We have now seen several flawed reasons for advocating a separation of labor between truth and truthmaking. Merricks’s reasoning, however, was close to the truth. Truthmaker theorists, we argue, are best understood as not offering an analysis of truth. Still,
certain truthmaker theorists disagree with Merricks and me here, and respond that they do indeed intend the notion of having a truthmaker to be giving an analysis of what it is to be true.32 As with X5 above, to be true just is to have a truthmaker. This route, however, is
unavailable to the truthmaker theorist. The reason is quite simple: the truthmaking relation itself must be defined in terms of truth. So truthmaking already presupposes the notion of truth; to rely on truthmaking to offer an analysis of truth would be to admit a viciously circular analysis.33 Turning back to the last chapter, one can notice that all of the accounts of the truthmaking relation given there employ either ‘is true’ or ‘truth’. Further, any other account of the truthmaking relation is going to involve truth, for it must account for the truth
of truth-bearers, and not their other features. Accordingly, truthmaker theory cannot offer an analysis of truth, for it must already presuppose one.34
To see why truthmaker theory itself is not in the business of offering a theory of truth, consider first that truthmaker maximalism—the thesis that every truth has a truthmaker— would have to be not only true but a necessary part of truthmaker theory itself if truthmaker theory were to offer a theory of truth. If truth consists (at least in part) in having a truthmaker,
32See again all those authors cited in section 2.1.
33Merricks himself also makes this point (2007: 15), but doesn’t explore it as deeply as I am about to. Cf. David
2009: 144 and Schulte Forthcoming: 8.
34Armstrong also recognizes this fact, and as a result refrains from calling his “theory of the nature of truth” a
definition of truth (2004: 17). Instead, he thinks his truthmaker principle offers necessary and sufficient
conditions for something to be true. Armstrong goes on to express sympathy with (something like) a primitive conception of truth.
then every truth would have to have a truthmaker.35 Otherwise there would be truths whose truth could not be accounted for by truthmaking. But maximalism is not a sine qua non of
truthmaker theory, and so truthmaker theory by itself offers no theory of truth.36
As we have already seen, many truthmaker theorists reject maximalism (e.g., Bigelow 1988 and Lewis 2001b), though of course the matter is controversial. The paradigm
counterexamples of truthmaker gaps—truths without truthmakers—are negative existentials.
It is true that there are no hobbits, but perhaps it need not follow that there exists something making it true that there are no hobbits. To think otherwise is to suppose that one must ground one’s “atheism” (about hobbits) with a separate kind of “theism” (about, say, negative facts, absences, or totalities)37. Regardless of whether this stance is the correct response to the problem of negative existentials, it is a defensible one, and one available to truthmaker theorists. Since one may be a truthmaker theorist without being a maximalist, truthmaker theorists qua truthmaker theorists are not in the business of offering a theory of
truth.
Now, some philosophers think that in abandoning maximalism, we abandon
truthmaker theory altogether.38 On such a view, there simply is no room in truthmaker theory for non-maximalism. George Molnar writes that admitting that some truths do not have truthmakers is “the way of ontological frivolousness. It is a truly desperate resort” (2000: 85). But this response is too quick. The foundational idea underlying truthmaker theory is that truth depends upon reality. Truths are true in virtue of the way the world is. Negative
35Cf. Smith and Simon 2007.
36Armstrong even claims that “most” truthmaker theorists reject maximalism, though he thinks they incur a
substantial theoretical debt by doing so (2006: 245).
