In defense of the possibilism–actualism distinction


In Modal Logic as Metaphysics, Timothy Williamson claims that the possibilism–actualism (P–A) distinction is badly muddled. In its place, he introduces a necessitism–contingentism (N–C) distinction that he claims is free of the confusions that purportedly plague the P–A distinction. In this paper I argue first that the P–A distinction, properly understood, is entirely coherent and historically well-grounded. I then look at the two arguments Williamson levels at the P–A distinction and find them wanting and show, moreover, that, when the N–C distinction is broadened (as per Williamson himself) so as to enable necessitists to fend off contingentist objections, the P–A distinction can be faithfully reconstructed in terms of the N–C distinction. However, Williamson’s critique does point to a genuine shortcoming in the common formulation of the P–A distinction. I propose a new definition of the distinction in terms of essential properties that avoids this shortcoming.

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  1. 1.

    There is, of course, a well-known alternative to this conception of possibilia, viz., David Lewis’s (1986). Following Williamson (ibid., p. 22), I do not consider Lewis’s reductionist account to be relevant to the modalist version of the debate under discussion here.

  2. 2.

    See also Caston (1999). My thanks to Professor Caston for pointing me to the Seneca quote here.

  3. 3.

    Quoted in Adams (1987, p. 1068). See also McGinnis (2010, pp. 162–163) and Wolter (2003b).

  4. 4.

    Cf. De Rijk (2005), pp. 33–37, 77–78, and Adams (1987), pp. 79–83.

  5. 5.

    See Adams, op. cit., chs. 24 and 25, Wolter (2003a) and De Rijk (2005), pp. 79–95.

  6. 6.

    Cf., respectively, De Rijk, op. cit., p. 81, Wolter (2003b), pp. 137–138, and Adams (1977), p. 147.

  7. 7.

    Meinong (1960) is the locus classicus of his account. See Marek (2013) for an illuminating and accessible exposition.

  8. 8.

    Meinong’s actual account is rather more subtle than this, although I think MSP is faithful enough for purposes here. See Parsons (1974, p. 573ff) formal reconstruction of Meinong’s semantics and Simons (1992) ch. 7 (esp. \(\S \)2.1 and \(\S \)3) more detailed philosophical account.

  9. 9.

    Obviously, lest such objects lead directly to contradiction, in a Meinongian object theory (expressed in classical logic), Fx will not follow from \(\lnot \overline{F}x\); equivalently, \(\overline{F}x\) will not follow from \(\lnot Fx\), i.e., failing to have F will not entail having its complement \(\overline{F}\). This is a familiar sort of restriction for avoiding Russell-style paradoxes in logics with property-denoting expressions. See, e.g., Turner (1987) and Menzel (1993).

  10. 10.

    This isn’t to say Meinong was skeptical of modality. But he never really appeals to his ontology to ground, or explain, such modal facts as our possible nonexistence or the possibility that there could have been more, or other, things. See Peter Simons’ (2013) detailed account of the elaborate theory of modality in Meinong’s huge (1915) treatise. Meinong also seems to suggest at one point that objects that are not in fact part of the causal order but could be are also real (Meinong 1899, p. 198). Unfortunately, he does not seem to have elaborated on this suggestion.

  11. 11.

    See Chisholm (1973) for an attempt to render Meinong’s Nichtseiende coherent. In fact, though, according to Meinong, all objects as such—even existing objects (hence more generally those that have being B!)—qua pure objects, are ausserseiend, or “beyond being and non-being”. See Meinong (1960), \(\S \)4, esp. p. 86, and Marek op. cit., \(\S \)4. This is Meinong’s “principle of the indifference of pure objects to being” (ibid.).

  12. 12.

    Once he had formulated his theory of descriptions, of course, Russell Russell (1905) denied that definite and indefinite descriptions, as well as ordinary proper names like ‘Pegasus’, were genuine denoting expressions.

  13. 13.

    See Meinong (1965), p. 152 for a particularly striking example.

  14. 14.

    I add the qualification “merely” here simply because Quine clearly intended to be discussing possibilia whereas, since actual individuals are possible, if by chance there happened to be an actual bald or portly man in the doorway, the expressions in question would (contrary to Quine’s intentions) pick him out rather than any (alleged) possibilia.

  15. 15.

    See Bolzano (1837a), §352, p. 406 and its translation in Schnieder (2007), p. 541.

  16. 16.

    See Adams (1981, p. 7), Menzel (2014, Introduction), Parfit (2011, p. 719), and Plantinga (1976, p. 143), among others.

  17. 17.

    The picture might be somewhat more complicated for modern actualists and modern possibilists alike whose ontology includes “impure” abstracta like the set \(\{\varnothing ,\text {Obama}\}\) and so-called “singular” propositions like Obama was born in Hawaii that contain, or “involve”, contingent individuals. Though fascinating, the issues are largely orthogonal to those under discussion here.

  18. 18.

    See note 22.

  19. 19.

