might be: metaphysical and anti-metaphysical essays, Oxford University Press, Oxford, 2003, pp 201–215; Williamson in Can J Philos 46:453–492, 2016). Kripke calls metaphysical necessity “necessity in the highest degree” (1980, p. 99). Van Inwagen claims that if P is metaphysically possible, then it is possible “tout court. Possible simpliciter. Possible period…. possib(le) without qualification (1997, p. 72).” And Stalnaker writes, “we can agree with Frank Jackson, David Chalmers, Saul Kripke, David Lewis, and most others who allow themselves to talk about possible worlds at all, that metaphysical necessity is necessity in the widest sense (2003, p. 203).” What exactly does the thesis that metaphysical possibility is absolute amount to? Is it true? In this article, I argue that, assuming that the thesis is not merely terminological, and lacking in any metaphysical interest, it is an article of faith. I conclude with the suggestion that metaphysical possibility may lack the metaphysical significance that is widely attributed to it.

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Notes

  1. Chalmers writes, “the metaphysically possible worlds are just the logically possible worlds (1996, p. 38)”, where logical possibility, in turn, is “possibility in the broadest sense (1996, p. 35).” Similarly, Murray and Wilson note that “[m]etaphysical necessity and possibility are commonly supposed to be necessity and possibility in the broadest…sense (2012, p. 189).” They then quote John Burgess as writing, “we may distinguish the species of physical necessity, or what could not have been otherwise so long as the laws of nature remained the same, from metaphysical necessity, what could not have been otherwise no matter what (2009, p. 46).” [Note that Murray and Wilson also reject the orthodoxy that metaphysical necessity is absolute, but for a very different reason. They hold that “metaphysical necessities and possibilities are relativized to indicative actualities” (Murray and Wilson 2012, p. 189)].

  2. I will switch between talk of necessity and possibility when this is natural, and the difference is unimportant.

  3. Note that some such notions do not entail the necessity of all classical logical truths. For instance, notions based on free logic do not have the consequence that []∃x(x = a), for a name in the language, ‘a’ [see, again, Girle (2017, p. 8.6)].

  4. This is especially clear when we consider higher-order logics, which lack sound and complete proof systems. (Rumfitt is focused on “broadly” logical necessity, according to which, while such things as that all bachelors are unmarried are logically necessary, that water = H2O is not. The considerations he adduces for regarding his notion of logical possibility as non-epistemic seem to me to serve equally to show that the present notion is non-epistemic. But if one were peculiarly suspicious of the notions of logical possibility to which I appeal, then my point that metaphysical possibility is not the most inclusive non-epistemic notion of possibility could be made equally by appealing to Rumfitt’s.)

  5. Thanks to an anonymous referee for pointing this out.

  6. Thanks to Rumfitt for emphasizing this to me. Moreover, if we want the system in question to assign truth-values to propositions, rather than to sentences, then Kaplan’s system with indexicals seems inapt. Kaplan himself notes that validity in his system “states a property of sentences”, rather than “of…a proposition” (1989b, p. 596). (Thanks to Alex Silk for discussion.)

  7. Kment (2016) uses “ontic” and Hale (2013) uses “alethic” to the same effect. Using “alethic” in this way is misleading, however, since the term normally used to mean satisfies the T axiom. More on this below.

  8. Although it is sometimes alleged that contingent identity is simply unintelligible, Kripke’s argument for the Necessity of Identity, in terms of rigid designation, seems to me weak. First, it assumes a possible worlds semantics, even though Kripke is explicit that possible worlds merely afford a “metaphor” (1971, p. 174). What is the argument, stripped of the metaphor? Second, as Cameron (2006) observes, Kripke appears to equivocate with the term “rigid designator”. If to say that names are rigid designators is just to say that, e.g., “Hesperus” and “Phosphorus” refer to what they actually refer to in every world, then showing that “Hesperus” and “Phosphorus” are rigid designators does nothing to show that the terms co-refer at every world. It merely shows that “Hesperus” refers to Hesperus in every world, and that “Phosphorus” refers to Phosphorus in every world, leaving open whether they ever refer to different objects in a world. On the other hand, if it means that “Hesperus” and “Phosphorus” co-refer in every world, given that they do in the actual world, then Kripke assumes what he seeks to prove. Either way, it is misleading to contend that “[i]f names are rigid designators, then there can be no question about identities being necessary (Kripke 1971, p. 181)”. (Note that ∀x∀y[(x = y  → [](x = y)] is certainly not self-evident, given that it is apparently false if [] means, e.g., it is known that.) See Cartwright (1997) for a more careful treatment.

