Abstract
Identifying plausible truthmakers for negative truths has been a serious and perennial problem for truthmaker theory. I argue here that negative truths (in particular contingent negative existential truths) are indeed made true but not in the way that positive truths are. I rely on a distinction between “existence-independence” and “variation-independence” drawn by Hoffman and Horvath (2008) to characterize the unique form of dependence negative truths exhibit on reality. The notion of variation-independence is then used to motivate a principle of truthmaking for contingent negative truths.
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Notes
I will abbreviate “the proposition that...” with angle brackets \(<\),\(>\).
Armstrong (2004, p. 6), Smith (1999, p. 276), Fox (1987, p. 189), Rodriguez-Pereyra (2005, p. 18), Lowe (2009, p. 209), Molnar (2000, p. 83), and Cameron (2008, p. 413) accept Necessitarianism. Not everyone agrees that truthmaking is or involves necessitation, e.g., Cameron (2005), Schaffer (2010b, p. 311), Parsons (1999, Sect. 2.1), and Heil (2000, p. 233). Briggs (2012) develops a sophisticated view of truthmaking without necessitation.
Below, in footnote 26, I will give some reasons for why I focus on contingent negative truths.
Another dissimilarity between \(<\)there are no unicorns\(>\) and \(<\)the ball is red\(>\) is that the difference between a world in which \(<\)there are not unicorns\(>\) is true and one in which it is false is a difference in what exists, unlike the case with \(<\)the ball is red\(>\) (if Dodd is correct).
See Bennett (2011, p. 188ff.) on “case-making.” Answering the question ‘what explains why \(<\)there are no unicorns\(>\) is true?’ with ‘that there are no unicorns’ leads naturally to the question ‘what makes it the case that there are no unicorns?’ It is not obviously implausible to think that this question could be answered in terms what there is and how it is. So I don’t see why it is always “confused” or “perverse” to try to account for negative truth in terms of what exists as Melia (2005, p. 69) and Merricks (2007, p. 66) say, respectively.
Perhaps there are other ways to understand ‘how things are,’ ‘depends,’ and ‘being’ than the ones I’m considering. Merricks says that truth “trivially” depends on being. He writes, “That hobbits do not exist is true because hobbits do not exist. And so on. And so we might say that truth ‘depends on the world’. But such ‘dependence’ is trivial” (2007, p. xiii). Merricks never explains the distinction between substantial and trivial dependence. See Bennett (2011, p. 188ff.) for discussion. Similarly, Smith and Simon (2007, pp. 81–82) imply that there is a non-literal way of understanding the phrase ‘a way the world is,’ but the notion is never explained. Hornsby (2005, p. 44) and Dodd (2007, pp. 396–400) suggest that the dependence of truth on being is, in some sense, conceptual. Both explain the asymmetry between ‘\(<\)p\(>\) is true’ and ‘\(p\)’ in terms of the latter being conceptually more basic than the former; it takes less to understand the latter than the former (which involves the notions ‘true’ and ‘proposition’). Prima facie, it is hard to see how conceptual asymmetries can serve to explicate the dependence of truth on being, since presumably being is not conceptual in nature. However, Dodd (2007, pp. 399–400) claims that the conceptual asymmetry between ‘\(<a\) is F\(>\) is true’ and ‘\(a\) is F’ “is a counterpart of” the identity dependence between \(<a\) is F\(>\) and its constituents \(a\) and F. Yet even if the identity dependence between \(<a\) is F\(>\) and its constituents serves to explain how the truth of \(<\)a is F\(>\) depends on being, Dodd says nothing about how to apply this to negative truths. Semantic descent from ‘\(<\)a is F\(>\) is true’ leads us to \(a\) and F, but to what does semantic descent from ‘\(<\)there are no unicorns\(>\) is true’ lead? If it leads to nothing, then the appeal to conceptual asymmetries reflecting identity dependencies in the world has not explained how \(<\)there are no unicorns\(>\) depends for its truth on being.