37See, respectively, Russell 1985, Martin 1996, and Armstrong 2004. 38See, for instance, Cameron 2008a: 412.
existentials do depend upon the way of the world for their truth—they depend on there not being any of the relevant things around. The case is very different for the suspicious phenomenalist and behaviorist counterfactuals that motivated contemporary truthmaker theory in the first place.39 Here philosophers were positing truths that depended in no way upon the world for their truth.40 But such counterfactuals are nothing like the negative truths involving hobbits or Arctic penguins. The latter are still true in virtue of the way of the world, even if no particular entities exist that necessitate those truths. The truth that there are no Arctic penguins admits of a perfectly worldly explanation; its truth is no metaphysical mystery. Not all truthmaker gaps, then, are alike. Some are offensive to the spirit of
truthmaking; others are not.41 So there are good reasons for rejecting truthmaker maximalism that are not reasons for rejecting truthmaker theory itself. Since rejecting maximalism is no automatic offense to truthmaker theory, it follows that truthmaker theory is not in the business of giving a theory of truth.
Putting truthmaking to work as a theory of truth requires a commitment to
maximalism. But not even maximalists can employ truthmaking in order to adequately say what truth is, for the truthmaking relation itself must be defined in terms of truth, and so any such analysis is circular. As we have seen, all of the accounts in the literature regarding the nature of the truthmaking relation (including the one for which I have argued) employ an antecedent notion of truth. For most, truthmaking is (at least) a matter of necessitation: x is a
truthmaker for y only if it is metaphysically necessary that if x exists, then y is true. Hence,
the necessitation condition already employs the notion of truth. The other approaches share
39See Armstrong 2004: 1-3.
40A recent defense of truthmaker-less counterfactuals can be found in Lange 2009, which employs them in
defending an account of the laws of nature.
this same feature. Any yet-to-be-defended account of the truthmaking relation is going to have to involve truth, for it must account for the truth of truth-bearers, and not their other
features. On pain of circularity, anyone trying to build a theory of truth from a theory of truthmaking must somehow dispense with truth from the notion of truthmaking.
Perhaps the advocates of a “truthmaker theory of truth” might respond by accepting the circularity point, but persisting in thinking that their theories still constitute a kind of correspondence theory. Such a theorist might simply identify the truthmaking relation with the correspondence relation, and identify the class of truthmakers as the class of
corresponding objects (which may or may not be limited to facts or states of affairs, if such things are included at all). Here we have a many-many correspondence relation, and a class of correspondents that need not be limited solely to facts; perhaps this is what Oliver has in mind by a “sanitised” correspondence theory. Indeed, Armstrong sometimes thinks of his truthmaker theory in just these terms (1997: 128). Can truthmaker theorists of this sort think of their theory as being a kind of correspondence theory? Such theorists can call their view whatever they want, but must realize that their “correspondence theory” is not in fact a theory of truth, if such theories aim to be non-circular analyses of the property of truth (as are all the traditional theories of truth).42 The circularity worry is avoided, in other words, only if we accept that the new “correspondence theory” on offer is not actually a theory of truth. For as
we have seen, the truthmaking relation presupposes the notion of truth, and so any
correspondence relation that is itself the truthmaking relation already presupposes the notion of truth. I have been assuming that correspondence theories of truth do aim to reveal the nature of truth in this way. If correspondence theory just is truthmaker theory, so be it. But
42Of course, many things might be meant by ‘theory of truth’, and I have no interest in arguing that truthmaker
theory cannot offer a theory of truth in any sense whatsoever. Nevertheless, what I mean by an adequate theory
then we should not think of correspondence theories as being theories of truth in the traditional sense.
It might also be thought that the appearance of truth in the above accounts is innocuous, and that it can be dispensed with by utilizing a familiar maneuver from the deflationist’s toolkit. For deflationary theories of truth, ‘true’ is primarily a logical device useful for expressing generalizations (among other things), and is not used to predicate a substantive property that admits of further metaphysical analysis (as correspondence and coherentist accounts hold). For instance, instead of reasserting each and every individual thing that Kant ever wrote, I can simply say that everything that Kant wrote is true.
Substantive theorists of truth can acknowledge such logical features of the truth predicate, so long as they reject the thesis distinctive to deflationism that such logical features exhaust all
there is to be said about truth. So we might hold that we can give an account of the
truthmaking relation that relies on ‘true’ only as a device for generalization,43 and that hence can emerge truth-free.