  9. Williamson is explicit that the mathematical truths are metaphysically necessary [as is Kripke (1980, p. 37)]. For instance, he says that “the structure of the hierarchy of pure sets…seems to be a metaphysically noncontingent matter” (2017, p. 199). See also his (2016, p. 454).

  10. There are independent problems with each of these proposals. For instance, assuming, contra Anselm, that nature does not “precede existence”, so that it cannot be part of numbers’ nature to exist, there are notions of possibility that are grounded in the nature of things, but according to which there could have failed to be any numbers. See Rosen (2002).

  11. Thanks to an anonymous reviewer for suggesting this proposal.

  12. This is one objection I have to the “modal fictionalism” of Rosen (1990), which takes something like the above form. (Actually, I suspect that a version of the objection just considered arises for Lewisans, Fineans, and Vetterians themselves. For example, even if it is “grounded in the nature of things” that you have the parents that you have, we could always introduce a notion of nature*, which is like nature, except that, e.g., it is no part of your nature* that you have the parents that you have. We could then say that something is metaphysically* necessary just when it is grounded in the nature* of things. Defining absolute* as before, what does it matter that metaphysical possibility is absolute, given that it is not absolute*? In fact, we could raise a similar problem by continuing to speak only of natures, but introducing a notion of ground*. See my (2017, Sec. 6), (Forthcoming A, Conclusion), and (Forthcoming B) for further discussion.).

  13. Thanks to an anonymous referee to highlighting the distinction between absoluteness (or “wideness”) and unqualifiedness, a distinction which I had obscured in a prior draft.

  14. It just so happens that a first-order non-modal sentence is logically necessary when it is provable in any standard (sound and complete) proof system and true in all models.

  15. Thanks to an anonymous referee for pointing out the second ground for skepticism.

  16. This locution is slightly misleading, since what is actual is metaphysically possible. Similarly, “counterfactual” suggests counter-to-fact, but there is no problem counterfactually conditionalizing on what is actual.

  17. Sometimes Williamson suggests that notions of necessity which fail to satisfy the Necessity of Identity are not objective in the sense that they are not about the states-of-affairs described. They are at least partly about the words used to describe them. But this is tendentious.  Advocates of contingent identity—such as Gibbard (1975), Wilson (1983), or Priest (2016)—should think that claims involving "Hesperus" and "Phosphorus" are about…Hesperus and Phosphorus!  They may even allow that "Hesperus" and "Phosphorus" are rigid designators in the sense of picking out what they pick out in the actual world. In general, advocates of contingent identity should maintain that we may have t = t', but, also, [](…t…) & ~ [](…t'…), where “(…x…)” is a formula with only x free, even though claims involving t and t’ are about the referents of t and t’.  (Gibbard, Wilson, and Priest are motivated by different examples than “Hesperus = Phosphorus”, but an analogous point holds for the cases they consider.).

  18. Thanks to an anonymous referee for pointing this out.

  19. Indeed, an anonymous referee pointed out that counterfactuals, to which Kripke, Williamson, and others routinely appeal when characterizing metaphysical possibility, are typically partly analyzed in apparently epistemic terms.

  20. The definition of Lewis (1986) is, of course, highly controversial.

  21. Balaguer (1995, p. 317) and Field (1989, Introduction) take the notion of logical possibility as primitive. Melia (2003) discusses this approach more generally.

  22. Again, while one can interpret claims about what is logically possible as misleading claims about proofs or models, one can equally interpret claims of metaphysical possibility this way [where the “axioms” now include non-logical principles of mathematics, mereology, etc., as in Sider (2011, Ch. 12)]. In both cases, we also have the option of interpreting the claims at face-value. [Actually, there are serious obstacles to even interpreting claims of logical possibility in this way. See Balaguer (1997, p. 317), Field (1989, Introduction) and Rumfitt (2010, 2015, Ch. 3)].

