The doctrinal approach to truthmaking

We have now settled on an account of what the truthmaking relation is, and hence on what it is to be a truthmaker. Truthmakers are grounding necessitators of purely synthetic truths.65 It is important to appreciate that I have not argued that all purely synthetic truths have truthmakers. I have only argued that if a truth has a truthmaker, then that truth is purely

synthetic. Still, TM has implications for our second basic truthmaking question, the question

of how wide the scope of truthmaking extends. Do all truths have truthmakers, or only some restricted class? We have already encountered the most obvious answer to the question, truthmaker maximalism, according to which all truths have truthmakers. If we proceed with

TM as our account of truthmaking (as I think we should), full bore maximalism is off the

table. But stepping back from our adoption of TM and its implications for the scope of

65_{I use the language of ‘grounds’ here as the inverse of ‘depends’, since nothing else is available. Where A}

depends upon B, B grounds A. I am not thereby assuming the loaded notions of ground found in Kit Fine (2001) and Schaffer (2010).

truthmaking, let us now consider some of the answers others have offered to our second question, so as to better appreciate the landscape of the truthmaking literature.

First, it seems that no one should be an advocate of truthmaker nihilism—the view that there are no truthmakers. As we have already seen, everything is a truthmaker. Take some existing object x. It is true that x exists. Further, x is a truthmaker for that x exists,

regardless of what one specifically thinks about the truthmaking relation.66 So every existing object is a truthmaker. Everything there is is a truthmaker. As noted above, truthmakers are not a special kind of entity—they’re any entity whatsoever. Consequently, the only

sustainable way to think that there are no truthmakers is to think (falsely, it goes without saying) that nothing exists.67

Truthmaker maximalism is often taken to be the heart of truthmaker theory.68 Frequently, in fact, “truthmaker theory” or “the truthmaker principle” is identified with truthmaker maximalism. For example, Milne writes: “Truthmaker theory maintains that for every truth there is something, some thing, some entity, that makes it true” (2005: 221). Marian David offers: “The truth-maker principle says that for every truth there is something

66_{To my knowledge, Schaffer is the only author who disagrees with this argument, but his disagreement is}

motivated by his other metaphysical interests (i.e., priority monism) (2010).

67_{Rodriguez-Pereyra writes that “many people believe that there are no truthmakers and so that there is nothing}

in virtue of which true propositions are true” (2006c: 961). Rodriguez-Pereyra does not name names, but I am genuinely curious to hear how they would respond to the utterly uncontroversial argument of this paragraph. My guess is that any self-proclaimed truthmaker nihilist is simply dissociating himself from some non-existent strawman truthmaker theorist. Perhaps Rodriguez-Pereyra has Davidson in mind, who once claimed that “Nothing, however, no thing makes sentences and theories true” (1973-1974: 16). Davidson is here expressing

his distaste for factive entities, among others (cf. Strawson 1950: 134-135). We know better, for truthmakers are not limited to facts. Understood in our sense, everything that exists makes some truth true. Maybe not all truths are made true in virtue of something, but it is beyond all doubt that some truths stand in the truthmaking relation.

68_{Advocates of maximalism include George Molnar (2000), Cameron (2008d), Schaffer (2010), and of course}

Armstrong (e.g., 2004). Julian Dodd (2002) and Merricks (2007) think that advocates of truthmaking should be

that makes it true, that every truth has a truth-maker” (2009: 137).69 Maximalism obviously accompanies significant theoretical simplicity. But it runs into trouble in certain cases, most infamously negative truths. Consider, for example, the true negative existential that there are no unicorns.70 A natural thought is that that there are no unicorns is true not in virtue of the

existence of anything, but precisely because nothing of a certain kind exists.71 If it does have a truthmaker, it’s highly contentious what it would be. Historically speaking, the debate over negative truths, and whether we must accept negative facts for them to correspond to, is already present in Russell (1985) and Wittgenstein (1921). Russell countenanced negative facts;72 Wittgenstein abhorred them. Nowadays, many take negative truths to be

counterexamples to maximalism.73 For them, negative existentials are one source of

truthmaker gaps. Others are more cavalier. As we have seen, Armstrong (following Russell 1985) expands his ontology with a totality state of affairs to find a truthmaker for negative existentials. Others try to make do with more meager resources, finding truthmakers for negative truths without turning to totality facts or negative facts.74 Stephen Mumford

69_{See also Kierland and Monton 2007: 489.} 70_{Throughout this work, I shall be supposing,}

contra Kripke 1972, that that there are no unicorns is only

contingently true. It strikes me that there is overwhelming linguistic evidence that unicorns are a perfectly possible creature.

