Abstract
Truthmakers, truth conditions, and analyses are closely related, but distinct in rather important ways. A failure to properly appreciate their differences has led to some confusion regarding the role that possible worlds ought to play with respect to modality. Those philosophers who initially proposed the existence of possible worlds were understood as providing an analysis of modality. More recently, many have interpreted them as providing modal truthmakers. But, possible worlds are (at best) only suited to serve as truth conditions for modal truths (or so I will argue). My goals are as follows: First, to dispel this confusion by detailing the differences between these three concepts. Second, to apply the lesson learned to the famous Humphrey objection against possible worlds. While this objection, if successful, does undermine Lewisian modal realism, it only partially undermines ersatzism, and leaves available a route by which ersatzers may avoid the objection altogether.
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Notes
See, for instance: Divers (2002, 106); Ney (2014, 195). In his (2009), Michael Jubien calls this the “fundamental tenet of world theory” (69), citing the “powerful prejudice that any [modal] analysis must somehow involve special entities called possible worlds, whether of Lewis’s variety or any other.” (77)
Or, if you prefer, the state of affairs of the Eiffel Tower’s existing. I will remain agnostic about whether it is the concrete object or the concrete state of affairs that makes the proposition true. However, for brevity, I will use the language of David Armstrong, who opts for the object here, rather than the state of affairs. Armstrong, though generally a proponent of states of affairs, rejects states of affairs of the form The Eiffel Tower’s existing because these treat existence as a property (2004, 4).
These distinctions are partially inspired by Alvin Plantinga’s discussion of analysis in (1987, 214–215). There is also some overlap here with John Divers’ division into what he calls the “semantic”, “conceptual”, and “ontological” applications of possible worlds (2002).
Though, it seems to me that Kripke was reluctant to identify the meaning of a name with its referent. For instance, he writes, “regarding the purely ‘Millian’ picture of naming, where only the referent of the name contributes to what is expressed”, he remarks, “I (and for all I know, even Mill) never intended to go so far.” Later, “I hope the idea of fixing the reference as opposed to actually defining one term as meaning the other is somewhat clear.” 1980, pgs. 20, 60).
Some deny that pain just is C-fibers firing, but nevertheless, pain occurs if and only if C-fibers fire. What sort of analysis are these philosophers offering? It seems to me that they are not offering one at all. Rather, they are offering truth conditions. I will say more about this in §4.
Note that, sometimes, we will be able to give one sort of analysis for a concept or proposition, but not another. Take redness, for instance. While someone like Mary (who has never seen the color red) might grasp the metaphysical analysis of redness (e.g., if redness just is the emission of a wavelength between 620 and 750 nanometers), she does not know what ‘red’ means. This is because a semantic analysis of color is impossible to give. Indeed, in the absence of a semantic analysis of color, the standard way of “defining” various colors is to give only an illustrative analysis rather than a semantic one. For instance, the “definition” of ‘red’ is commonly stated as something like, “The color of ripe tomatoes, blood, or rubies”.
Truthmakers, truth conditions, and analyses each involve a relation; namely, between a truth and its truthmaker, a truth and its necessary and sufficient conditions, and an analysans and its analysandum, respectively.
Can truth-bearers be truthmakers? For example, is the proposition < The Eiffel Tower exists > a suitable truthmaker for < The proposition < The Eiffel Tower exists > exists > ? Perhaps, but I think there are some plausible ways to deny this. We could for instance: (1) Choose not to remain agnostic about Armstrong’s claim (see note 2) and argue that the truthmaker for the latter truth is not the former proposition itself, but rather the state of affairs of that proposition’s existing. (2) Claim that the truthmaker for both < The Eiffel Tower exists > and < The proposition < The Eiffel Tower exists > exists > is just the concrete object, the actual Eiffel Tower.
What, then, should we make of T-schema propositions, e.g., <‘Snow is white’ is true iff snow is white > ? We may be tempted to claim that the right side of this biconditional is a state of affairs rather than a proposition. But, this would be a mistake. The iff operator operates only on statements, which have truth-values. As such, both sides of the bi-conditional must be the same in kind (namely, they are both truth-bearers; e.g., propositions). As Armstrong points out (2004, 17), a truth condition is “to be sharply distinguished from the notion of a truthmaker—a truth-condition is no more than a proposition.”
