The Possibility Principle and the Truthmakers for Modal Truths

Abstract

A necessary part of David Armstrong's account of truthmakers for modal truths is his Possibility principle: any truthmaker for a contingent truth is also a truthmaker for the possibility of the complement of that contingent truth (if T makes p true and p is contingent, then T makes ⋄∼p true). I criticize Armstrong's Possibility principle for two reasons. First, his argument for the Possibility principle both relies on an unwarranted generalization and vitiates his desire for relevant truthmakers. His argument undercuts relevant truthmakers by entailing that each contingent being is a truthmaker for all modal truths. Second, even if the argument seems successful, the Possibility principle is subject to counterexamples. Armstrong's being composed of more than fifty atoms makes it true that something composed of more than fifty atoms exists and that truth is contingent, but his being composed of more than fifty atoms does not make it true that it is possible that it is not the case that something composed of more than fifty atoms exists.

Notes

¹Cameron 2005, McDaniel 2005, Mumford 2005 and Tallant 2005 all provide careful reviews of the book, but none mentions the Possibility principle. Alward 2004: 76–7] and Bostock 2005: 369] briefly discuss the principle without calling it into question; Hochberg 2006: 187–8] doesn't argue that the Possibility principle is false, but he does claim that Armstrong does not go far enough in showing how the intrinsicality of contingency should be understood in his argument and that Armstrong must, in the end, appeal to a fundamentally modal entity in his account of truthmakers for modal truths; Keller 2007 argues clearly that Armstrong's 2004 argument for the Possibility principle is flawed, but does not provide an argument that the principle itself is false; and Simons 2005: 254] claims that the argument is invalid and that the Possibility principle is implausible, but offers no reasons for thinking the principle implausible.

²Kalhat 2008 provides the one extant argument for the falsity of the Possibility principle. It is problematic because it, like Armstrong's 2007: 103] argument, has de re–de dicto confusions. I will discuss this problem later as my second smallish point in §3.

³To see the accounts that elicit this charge of extravagance, see Plantinga 1974 and Lewis 2001b, especially §1].

⁴Lewis 2001b, especially §1.8. This isn't the whole story for Lewis. The actual world and its parts make some modal truths true as well. The point here, though, is that Lewis needs unactual worlds and their parts in addition to the actual world and its parts.

⁵I say a strong incentive since each thinker claims that other benefits accrue from his preferred ontology.

⁶I've changed the denotation of propositions in his argument to match the style I use in this article. Armstrong uses angled brackets (<p>) to denote propositions, whereas I italicize to denote propositions (p). Otherwise, this is how he presents his argument. One might notice that in this argument for the Possibility principle Armstrong writes of p and the possibility of not-p, whereas in the Possibility principle itself he writes of not-p and the possibility of p. This change has no effect on the logic of the argument or the viability of my coming criticisms.

⁷Again, I've modified the way in which propositions are referred to in this quotation. Rather than using Armstrong's brackets, I've continued to use italics to denote propositions.

⁸For more discussion of the problems with Armstrong's 2004 argument, see Keller 2007.

⁹Armstrong 1997, especially chapter 8. Perhaps you wonder what sort of beast non-mereological constitution could be. Isn't mereology the study of constitution? David Lewis, in more than one place, expresses his perplexity at Armstrong's notion of non-mereological constitution; cf. Lewis 2005: 34].

¹⁰Here and elsewhere in this article I affix the box (□) and diamond (⋄) to propositions to represent modal propositions. Since I represent propositions by italicizing that-clauses, I've affixed the modal operators to the that-clauses, rather than removing the that from the that-clause (e.g., ⋄T exists rather than ⋄that T exists), as is sometimes done.

¹¹See also Kalhat 2008: 174]: ‘I argued that the Possibility Principle is false, since the truthmaker for, say, the proposition <Armstrong exists> cannot plausibly be taken to be also a truthmaker for the possibility of his non-existence’. Kalhat goes on to provide an additional argument for the falsity of the Possibility principle which I will not discuss here: the Possibility principle requires an application of the Entailment principle, and the Entailment principle is false, so the Possibility principle must be false as well.

¹²What about him does the work of making it true that it is contingent that Armstrong exists? And couldn't it be the case that it only does the work because of something that is true of all beings of his type? Couldn't it be that he is contingent only because he is a human (which he makes true) and that all humans are contingent (which something besides Armstrong alone makes true, or nothing at all makes true)? This suggestion seems plausible as well.

¹³Another way of stating the same desideratum is that truthbearers must be about the truthmakers that make them true. See, for instance, Merricks 2007: 28–34] and Lewis 2005: 25].

¹⁴That modal truths are themselves necessarily true follows from the S5 system.

¹⁵I owe this objection to Joe Salerno.

¹⁶This paper benefited from comments by or discussion with Scott Berman, Marian David, William Demsar, Trent Dougherty, Michael Foland, Jon Jacobs, Faith Glavey Pawl, John Putz, Joe Salerno, Kevin Sharpe, Eleonore Stump, Kevin Timpe, René van Woudenberg, and Bill Wood, and the audience at the 2008 Central States Philosophy Conference, where I presented this paper. Part of the writing of this paper was made possible by a Dissertation Fellowship at the Center for Philosophy of Religion at Notre Dame.