  23. Glazier suggests that real notions of necessity are those which support a certain kind of explanation. I suspect that this suggestion faces problems analogous to the suggestion that the real necessities are grounded in the nature of things. There are different notions of “explanation” giving rise to different notions of real necessity. But even if I am wrong, metaphysical possibility is not the most inclusive notion of real possibility by Glazier’s criteria, since logical necessity is explanatory. See Glazier (Forthcoming). (Thanks to Glazier for discussion.) Another pertinent discussion is that of Bacon (2018). I have rejected his assumptions about what makes for a “modality” above. For instance, Bacon assumes that logical necessity is not a modality in the relevant sense, since it concerns sentences, not propositions. But this is tendentious. Advocates of logical necessity, such as Field (1989, Introduction) or Balaguer (1995, p. 317), treat the notion as applying to propositions. In any event, metaphysical possibility is not absolute by Bacon’s lights either. (His “broadest” necessity does not even validate the Necessity of Distinctness or the S5 Axiom.) So, I set his discussion aside as well.

  24. Although this is the standard view, it can be questioned. See Van Fraassen (1977) and Fine (2002). (Note that T may not be a finite conjunction, so I am not working in a typical modal language here.)

  25. Nolan (2011) identifies notions of possibility with classes of worlds, and understands worlds as Lewis’s “ersatz” worlds, such as arbitrary sets of sentences. But this trivializes the question of absoluteness. Given these stipulations, metaphysical possibility is trivially not absolute, but the notion of Mortensen (1989), according to which literally anything is possible, trivially is.

References

  • Bacon, A. (2018). The broadest necessity. Journal of Philosophical Logic, 47, 733–783. https://doi.org/10.1007/s10992-017-9447-9.

    Article  Google Scholar 

  • Balaguer, M. (1995). Platonism and anti-platonism in mathematics. New York: Oxford University Press.

    Google Scholar 

  • Bealer, G. (2002). Modal epistemology and the rationalist renaissance. In T. Gendler & J. Hawthorne (Eds.), Conceivability and possibility (pp. 71–125). Oxford: Oxford University Press.

    Google Scholar 

  • Berto, F. (2013). Impossible worlds. In E. N. Zalta (Ed.), The stanford encyclopedia of philosophy (Winter 2013 Edition). https://plato.stanford.edu/archives/win2013/entries/impossible-worlds/.

  • Bostock, D. (1988). Necessary truth and a priori truth. Mind, 49, 343–397.

    Article  Google Scholar 

  • Burgess, J. (2009). Philosophical logic. Princeton: Princeton University Press.

    Book  Google Scholar 

  • Cameron, R. (2006). Comment on ‘Kripke’s (Alleged) argument for the necessity of identity statements’. Wo’s Weblog. Online at: https://www.umsu.de/wo/archive/2006/08/09/Kripke_s__Alleged__Argument_for_the_Necessity_of_Identity_Statements.

  • Cartwright, R. (1997). On singular propositions. Canadian Journal of Philosophy. Supplementary, 23, 67–83.

    Article  Google Scholar 

  • Chalmers, D. (1996). The conscious mind. New York: Oxford University Press.

    Google Scholar 

  • Clarke-Doane, J. (2017). Modal objectivity. Noûs. https://doi.org/10.1111/nous.12205.

    Article  Google Scholar 

  • Clarke-Doane, J. (Forthcoming A). Morality and mathematics. Oxford: Oxford University Press.

  • Clarke-Doane, J. (Forthcoming B). Objectivity and evaluation. In C. Cowie & R Rowland (Eds.), Companions in guilt arguments in metaethics. Routledge.

  • Field, H. (1989). Realism, mathematics, and modality. Oxford: Blackwell.

    Google Scholar 

  • Fine, K. (2002). The varieties of necessity. In T. S. Gendler & J. Hawthorne (Eds.), Conceivability and Possibility (pp. 253–281). Oxford: Oxford University Press.

    Google Scholar 

  • Gibbard, A. (1975). Contingent identity. Journal of Philosophical Logic, 4, 187–221.

    Article  Google Scholar 

  • Girle, R. (2017). Modal logics and philosophy (2nd ed.). Chicago: McGill-Queens University Press.

    Google Scholar 

  • Glazier, M. (Forthcoming). The difference between epistemic and metaphysical necessity. Synthese.

  • Godel, K. (1947). What is Cantor’s continuum problem? American Mathematical Monthly, 54, 515–525.

    Article  Google Scholar 

  • Hale, B. (1996). Absolute necessities. Philosophical Perspectives, 10, 93–117.

    Google Scholar 

  • Hale, B. (2013). Necessary beings: An essay on ontology, modality and the relations between them. Oxford: Oxford University Press.