The thesis that all truths have truthmakers (“Truthmaker Maximalism”) is controversial and has been challenges on a variety of fronts. A number of authors hold that negative truths do not need truthmakers, e.g., Lewis (1999, p. 204), Melia (2005, p. 69), Mellor (2003, p. 213), Merricks (2007, p. 66), Mulligan, et al. (1984, p. 315), Saenz (2014, p. 92ff.), and Simons (2005, p. 255ff.). It is not feasible to address all these arguments, which is why below I condition my thesis on the acceptance of, or at least sympathy for, truthmaker theory. Nevertheless, there are arguments for Maximalism that should be mentioned. Cameron (2008, p. 411) argues that once we’ve absolved some truths from needing truthmakers, there is no motivation for thinking that any truth needs a truthmaker (which he regards as implausible). Fiocco (2013, p. 14ff.) argues that denying that a truth has a truthmaker leads to a contradiction. Jago (2012, Sect. 4) argues that non-Maximalism collapses into Maximalism because the former is committed to truthmakers for negative truths that are entailed by certain positive truths. Rodriguez-Pereyra (2005) argues that truths are grounded in what there is since grounding is a relation and relations relate entities. (See Hornsby (2005) for response and Rodriguez-Pereyra (2009) for rejoinder.) Finally, some have suggested that an unpalatable consequence of non-Maximalism is a commitment to a dualistic view of truth itself where we have grounded and ungrounded truth. See my (ms.) for this argument. Barker and Jago (2012, p. 136) also flag this as a consequence of non-Maximalism. Saenz (ms.), a non-Maximalist, recognizes and embraces this consequence of the view.
Or perhaps, if your only reservation about truthmakers for negatives is the lack of attractive positions currently on offer, then the following is a promising account of how negative truths depend on what exists in the world beyond them.
Cf. Molnar (2000, p. 72). Molnar (2000, p. 72ff.) worries that we cannot identify a formal criterion for distinguishing positive from negative truths, but holds out hope that we will be able to identify which predicates pick out positive properties, something which can only be done via an a posteriori investigation into what properties there are. While drawing the distinction between positive and negative truths may be difficult, denying the distinction is a substantive, unintuitive, and controversial position. The assumption that there is a distinction between positive and negative truths should be considered the default position given that both proponents and detractors of Maximalism rely on the distinction. Proponents of Maximalism often attribute importantly different truthmakers to positive truths than they do negative truths (e.g., Cameron (2008, pp. 413, 418) and Armstrong (2004, Chaps. 5 and 6). Moreover, if there weren’t a distinction between positive and negative truths, then it would not be clear why truthmaker theorists (or correspondence theorists of truth) face the challenge of providing negative truths with truthmakers (or correspondents), a challenge they clearly do seem to face. Those who deny that negative truths have truthmakers (e.g., Lewis (2001, p. 610), Bigelow (1988, p. 133), Smith and Simon (2007, pp. 255–256), and Mellor (2003, p. 213)) are committed to a distinction between negative truths and other truths, for they must have some criteria with which to distinguish those truths without truthmakers from the others. Mumford (2005, 2007) is one of the few to bite the bullet and deny the existence of negative truths altogether. However, his denial is primarily motivated by the problem of providing truthmakers for negatives rather than any difficulty with drawing the positive/negative truth distinction (2007, p. 46). This provides prima facie justification for the assumption that there is a distinction between positive and negative propositions.
Even Armstrong, Maximalism’s most prominent defender, admits “the truth-maker principle seems to me to be fairly obvious once attention is drawn to it, but I do not know how to argue for it further” (1989, p. 89). See footnote 9 above for a list of other attempts to argue for Maximalism. See footnote 35 below on some problems facing arguments for Necessitarianism.
This example casts doubt on the thought that false propositions are only ever false because they lack truthmakers. See Schaffer, for instance, who says “falsehoods are false because they lack a (successful) truthmaker” (2010b, p. 317).