    In a nutshell, Williamson rejects Lewis’s modal reductionism that interprets the modal operators as quantifiers over Lewisian worlds, i.e., maximally inclusive, mutually non-overlapping spatio-temporal regions (Lewis 1986, p. 2; Menzel 2016, \(\S \)2.1.1). On such a conception, Williamson writes (ibid.), “we cannot explain what is at stake in the actualism–possibilism debate”. This can be spelled out in terms of the subsistence conception. For Lewis, there is no bifurcation of being: the denizens of other worlds exist in a manner no different from those in our world (cf. ibid., pp. 2–3); they are simply not here, in the broadest possible sense of ‘here’. Hence, the existence predicate E!—under its intended meaning on the subsistence conception, i.e., the more robust of two modes of being—in Lewis’s framework is simply true of everything in every world, i.e., we have \({{\Box \forall x(}}E!x\leftrightarrow \exists y\,y=x)\). Lewis’s modal reductionism thus renders Poss trivially false and Act trivially true. Hence, Lewis’s reductionist framework begs the question in favor of actualism and so “we cannot explain what is at stake” in the P–A debate.

  20. 20.

    Under reasonable assumptions there are (in a possibilist ontology) incompossibles—pairs of objects that can’t be jointly actual. Hence, necessarily, not all possible objects are actual.

  21. 21.

    Bennett (2005, pp. 298–299) also expresses a concern about the logical triviality of the “actualist slogan” Everything is actual. As she does not formalize the slogan, I found her precise concern difficult to pin down. However, the source of its alleged triviality is that, if the range of its quantifier is understood (in terms of Kripke semantics) to be world-relative (as I would say it is, albeit in a sense acceptable to actualists—see Menzel 1990), “its truth is just the straightforward result of the way that the quantifier interacts with the ‘actually’ operator”. So, whatever exactly Bennett has in mind, the problem in question is similar to the one Williamson noted above when he attempted to render the slogan in terms of the “actually” operator. Hence, she is simply not addressing modern actualism \({\mathbf{Act }}^{\varvec{*}}\); and as noted in the current paragraph, formalizing the slogan with an “is actual” predicate and understanding (the necessitation of) the slogan as a response to possibilism is critical to addressing concerns over logical triviality.

  22. 22.

    In chapter 7 of his book, Williamson casts further aspersions on the P–A distinction, claiming that “obscure disputes” over “systematic mappings from the talk of one side to the talk of the other [have] figured in [the debates between possibilists and actualists] significantly” (2013, p. 305). However, the disputes in question are small in number and, by my lights, play no significant role in the P–A debate as I have (fairly, I hope) portrayed it. Specifically, these discussions frame the P–A distinction in terms of translation schemes between so-called possibilist and actualist languages—a framing chiefly due to Prior and Fine (1977), Fine (1985) and, to a lesser degree, Pollock (1985). (Williamson also cites Melia (1992) and Forbes (1992) in this regard, but their debate solely concerns the expressive adequacy of a modalist language that Forbes proposes; neither philosopher characterizes it as the P–A debate). As Williamson notes, such a framing threatens to reduce the P–A debate to a mere “verbal disagreement”. But if my characterization above is correct, that is simply not the proper framing. The P–A debate has nothing whatever to do with “systematic mappings” between distinct possibilist and actualist languages. To the contrary, possibilists and actualists share a basic quantified modal language that (thanks to the possibilist) includes an existence/actuality predicate E! (though of course each might extend this basic language in different ways) and their very real disagreement concerns the truth values of certain specific sentences in that language, notably, Poss and Act. For possibilist and actualist alike, the quantifiers of this common language necessarily range over everything there is, in the broadest sense. Where they differ, crucially, is over the ontological question of whether the range of those quantifiers could include possibilia, things that fail to be actual, and, hence, whether the existence predicate E! could be true of fewer things than are in the range of the quantifiers. (This is roughly Plantinga’s take in his cogent 1985 replies to Fine (pp. 329–349) and Pollock (pp. 313–329).)

  23. 23.

    Thought of semantically, this last step here requires that accessibility be symmetric (as it is in Williamson’s S5-based logic).

  24. 24.

    Suppose \({\mathbf{CnC }}^{\varvec{+}}\) is true, i.e., true in the actual world @. Then there is a world \(w_{1}\) (accessible from @) where \({\mathbf{C! }}^{+}\) is true, i.e., where an individual a is non-concrete and possibly concrete. Let \(w_{2}\) be a world accessible from \(w_{1}\) where a is concrete. Then, since accessibility is symmetric, \(w_{1}\) is accessible from \(w_{2}\) and so it’s true in \(w_{2}\) that there is something (viz., a) that is concrete but possibly non-concrete, i.e., \({\mathbf{C! }}^{\text {-}}\) is true \(w_{2}\). Since accessibility is transitive, \(w_{2}\) is accessible from @, so \({\mathbf{CnC }}^{{-}}\) is true. Exactly parallel reasoning demonstrates the converse.

  25. 25.

    This claim might require minor modification if there are contingent abstracta of the sort mentioned in note 17. Terminological note: “non-concreta” is admittedly barbarous but a suitable Latin-ish correlate to “possibilia” seems desirable. My thanks to Alex Dressler for his counsel regarding the Latin plural. He will appreciate my noting that he is not responsible for my choice of the term.

