1. Truthmaking and Truthmakers
1.5. Appendix: truthmakers and truth-conditions
Thus far, our investigations have been thoroughly metaphysical. To embrace a collection of truthmakers is to embrace a metaphysics. Still, it will be worthwhile to explore
98Obviously I am presupposing that the notion of explanation is contextual. But how can that be denied? The
contextual nature of explanation should be recognized for what it is: plain Moorean fact. The sooner philosophers realize this the better. It is simply evident that there is no single explanatory request for some simple truth, say, that Adam ate the apple. Why did Adam eat the apple? Why did Adam eat the apple? Why did
Adam eat the apple? For a single truth, we have several explanations, depending on the contrast class generated
by the request. Which explanation is appropriate is a matter that must be settled (at least in part) by context. I borrow the example (and general approach to explanation) from van Fraassen 1980: 127.
briefly what connections there may be between truthmakers, on the one hand, and the
semantic concepts of truth-condition and meaning on the other. Such an investigation may be
useful even if only to clear up or anticipate any potential misconceptions that may still be lurking about the notion of truthmaking. Others have conflated the notion of a truthmaker and the notion of a truth-condition (e.g., Blackburn 1986: 119 and Vision 2003; see also Jacquette 1996 and 2010 for overly-semanticized accounts of truthmaking). The point of this appendix is to forestall anyone making such an identification. I do not think that the notion of truthmaking can or should play any pivotal role in the philosophy of language, as I think it can in metaphysics.99 Still, let us pause to explore how we should understand the relationship between truthmaking and the theory of meaning.100
First off, we can set aside for the most part the family of “use” theories of meaning. Such theories draw their inspiration from the work of Wittgenstein (1953) and Wilfrid Sellars (1954), and perhaps have reached their highest sophistication in the work of Robert Brandom (1994). Use theories offer accounts of the meaning of natural language statements by
appealing to social practices and conventions. Words and sentences have their meanings in virtue of the roles they play in certain kinds of social practice. What is absent from the foreground of such theories is the notion of truth. Meanings of statements are determined via their social roles, not via their truth-conditions. Thus, use theories of meaning and truthmaker theory seem to be orthogonal to one another. Our attention, then, shall focus on theories of meaning that incorporate the notion of truth-conditions.
99Cf. Vision 2005: “There is all the difference in the world between identifying truth-conditions and identifying
their satisfaction” (376).
For truth-conditional accounts of meaning, we must turn first, of course, to the work of Davidson (e.g., his 1967 and 1984). The basic idea behind Davidson’s semantic project is that (at least part of) a theory of meaning for a language is given by a Tarski-style semantic definition of truth for that language (Tarski 1956). That definition of truth will consist of a number of axioms that serve to satisfy Alfred Tarski’s “Convention T”, which states that an adequate definition of truth must entail a series of “T-sentences” conforming to the following schema:
(T) s is true if and only if p.
Here ‘s’ stands for some sentence in the language, and p gives the truth-condition for that
sentence. A definition of truth for a language in Tarski’s sense will offer an instance of T for
every sentence of the language. The collection of such axioms constitute (or partially constitute) a theory of meaning for a language. Hence Davidson writes:
the definition [of truth] works by giving necessary and sufficient conditions for the truth of every sentence, and to give truth conditions is a way of giving the meaning of a sentence. To know the semantic concept of truth for a language is to know what it is for a sentence—any sentence—to be true, and this amounts, in one good sense we can give to the phrase, to understanding the language. (1967: 310)
At the very least, then, a complete theory of meaning for a language will offer the truth- conditions for each sentence belonging to it. Now, the relationship between s and p will not
always be one of disquotation. Not all sentences wear their “logical form” on their sleeves. The linguist and/or philosopher bears the burden of giving a satisfying account of the correct logical form of certain sentences. To name one common example, Davidson argues that certain sentences that involve change entail that there are events. Since Davidson accepts that some sentences involving change are true, he embraces a metaphysics of events (1966).
By contrast with Davidson’s “extensional” approach to truth-conditions, other
philosophers have advocated “intensional” approaches to meaning (e.g., Lewis 1970). Briefly, according to such views, the meaning of a sentence can be identified with the set of possible worlds in which that sentence is true.
In order to ask what the relationship is that holds between truth-conditions and truthmakers, we must know what truth-conditions are. On the Lewisian approach, truth- conditions are sets of possible worlds. For Davidson, truth-conditions are given by the right- hand side of his T-sentences. Davidson might therefore think of truth-conditions
linguistically—they are sentences, propositions, or states of affairs (linguistically understood, not objectually like Armstrong and Mellor). Either way, we can see an important difference between truthmakers and truth-conditions.
Let us attend first to truth-conditions in the spirit of Davidson. Except in rare cases, truthmakers will not be truth-conditions. I am not a truth-condition for any sentence; neither are you. But we are truthmakers. Here is the rare case: Taking truth-conditions to be
propositions (and propositions to exist), the proposition that there are propositions is both a truth-condition for ‘There are propositions’ and a truthmaker (but not the only one) for ‘There are propositions’ as well. If truth-conditions exist, they like everything else will be a truthmaker for at least some truth. But in most cases, a sentence’s truth-condition will not be its truthmaker, as most sentences are not about truth-conditions. The proposition that snow is white is not a truthmaker for ‘Snow is white’, for there are worlds in which the proposition exists (for propositions are necessary creatures), but where ‘Snow is white’ is false.