Different entities may ‘make a difference’ to the truth-value of different propositions in different ways. For example, \(<\)Fido exists\(>\) is existence-dependent on Fido the dog, since neither (b) nor (c) are possible with respect to this proposition and Fido. Similarly, \(<\)some dogs exist\(>\) is existence-dependent on Fido because (b) is not possible with respect to this proposition and entity. But unlike the previous example, (c) is possible for \(<\)some dogs exist\(>\) and Fido, since this proposition is true as long as some dog or other exists. The difference in these two cases tracks the difference between rigid and non-rigid or generic dependence. \(<\)Fido exists\(>\) rigidly depends for its truth on Fido since it is true in virtue of Fido being the very entity he is. On the other hand, \(<\)some dogs exist\(>\) generically depends for its truth on Fido because it is true in virtue of Fido being a dog. When a proposition/entity pair fails (b) and (c), then the proposition rigidly depends upon the entity for its truth; when a proposition/entity pair fails only (b), then the proposition generically depends upon the entity for its truth. It is also important to note that being existence-dependent upon an entity is not sufficient for truthmaking. \(<\)The rose is red\(>\), for instance, existence-depends on the individual rose because (c) is not possible with respect to this proposition and the rose. But most do not consider the rose to be a plausible truthmaker for this proposition, since it’s possible for the rose to exist and the proposition be false, i.e., (b) is possible. At best, when a proposition/entity pair fails only (c), the entity helps make the proposition true.
See Schaffer (2008), Audi (2012a, b), and Fine (2012) for accounts of grounding. See Lowe (2009), Fine (1995), and Koslicki (2012) on ontological dependence. Thanks to an anonymous referee and Noël Saenz for encouraging me to clarify that existence-dependence should not be defined purely in modal terms.
Hofmann and Horvath draw the existence/variation independence distinction to defend the notion of metaphysical analyticity. They suggest that analytic truths are variation but not existence independent of reality, just the reverse of what I’m suggesting for negative existential truths. I am unsure whether they would endorse the use to which I’m putting their distinction.
A “variation” in \(x\), let us say, is some change in \(x\), i.e., gaining or losing a property, relation, or part. We should not, I think, include \(x\)’s coming into or going out of existence as a change in \(x\). If we did, then every instance of existence-dependence would also be an instance of variation-independence. This restriction on what counts as a change allows us to say that \(p\)’s being existence-dependent on \(x\) for its truth-value does not entail \(p\)’s being variation-dependent on \(x\) for its truth-value.
I’ll use ‘being,’ ‘reality as a whole,’ and ‘the world’ interchangeably in this paper. More on how I am using ‘the world’ below.
Cf. Hofmann and Horvath (2008, p. 306).
My primary aim is for TMn to capture the way in which negative existential truths are made true. However, TMn can be applied to contingent negative predications such as \(<\)liquid L has no odor\(>\). Plausibly, this proposition is about liquid L and it would only be in virtue of a change in L that the proposition would be false. The relevant change would be a change in L’s olfactory qualities. This would be a change in existence since L’s coming to have the property smelling sulfurous is the coming into existence of a state of affairs or a trope. But one might think that the difference is not in what exists, but in how L is. In this case, we would have to consider the nature and scope of falsemaking. See below for a principle of falsemaking.
Can and should TMn be extended to necessary negative existential truths such as \(<\)there are no square circles\(>\)? I think it can be, but only trivially. The second conjunct on the right-hand side of the bi-conditional is equivalent to this conditional: if \(p\) were false, then \(p\) would only be false in virtue of a change in \(x\). Since no necessary negative is false, the antecedent is always false; hence the conditional is always true for the substitution of any necessary negative truth. Despite this, I do not think we should extend TMn to necessary negative truths. Such truths cannot change their truth-values; they are true in spite of any possible change in being. As such, they do not depend for their truth-value on possible variations in what exists, i.e., they do not variation-depend on being. If necessary negative truths are made true, I suspect that their truthmaking involves existence-dependence. Though I do not want to defend this here, it seems reasonable to me to think that \(<\)there are no square circles\(>\) is made true by squares and circles or perhaps the properties being a square and being a circle. Given the nature of these properties, they cannot be instantiated by one and the same thing at the same time. Is it a problem that TMn doesn’t apply to necessary negative truths? Admittedly, it does reduce the unity of the view. On the other hand, some philosophers deny that necessary truths need truthmakers. If they are correct, then TMn provides a unified account of how negatives are made true. But even if they are wrong, contingent negatives have caused enough problems for truthmaker theorists that a solution to their truthmakers would be significant boon to the project. Thanks to an anonymous referee for prompting me to think further about the scope of the account. Another referee for this paper suggested that TMn may face a form of Parmenides’ Paradox for the sentence “There is nothing this sentence is about.” I am inclined to say that the proposition expressed by the sentence—if it in fact expresses any proposition—is just false since it is about itself.