71_{Cf. Pendlebury 2010: 142.}

72_{In so doing, Russell reports having “nearly produced a riot” at a seminar at Harvard (1985: 74). JC Beall}

(2000) and Dale Jacquette (2010) have recently taken them up.

73_{For instance, Mulligan, Simons, and Smith 1984, Bigelow 1988, Lewis 1992 and 2001b, Linsky 1994, Smith}

1999, Dodd 2002 and 2007, Mellor 2003, Cameron 2005, Melia 2005, Mumford 2005, Simons 2005 and 2007a, Parsons 2006, and Merricks 2007.

74_{For instance, Demos 1917, van Fraassen 1969, Pendlebury 1986 and 2010, Hochberg 1994, Martin 1996, Heil}

2000, Lewis and Rosen 2003, McGrath 2003, Cheyne and Pigden 2006, Kukso 2006, Cameron 2008a, and Veber 2008.

preserves maximalism by denying the existence of negative truths (2007a and 2007b).75 Some just end up in aporia (Molnar 2000). Here is Rodriguez-Pereyra: “one also has to find

a truthmaker, for instance, for negative existential truths, like the truth that there are no penguins in the Northern Pole. What that truthmaker is, I don’t claim to know. All I claim is that there must be one” (2005: 31).

Those who retreat from maximalism endorse the existence of truthmaker gaps: truths that lack truthmakers. In so doing, however, they do not automatically abandon the

truthmaking enterprise. Several theorists, although they reject maximalism, endorse a different thesis that they claim to be the essence of truthmaker theory. John Bigelow (1988) and Lewis (at least in his 2001b)76 advocate the view that while some truths lack truthmakers, truths nevertheless supervene on being.77That there are no Arctic penguins is true not in

virtue of the existence of some particular thing, but is nonetheless true in virtue of the way the world is. Thus, if two worlds W1 and W2 differ with respect to the truth of that there are

no Arctic penguins, the difference obviously must involve there being Arctic penguins in one,

but not the other. But in the world with no Arctic penguins, that there are no Arctic penguins

is not made true by anything existing in the world, contra Armstrong. It is true in virtue of

the fact that the world lacks any falsemakers—namely, Arctic penguins—for it. Bigelow and Lewis disagree on how to formulate their shared idea. Bigelow thinks that the difference must be one of existence—if two worlds are distinct in terms of what is true, that is because something exists in one of them but not the other. For Lewis, if two worlds are distinct in terms of what is true, that is because either there is a difference in what exists, or a difference

75_{I have a hard time seeing how Mumford’s view is even coherent. For a brief refutation, see Simons 2007a.} 76_{But see Lewis 2003 and Lewis and Rosen 2003 for a maximalist application of Lewis’s later approach to}

truthmaking that stands as his last word on the topic.

in the distribution of properties and relations among the things that do exist. (So, contra

Bigelow, two worlds could agree on what exists, but be distinct nonetheless.) Bigelow’s principle relieves him of the need to offer truthmakers for negative truths; Lewis’s principle, in addition, relieves him of the need to offer truthmakers for contingent predications.78

We may next acknowledge other advocates of truthmaking who subscribe to neither of the above views, which Chris Daly describes as “stronger” and “weaker” versions of the truthmaker principle (2005: 85). Mulligan, Simons, and Smith advocate the view that only atomic truths have truthmakers (1984; Linsky 1994 agrees), whereas Rodriguez-Pereyra thinks that “necessarily the members of an important class of synthetic true propositions, including inessential predications, have truthmakers” (2005: 18).79 Roy Sorensen defines the “truthmaker principle” as the thesis that “for each contingent truth there must be something in the world that makes it true” (2001: 171).80 Barry Smith (1999) also considers a restricted view of truthmaking. So we seem to have several different ways that truthmakers have been advocated. We have those who, with Armstrong, believe that all truths have truthmakers. We have those like Bigelow and Lewis (2001b) who think that truths supervene on being, a view entailed by but not entailing Armstrong’s stronger view. Finally, we have those who argue for various restricted versions of truthmaking—some, but not all truths have truthmakers.81,82

78_{Note that Armstrong’s maximalism is stronger than the other two’s views, such that he too thinks that truth}

supervenes on being.

79_{Notice also that Rodriguez-Pereyra adds necessity to his truthmaker principle. Other writers tend not to}

modalize the various truthmaker principles. Nothing will turn on the issue in what follows.

80_{See also Armstrong 1989b: 88.}

81_{The Bigelow/Lewis view is also a kind of restricted view of truthmaking, but is often discussed separately}

from the other restricted views (as in Merricks 2007). So I too shall distinguish it from the others.

82_{Beware also of the ambiguity in the literature behind ‘the truthmaker principle’. Most commonly, it is taken to}