  26. 26.

    E.g., possibilia have the property nonexistence while contingent non-concreta do not.

  27. 27.

    Williamson himself introduces the notion of chunkiness (p. 313), which corresponds pretty much exactly to the definition of ‘E!’ here.

  28. 28.

    For reasons discussed in note 17, the relabeling may not yield identical ontological categories. Notably, if there are “mixed” abstracta like \(\{\varnothing ,\text {Obama}\}\), they belong in the upper left quadrant of, at least, the circle representing modern actualism in Fig. 2. But since, necessarily, it is not the case that such abstracta are concrete, they belong in the lower left quadrant of the circles in Fig. 3.

  29. 29.

    Linsky and Zalta (ibid.) themselves only spell out this necessitist gambit without explicitly committing to it. See also Cameron (2016).

  30. 30.

    Cf., e.g., Plantinga (1974), pp. 55–56.

  31. 31.

    See, e.g., Fine (1994) and Zalta (2006) for criticisms of the definition and Robertson and Atkins (2018) for an overview of various alternatives.

  32. 32.

    See in particular Williamson (2013), p. 11ff.

  33. 33.

    In particular, like the original distinction, it makes no reference to possible worlds. Williamson claims (2013, p. 333) that “[m]uch of the debate between actualists and possibilists revolve[s] around the legitimacy or illegitimacy of quantification over possible worlds”, such quantification being “seen as far more problematic for actualists than for possibilists.” But, very little if anything in the debate has revolved around the legitimacy of such quantification; as should be clear from the principles Poss/Act and POSS/ACT, the question of possibilia on the subsistence conception is entirely orthogonal to it. There are, in particular, actualists who embrace worlds (e.g., Plantinga 1974 and Adams 1981) and those that do not (e.g., Menzel 1990). Moreover, while the project of defining worlds as abstract objects of some ilk is usually associated with actualism (though see Zalta 1993), the problems involved in the project are largely independent of one’s commitment to possibilia (see, e.g., Grim 1984, 1986; Menzel 1986, 1989; Menzel 2012). It’s also worth noting that similar problems arise for the worlds of Lewisian reductionism [see, e.g., Forrest and Armstrong (1984) and Lewis (1986)].

  34. 34.

    If one wishes to insist that numbers and other abstracta are (contrary to most any modern conception of essence) essentially Fif concrete, ACT* could be restricted to things that are possibly F.

  35. 35.

    It’s important not to get the scoping wrong here. Formally, where \(\Sigma (G,x)\) means that G is essential to x, ACT* says that \(\Box \forall F\forall x(\Sigma (F_{C!},x)\rightarrow Fx)\). Thus, the actualist can accept that Toni is essentially, hence necessarily, a tiger if concrete, \(T_{C!}\), but Toni won’t be in the range of the quantifier at worlds where she doesn’t exist and, hence, though not a tiger at those worlds, she won’t be a value of the variable x for which \(\Sigma (F_{C!},x)\) is true at those worlds and, hence, won’t serve as a counterexample to ACT*.

    An objection to these modifications of POSS and ACT might be heard from so-called serious actualists, who hold that property exemplification entails existence (Prior (1957, p. 31); Plantinga (1983); Plantinga (1985); Hudson (1997); Caplan (2007); Stephanou (2007)). For, on the account of essential properties that the actualist is conceding to Williamson here, contingent beings have their essential properties necessarily. But if exemplification entails existence—i.e., if \(\Box (Fx\rightarrow E!x)\), for any property F and entity x—then no contingent being has any essential properties; Toni, in particular, will not be a tiger if concrete essentially. However, in Menzel (1993, pp. 136–142) it is argued in detail that a simple change of semantic perspective allows the actualist to agree that Toni is necessarily a tiger if concrete, i.e., that \(\Box [\lambda x\,C!x\rightarrow Tx]t\), without abandoning the metaphysical intuitions that underlie serious actualism. See also Fine (1985), \(\S \)4, esp. p. 163ff, Pollock (1985), \(\S \)2, Hinchliff (1989) and Yagisawa (2005).


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My thanks to Ross Cameron, Matt Davidson, Kris McDaniel, and Ed Zalta for helpful comments on earlier versions of this paper, and to audiences at the Munich Center for Mathematical Philosophy, the University of Utah, the Society for Exact Philosophy (2016 meetings), the University of Notre Dame, Georgetown University, the University of Vienna, the Kurt Gödel Research Center for Mathematical Logic, and the universities of Oslo and Bergen for fruitful, challenging, and stimulating discussions in response to talks I gave based on the issues discussed herein. I am particularly grateful to Benjamin Schnieder for his detailed answers to several questions I had concerning his important and informative paper on Bolzano’s modal metaphysics. Finally, special thanks to the Notre Dame Center for Philosophy of Religion, where I completed a significant draft of this paper during my tenure as the 2016–2017 Alvin Plantinga fellow.

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Menzel, C. In defense of the possibilism–actualism distinction. Philos Stud 177, 1971–1997 (2020).

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  • Actualism
  • Possibilism
  • Necessitism
  • Contingentism
  • Modality
  • Modal logic