One might be skeptical that \(<\)there are unicorns\(>\) is about any particular unicorn \(U\). Admittedly, \(<\)there are unicorns\(>\) is not about \(U\) in the same way that \(<\) \(U\) exists\(>\) is about \(U\). Still I think we can say that \(<\)there are unicorns\(>\) is about \(U\) in virtue of \(U\) satisfying the predicate ‘being a unicorn’ (or perhaps instantiating the property being a unicorn). \(<\) \(U\) exists\(>\) is, let us say, directly about \(U\), while \(<\)there are unicorns\(>\) is indirectly about \(U\).
I write in terms of the world as a whole changing in time, but we need not make any temporal references to make the point: it is possible for the world to vary by simply having one or more entities than it actually does. So the possibility I’m discussing can be given a temporal or modal reading. The temporal reading is that possibly, the world at time \(\hbox {t}_{2}\) contains one or more entities than the world at \(\hbox {t}_{1}\) (where \(\hbox {t}_{1}\) is earlier than \(\hbox {t}_{2})\). Read modally, it says, possibly, there is a counterpart v of the actual world w that contains everything w contains and some more. See Pawl (2013) of the interaction between principles like these and Truthmaker Necessitarianism.
These are the changes the world would undergo if it simply expanded to include a unicorn and everything else remained the same, e.g., if the world expanded to include an “island universe” (i.e., a universe spatiotemporally disconnected from our universe), a proper part of which is a unicorn. See Parsons (2006, p. 594) for discussion of this possibility and why it entails that the actual configuration of the universe does not necessitate the truth of \(<\)there are no unicorns\(>\). Nevertheless, there may be other ways that the world would be different if unicorns existed. If a unicorn were to exist in my office, certain things would be different, e.g., the configuration of air molecules at a particular location would be different than it in fact is. Perhaps more drastic changes would also be required, e.g., life on earth would have a different evolutionary history than it in fact does, in order to produce unicorns. And if unicorns have magical powers, as their mythology sometimes suggests, then it is likely that the laws of nature would be different too. But if the unicorn exists on some distant, not-yet-discovered planet, then evolutionary history on earth would remain unchanged; the only change would be in the history of that distant planet. In general, the changes undergone by the world needed to make negative existentials false will be more-or-less significant depending upon what the false-maker is, as well as when and where the false-maker comes into existence. However, Kripke (1980, pp. 23–24, 156–158) argues that unicorns and other mythical creatures are not possible objects since their mythology doesn’t specify their essential traits (e.g., genetic makeup, evolutionary history, etc.). If he is right, I would need to change my example of a contingent existential truth— \(<\)there are no unicorns\(>\), which would be necessarily true—to something else, e.g., \(<\)there are no Arctic penguins\(>\). I thank an anonymous referee for raising this issue.
In Lewisian terms, Necessitarians must adopt a “two-way difference-making” principle: if two worlds W and V differ, then at least W contains an entity \(x \) that V does not and V contains an entity \(y\) that W does not (2001, p. 609). This is opposed to a “one-way difference-making” principle that he prefers: two worlds W and V can differ simply by V containing more entities than W.
In my (2012) I give reasons for thinking that these views fail to supply negatives with truthmakers.
This is not to say that the account makes no substantial commitments. In addition to the world, the view requires domains that negative truths are about, the particulars, properties, and relations occupying those domains, and the relation of variation-dependence. Although Briggs (2012) offers a similar account to the one given here (her view eschews Necessitarianism), I prefer mine because it doesn’t require everything that hers does, ontologically (viz. a duplication relation and a counterpart relation) or theoretically (viz. set-theoretical and possible worlds-theoretical frameworks) (Briggs 2012, Sect. 2). See van Fraassen (1995), Simons (2003), and van Inwagen (2002, p. 127) for arguments against thinking the world is an entity. See Varzi (2006) for critical discussion of Simons (2003). Schaffer (2010a, pp. 34–35) gives non-truthmaker related reasons for believing that the world is an entity. First, we have a singular term in natural language—the ‘world’ or the ‘cosmos’—for this entity. Second, common sense recognizes the world as an entity, Third, the world is the object studied by physical cosmology (and other disciplines). Finally, classical mereology contains the axiom of unrestricted composition, which guarantees that there is a world/cosmos, the fusion of all actual objects. Schaffer writes, “But any account of when composition occurs that preserves common sense and fits science should recognize the cosmos. It is only the most radical views of composition—views that do not even recognize tables and chairs—that do not recognize the cosmos” (2010a, pp. 34–35).