For agreement, see Julian Dodd’s discussion of why “such grounding is asymmetrical” (2007, 393).
If it seems to the reader that the relation is not symmetric, this may be due to one of the following reasons:
(i) First, consider my claim that < x is an unmarried male > is the truth condition for < x is a bachelor>. One might point out that the first proposition is more basic than the second—and if one of the relata of a relation is more basic, this indicates some asymmetry. This, however, mistakes truth conditions for analyses (the asymmetry of analyses is discussed immediately following this footnote).
(ii) Second, philosophers commonly claim things like “being male is a truth condition for being a bachelor.” But, <x is a bachelor iff x is male > is clearly false. So, since someone cannot be a bachelor without being male, but someone can be male without being a bachelor, the relation cannot be symmetric. It is my position that we are speaking improperly when we speak this way, however. Strictly, if the relation is symmetric (as I suggest), then < x is male > is not a truth condition for < x is a bachelor>. Rather, it is merely a part of some truth condition for that proposition—for instance, the conjunction of < x is male > and < x is unmarried>.
One might be tempted to think that analyses must allow for substitution of analysans for analysandum (and vice versa) in all instances, and that the relation is therefore symmetric. For example, if < Harry is a bachelor > is true, then it follows that < Harry is an unmarried male > is also true. However, this is not always the case. As Graeme Forbes notes (1993, 311), the “substitution of analysans for analysandum can fail to preserve truth-value.” For example, <“Bachelor” is more basic than “unmarried male” > is true. But, it does not follow from this that < “Unmarried male” is more basic than “bachelor” > is also true. Indeed, the latter is false. This the paradox of analysis. In short, it cannot be the case that an analysans is both informative (which is the project of analysis) and also symmetrically related to the analysandum. See also Kripke (1979).
Though they are not important to my project here, there are two other differences worth noting:
(3) Reflexivity: The truthmaker relation is irreflexive. For agreement, see Schaffer (2008, 17), who claims that the truthmaking relation is a grounding relation, and that “Grounding is an asymmetric, irreflexive, and transitive relation.” Truthmakers are portions of reality that are distinct from the truths that they make true. As such, these (non-truth-bearing) portions of reality cannot be the truthmakers of themselves—simply because they are not truth-bearers in the first place (though, some may find it plausible that the proposition, <A proposition exists > is its own truthmaker; see note 8 for further discussion). The truth condition relation is reflexive. Clearly, P is a necessary and sufficient condition for P. That is, <P ↔ P > is true. Analysis is irreflexive. That is, nothing is an analysis of itself. The analysis relation is asymmetric, such that one of the relata is more basic than the other. And nothing can be more basic than itself. (Note that this does not rule out the possibility that some concepts are basic—that is, admitting of no further analysis.)
(4) Necessity: The truthmaker relation is not a necessary one. For, it is contingent in at least one direction. For example, the dog Fido makes true the proposition, <A dog exists>. But, that particular dog (Fido) need not exist in order for that proposition to be true (the dog Sparky would also make it true, for example). Thus, the relation between true propositions and their truthmakers is sometimes contingent—as in the relation between < A dog exists > and the particular dog, Fido. Truthmaker theorists do typically claim that the relation is not contingent in the other direction, however. For example, even though < A dog exists > can be true in the absence of Fido, it is not the case that Fido can exist without making < A dog exists > true (assuming, of course, that Fido is essentially a dog). But, my claim here is only that the truthmaking relation is non-necessitating in at least one direction.
Meanwhile, the truth condition relation is also non-necessitating. For, while some truth conditional claims will be necessary truths—e.g., <x is a bachelor iff x is an unmarried male > —others will not. For instance, <Benjamin Franklin was born in 1706 iff the inventor of the bifocals was born in 1706 > is a contingent truth. By contrast, the analysandum-analysans relation is a necessary one. That is, for any analysandum-analysans pair, it is metaphysically impossible for that analysandum to be irreducible to that analysans. For example, there is no metaphysical possibility where the concept “bachelor” is not reducible to the concepts “unmarried male”, or where water is not H2O.