This deflationist-inspired response, however, is not available to those who seek to use their truthmaker theory for revealing the nature of truth.44 For expository purposes, let us stick with the necessitation condition on truthmaking:
(N) For all x and y, x is a truthmaker for y only if it is metaphysically necessary
that if x exists, then y is true.
Equipped with N, we may use it in giving a necessary condition for our truthmaking account
of truth:
43For the generalizing role of ‘true’ in truthmaker theory, see Fox 1987: 189, Bigelow 1988: 125-127, Lewis
2001a: 278 and 2001b: 603-604, and Künne 2003: 164.
44 It is a perfectly fine response for those who are
deflationists about truth and want to understand the axioms of
(TT1) For all y, y is true only if there exists some x such that it is metaphysically
necessary that if x exists, then y is true.
Noticing the way that ‘is true’ is redundant, we may turn TT1 into:
(TT2) For all y, y is true only if there exists some x such that it is metaphysically
necessary that if x exists, then y.
TT2 avoids TT1’s use of ‘true’, but at the cost of unintelligibility. The quantifier
accompanying ‘x’ is the ordinary objectual quantifier. If we also quantify over ‘y’
objectually—substituting it with truth-bearers like sentences, beliefs, and propositions—then the final substitution will fail. We would have the following bit of nonsense as an instance:
(1) ‘Bill will kill Jill’ is true only if there exists some x such that it is
metaphysically necessary that if x exists, then ‘Bill will kill Jill’.
What we need at the end of the instance is a used sentence, not a mentioned one. For example: (2) ‘Bill will kill Jill’ is true only if there exists some x such that it is
metaphysically necessary that if x exists, then Bill will kill Jill.
In order to derive axioms like 2, we need to transform TT2 into:
(TT3) For all y, ‘y’ is true only if there exists some x such that it is metaphysically
necessary that if x exists, then y.45
To interpret TT3, we need to employ both objectual quantification (for ‘x’) and substitutional
quantification, for ‘y’ is now varying over sentential expressions. (Otherwise we would be
unintelligibly quantifying objects into quotes.)
There is a serious problem, however, with resorting to substitutional quantification here: the traditional semantics given for the substitutional quantifiers already employs the notion of truth. As Horwich notes: “the notion of substitutional quantification is trivially interdefinable with that of truth and itself requires theoretical elucidation” (1990: 27; see also Kripke 1976).A particular substitutionally quantified sentence ‘Σx(…x…)’ is true if and only
45
TT3 is built for sentences. We could replace the ‘‘y’’ with ‘the proposition that y’ for a propositional version,
if there is an expression (from the relevant substitution class) such that substituting it for ‘x’
in ‘…x…’ yields a true sentence. A universally substitutionally quantified sentence
‘Πx(…x…)’ is true if and only if every expression (from the relevant substitution class) is
such that substituting it for ‘x’ in ‘…x…’ yields a true sentence. Employing substitutional
quantification to define the truthmaking relation still leaves us with an explicitly circular definition of truth.46 Thus, in order to rely on something like TT3 to offer a truth-free
truthmaker theory of truth, we have to formulate an account of substitutional quantification that in turn does not rely on the notion of truth.47, 48
Perhaps the answer for the truthmaker theorist seeking to analyze truth in terms of truthmaking lies not in substitutional quantification, but in infinite lists. Horwich (1990) thinks that truth cannot be defined finitely because he rejects as circular any substitutionally quantified truth schema. Truth is defined instead by the T-sentences, the infinitely many non- paradoxical instances of the propositional truth schema: the proposition that p is true if and
only if p. Perhaps we can do the same for TT1. Even if we cannot adequately remove ‘is true’
46It has been pointed out to me by an anonymous referee for a related paper that defining truth in terms of
objectual quantification, or even any logical connective for that matter, will also result in circularity as these notions may also need to be defined in terms of truth. If so, then there is no special problem with substitutional quantification. If these other logical notions are also defined in terms of truth, then so much the worse for
anyone trying to define truth, including truthmaker theorists. I take this to be a strong argument in favor of
primitivism.