See Armstrong (2004, p. 70ff.). Cameron writes, “Why should you believe my claim? Well I’m just doing what the truthmaker theorist always does: urging you to believe in a certain entity with certain essential properties on the grounds that this entity is a suitable truthmaker for otherwise recalcitrant truths” (2008, p. 415). Schaffer should be excluded from this charge. See his (2010a) for non-truthmaker related arguments for priority monism.
Again, this is not to say that none of these accounts are correct. There have been a few attempts to make putative ‘negative’ entities ontologically respectable. See Björnsson (2007) and Barker and Jago (2012) for defenses of negative facts. I have reservations about both accounts. Barker and Jago’s account relies on positing a “tie” of non-mereological composition (cf. Armstrong 1997, p. 122) they call “anti-instantiation” between the constituents of negative facts. They suggest that once we allow for non-mereological composition, negative facts should be no stranger than positive facts. They admit that they don’t clearly distinguishing between instantiation and anti-instantiation (2012, p. 127). But without an explanation of what anti-instantiation is, in what sense it qualifies as a ‘tie’ between objects and properties, or a form of composition, it’s hard to gauge the prospects of the proposal. Concerned with Bradley’s regress, Björnsson denies that there is a further constituent of facts binding together their objects and properties. According to him, “whether an object has a property is an affair internal to the object and the property,” but admits, “The exact nature of this internal affair is beyond the scope of this paper, depending as it does on the exact nature of objects and properties” (2007, p. 13). Although he gestures at some possible ways of understanding this “internal affairs,” each is sketchy and in need of much further development to properly substantiate his thesis. Moreover, Björnsson appeals to Beall’s (2000) notion of a negative “polarity” to explicate his view, a notion that Dodd criticizes in his (2007, Sect. 3). Both accounts of negative facts gain support from the thought that if you’re already committed to positive facts, you ought to be committed to negative facts. If they are right, this may not actually lift prospects of an ontology of negative facts as much as sink those for an ontology facts in general. In that case, truthmaker theorists might wish to opt for tropes as truthmakers.
See Armstrong (2004, pp. 6–7) and Merricks (2007, p. 9) for attempts to argue for the thesis. Armstrong’s argument simply presupposes the need for necessitating truthmakers. Merricks’s first argument (2007, p. 9) only shows that when there are two ‘contenders’ for being truthmaker for a proposition that we should think a necessitating entity is a better candidate for being a truthmaker than a non-necessitating entity. Merricks’s second argument (2007, pp. 9–10) only shows that some truths, e.g., positive existentials, have necessitating truthmakers. He generalizes the argument to all truths on the (unargued) assumption that all truths are made true in the same way.
Lewis supplements Bigelow’s principle by also allowing truth to supervene on what fundamental properties and relation are instantiated in addition to what exists.
These examples are inspired by Smith (1999, p. 278).
See my manuscript “Towards a Pluralist Theory of Truthmaking,” for an introduction to this new approach to truthmaking.
I would like to thank Sven Bernecker, M. Oreste Fiocco, Joshua Rasmussen, Brad Rettler, Noël Saenz, Jonathan Schaffer, Gila Sher, David W. Smith, Cory Wright, and audiences at the 2014 Eastern and Pacific APA meetings for their helpful questions and comments on earlier drafts of this paper.
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Griffith, A.M. How negative truths are made true. Synthese 192, 317–335 (2015). https://doi.org/10.1007/s11229-014-0570-7
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DOI: https://doi.org/10.1007/s11229-014-0570-7