See also Lewis (ibid., 17–21), where he repeatedly states that he is providing an analysis of modality. I understand this to be a metaphysical analysis. For instance, he tells us that what it is for talking donkeys to be possible is for there to be some world where donkeys talk. Ted Sider also reads Lewis in this way, claiming that, “according to counterpart theory, the property of possibly winning is the property of having a counterpart who wins” (2006, 1). Trenton Merricks confirms this, writing, “the counterpart theorist thinks that O’s having a counterpart that is F is what it is for O to be possibly F. Standing in the relevant counterpart relation is what it is to have the ‘corresponding’ modal property. Thus, counterpart theory is about analyzing modal properties.” (2003, 522, emphasis in original).
Note, however, that Lewis did eventually reject the thesis that possible worlds serve as modal truthmakers—but only because he took issue with the project of truthmaker theory in general. He writes, “I think, the demand for truth-makers is wrong in the first place” (1992, 218), and in his (2001), he explicitly rejects truthmaker theory in favor of the competing thesis that truth supervenes on being.
For, in that case, the truth conditional claim, <Humphrey could have won the election iff at some world, Humphrey’s counterpart wins the election > comes out true. Furthermore, if we endorse truthmaker theory, Humphrey’s victorious counterpart will also be the truthmaker for < Humphrey could have won the election > .
For instance, Michael Loux states, “Not only do we believe that there are many different ways things could be; we take the different ways things could be to constitute the truth makers for our prephilosophical modal beliefs.” (2006, 159) In the Stanford Encyclopedia of Philosophy we find: “Realism about possible worlds in the metaphysics of modality maintains that (i) facts about possible worlds are the truth-makers for modal statements …” (Vaidya, 2015, emphasis in original). For other examples of philosophers who address the issue of abstract possible worlds as modal truthmakers, see: Bigelow and Pargetter (1990, ch. 4); Divers (2002, §3.2); Pruss, (2002, pg. 319); Armstrong (2004, pg. 83); Martin (2008, §§3.3-3.4); Cameron (2008); Jacobs (2010).
In his (1984), Kim writes, “A strongly supervenes on B just in case, necessarily, for each x and each property F in A, if x has F, then there is a property G in B such that x has G, and necessarily if any y has G, it has F.” (165, emphasis in original)
For instance, David Armstrong mentions (1997, 173) that the existence of possible worlds might be grounded in something like this way; if so, they would be what he calls “second-class states of affairs.”
I am of course speaking loosely here. Note that, strictly speaking, it need not be Humphrey himself who makes these propositions true. For, Humphrey is just one of many modal truthmakers for these truths. Consider, for instance, Alexander Pruss’s statement of the dispositionalist view of modal truthmaking:
[I]t is possible that s if and only if either s, or there is something that has the causal capability to make it be that s, or there is something that has the causal capability to make it be that there is something that has the causal capability to make it be that s, or … And we can summarize this by saying that a non-actual state of affairs is made possible by something capable of initiating a chain of causes leading up to that state of affairs. (2011, 213, ellipsis in original)
So, even if Humphrey had never existed, there would still be true modal propositions about him because there would still have existed other objects capable of initiating a causal chain that could have produced Humphrey and the relevant dispositions (e.g., his parents). The idea that truths have multiple, distinct truthmakers is not controversial (for instance, consider that < A dog exists > is made true by Fido, and Sparky, and Lassie, and so on). However, one (potentially counter-intuitive) result of the present proposal is that, in order to preserve an S5 modal logic where every possible world is accessible at every possible world, this dispositionalist view is committed to the claim that every possible world shares some initial causally potent individual(s) in common (see, e.g., Vance, 2014; Vetter, 2015). The result is that it is metaphysically impossible for things to have been entirely different.
Note that possible worlds would still serve as something very much like truthmakers on this view. For, the truth of the proposition < There is a possible world where I am represented as driving a truck > will still entail the truth of < I could have been a truck driver>. It is just that the former would not be the reason that the latter is true, i.e., the former would not be the latter’s truthmaker. Furthermore, though possible worlds serve as neither a semantic nor a metaphysical analysis on this view, they nevertheless still provide an illustrative analysis, since truths about possible worlds will serve to shed some light on our concepts of possibility and necessity.
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Vance, C. Modal Truthmakers, Truth Conditions, and Analyses: or, How to Avoid the Humphrey Objection. Acta Anal 32, 145–159 (2017). https://doi.org/10.1007/s12136-016-0299-7
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DOI: https://doi.org/10.1007/s12136-016-0299-7