    Book  Google Scholar 

  • Kaplan, D. (1989a). Demonstratives. In J. Almog, J. Perry, & H. Wettstein (Eds.), Themes from Kaplan. Oxford: Oxford University Press.

    Google Scholar 

  • Kaplan, D. (1989b) Afterthoughts. In Almog, Perry & Wettstein (Eds.).

  • Kment, B. (2014). Modality and explanatory reasoning. Oxford: Oxford University Press.

    Book  Google Scholar 

  • Kripke, S. (1971). Identity and Necessity. In M. K. Munitz (Ed.), Identity and individuation (pp. 161–191). New York: New York University Press.

    Google Scholar 

  • Kripke, S. (1980). Naming and necessity. Cambridge: Harvard University Press.

    Google Scholar 

  • Lewis, D. (1986). On the plurality of worlds. Oxford: Blackwell.

    Google Scholar 

  • Melia, J. (2003). Modality. New York: Acumen.

    Book  Google Scholar 

  • Mortensen, C. (1989). Anything is possible. Erkenntnis, 30, 319–337.

    Article  Google Scholar 

  • Murray, A., & Wilson, J. (2012). Relativized Metaphysical Modality. In K. Bennett & D. Zimmerman (Eds.), Oxford studies in metaphysics. Oxford: Oxford University Press.

    Google Scholar 

  • Nolan, D. (2011). The extent of metaphysical necessity. Philosophical Perspectives, 25, 313–339.

    Article  Google Scholar 

  • Priest, G. (2008). An introduction to non-classical logic: From if to is (2nd ed.). New York: Cambridge University Press.

    Book  Google Scholar 

  • Priest, G. (2016). Thinking the impossible. Philosophical Studies, 10, 2649–2662.

    Article  Google Scholar 

  • Rayo, A. (Manuscript). The open-endedness of logical space.

  • Rosen, G. (1990). Modal fictionalism. Mind., 99, 327–354.

    Article  Google Scholar 

  • Rosen, G. (2002). A study of modal deviance. In T. S. Gendler & J. Hawthorne (Eds.), Conceivability and possibility. Oxford: Clarendon.

    Google Scholar 

  • Rumfitt, I. (2010). Logical Necessity. In B. Hale & A. Hoffmann (Eds.), Modality: Metaphysics, logic, and epistemology. Oxford: Oxford University Press.

    Google Scholar 

  • Rumfitt, I. (2015). The boundary stones of thought: An essay in the philosophy of logic. Oxford: Oxford University Press.

    Book  Google Scholar 

  • Sider, T. (2011). Writing the book of the world. New York: Oxford University Press.

    Book  Google Scholar 

  • Stalnaker, R. (Ed.). (2003). Conceptual truth and metaphysical necessity. In Ways a world might be: Metaphysical and anti-metaphysical essays (pp. 201–215). Oxford: Oxford University Press.

    Chapter  Google Scholar 

  • Strohminger, M., & Yli-Vakkuri, J. (2017). The epistemology of modality. Analysis, 77, 825–838.

    Article  Google Scholar 

  • Van Fraassen, B. (1977). The only necessity is verbal necessity. Journal of Philosophy, 74, 71–85.

    Article  Google Scholar 

  • Van Inwagen, P. (1997). Modal epistemology. Philosophical Studies, 92, 68–84.

    Google Scholar 

  • Vetter, B. (2015). Potentiality: From dispositions to modality. Oxford: Oxford University Press.

    Book  Google Scholar 

  • Vetter, B. (2016). Williamsonian modal epistemology, possibility-based. Canadian Journal of Philosophy, 46, 766–795.

    Article  Google Scholar 

  • Williamson, T. (2016). Modal science. Canadian Journal of Philosophy, 46, 453–492.

    Article  Google Scholar 

  • Wilson, M. (1983). Why contingent identity is necessary. Philosophical Studies, 43, 301–327.

    Article  Google Scholar 

Download references

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    Justin Clarke-Doane

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Thanks to Derek von Barandy, Martin Glazier, Max Khan Hayward, Ian Rumfitt, Alex Silk, Juhani Yli Vakkuri, and two anonymous referees for comments.

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Clarke-Doane, J. Metaphysical and absolute possibility. Synthese 198 (Suppl 8), 1861–1872 (2021). https://doi.org/10.1007/s11229-019-02093-0

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