47Christopher Hill (2002) has attempted such a project in his recent work (though his interests are disconnected
from truthmaking). His aim is to offer an inferentialist treatment of substitutional quantification. This is not the place to evaluate Hill’s proposal in full (see Simmons 2006 for more criticism), but I have some initial doubts. One may well wonder whether the notion of inference will admit of a full elucidation without somehow relying on truth. It seems like inference is just another notion that we can make better sense of if we have a notion of truth already in hand. Regardless of the success of a project like Hill’s, truthmaker theorists who want their theory to serve double duty as a theory of truth have a steep hill to climb here (no pun intended).
48One might respond by rejecting the semantics for the substitutional quantifiers given here, and taking them
instead as logical primitives. (Thanks to Thomas Hofweber and Jody Azzouni for pointing out this response.) This maneuver does indeed sidestep the circularity worry, but invokes a theoretical primitive that requires some further theoretical justification. It’s unclear what could motivate taking on this additional primitive, given that the advocate of TT3 doesn’t get to say anything above and beyond what a deflationist who accepts truthmaker
from TT1, we can take its instances, pair them with the T-sentences, and derive both 2 and
the following:
(3) ‘Jill will kill Bill’ is true only if there exists some x such that it is
metaphysically necessary that if x exists, then Jill will kill Bill.
(4) ‘Jill will thrill Bill’ is true only if there exists some x such that it is
metaphysically necessary that if x exists, then Jill will thrill Bill.
Here we have some of the needed non-circular axioms of our truthmaker theory of truth. One could point to 2, 3, 4, and countless others and suggest that they are the key to understanding
the nature of truth, just as Horwich points to the list of T-sentences and says that they are the key to understanding the nature of truth. Call this view ‘TT4’.
TT4 faces three major difficulties. First, anyone who advocates such a view
relinquishes the ability to give a finitely stateable theory of truth, a common desideratum for non-deflationary theories of truth.49 By “going infinite”, a view concedes that nothing in general can be said about a particular notion—truth may be defined only implicitly, not
explicitly. Such an attitude is appropriate for deflationary views of truth that deny that there is anything in common between truths.50 Substantive theories of truth, however, do hold that there are important commonalities between truths, and thus the absence of an explicit, general statement of what it is in which truth consists is a serious shortcoming.51
49See David 1994: 107-110.
50Which is not to say that all deflationists are happy with the infinite approach. See Hill 2002 and Künne 2003. 51There is another closely related worry about pairing a substantive theory of truth with the infinite list approach.
If truth is defined by or in conjunction with an infinity of T-sentences, then truth appears to be defined in terms of all the many notions that appear in those T-sentences. This lead Anil Gupta to charge that, according to infinitary deflationists, “an understanding of ‘true’ requires the possession of massive conceptual resources” (1993: 69). In short, you don’t understand truth unless you understand everything. Deflationists may well find
something right in this conclusion: you don’t understand the truth of ‘Electrons are negatively charged’ unless you understand what electrons and negative charge are, for the truth of ‘Electrons are negatively charged’
consists in nothing more than the negative charge of electrons. Substantivists about truth say that its truth consists in something else (something that is common to all and only truths), like correspondence with the facts
Secondly, T4 exhibits a sort of motivational schizophrenia. Anyone who takes 2, 3, 4,
and their cousins to constitute a theory of truth is advocating a union between anti-
deflationist attitudes about truth (that it has an underlying nature, to be given by truthmaking) with deflationary maneuvers for dispensing with truth. It is deflationists who avail
themselves of infinite lists, not those who think that the nature of truth can be analyzed into further, more basic notions. The tension between these competing attitudes can best be