The stark difference between truthmakers and truth-conditions is quite unsurprising. For one thing, only truths have truthmakers. Falsehoods do not have truthmakers. But truths
and falsehoods do not diverge on the subject of truth-conditions: they are both possessed of them. Further, while many truths have multiple truthmakers, it is not the case that any truth has multiple truth-conditions.101 Take the truth that there are humans. Each and every human
that exists counts as a truthmaker for that truth (assuming that we humans are essentially so). But the sentence ‘There are humans’ has a single truth-condition: that there be humans. Finally, note that the truthmaker theorist stresses the perhaps obvious point that truthmakers must exist. Truthmaker theorists may take no recourse to non-existent entities in their truthmaking theories. The very idea of truthmaking is founded on the idea that truths are grounded in reality—in what exists. So no advocate of truthmaking would ever cite something that does not exist as a truthmaker for some truth. Truthmakers must be found inside one’s ontology. (And, indeed, truthmakers are found everywhere inside one’s
ontology.)
But it is not hard to imagine a truth-conditional theorist of meaning offering the following (admittedly optional) line of reasoning: The truth-conditions for falsehoods are non-existent states of affairs. The truth-condition for ‘Snow is green’ is the state of affairs of snow’s being green, and that state of affairs does not exist. So the truth-condition for ‘Snow is green’ is a non-existent state of affairs. Here we have an account of truth-conditions that appeals to what does not exist;102 the analogous path is in no way open to the truthmaker theorist. Of course, one might instead say that the truth-conditions for false sentences are non-obtaining states of affairs. Here, the truth-condition for ‘Snow is white’ is the obtaining
101Or so I assume. I am assuming that the truth-condition for, say, a disjunctive sentence is itself a disjunction,
not that the sentence has two separate truth-conditions. But perhaps that assumption about the individuation of
truth-conditions is not warranted without argument.
102I do recommend this line. It flirts too strongly with Meinongianism. I admit that I do not know what
Davidson himself thinks truth-conditions are, because he does not believe in the existence of propositions, or of facts. Are they just further sentences? Why then are sentences not just their own truth-condition?
of the state of affairs of snow’s being white. Such a view avoids recourse to non-existent states of affairs, but at the cost of embracing the existence of necessarily existing states of affairs, understood either Platonically or ersatzly. Such things, even if they exist, will typically not be truthmakers for those sentences for which they are the truth-conditions. No necessary being can be a truthmaker for a contingent truth.103 No matter how one chooses to articulate what truth-conditions are, they will end up being importantly different from truthmakers.
Turning now to Lewis’s intensional account of truth-conditions, we can bring out another fundamental contrast between the theory of truth-conditions and the theory of truthmaking. For Lewis, the meaning of a sentence is given by all the worlds in which the sentence is true. Let us then identify the truth-conditions of a sentence with the set of worlds in which that sentence is true. On that view, truth-conditions just are groups of possible
worlds, and so it makes little sense to ask whether a sentence has different truth-conditions in different possible worlds.104 But contrast that case with truthmaking. Here we can say that truths have different truthmakers in different possible worlds. I am a perfectly adequate truthmaker for that there are humans. Note that when I say that I am a truthmaker for that there are humans, it is implicit that I am taking myself to exist in the actual world, and that that there are humans is true in the actual world. Advocates of truthmaking, after all, search
after the truthmakers (the things that exist in the actual world) for the truths that they accept (those things that are true in the actual world). So when I speak of x being a truthmaker for y,
I am discussing a relation that obtains in the actual world. It would be false to say that
103Proof: Suppose necessary being T makes true contingent proposition
p. Hence, by TM, in every world in
which T exists, p is true. But T exists in every world, and so p is true in every world. But that is impossible,
since p is contingent.
Batman is a truthmaker for that there are humans, for Batman does not exist. One’s stock of
truthmakers is exhausted by the contents of one’s ontology. Moreover, it also would be false to say that Batman is a truthmaker for that Batman exists, because that Batman exists is not
true, and hence not made true by anything.105 Nonetheless, we can employ counterfactual language when discussing truthmaking. Batman might have been a truthmaker for that there are humans, had he only existed.
Further, although I am a truthmaker for that there are humans, I might not have
existed, and hence might have failed to be a truthmaker for that there are humans.
Furthermore, it might have turned out that none of the truthmakers for that there are humans
existed, but that some other humans did in their place. In that counterfactual situation, there would have been truthmakers for that there are humans, but the stock of truthmakers
available in that scenario would be completely disjoint from the actual stock of truthmakers. It might have been the case that Batman was the only human. If so, then he would be the sole (minimal) truthmaker for that there are humans. In more loaded language: there are possible
worlds where the only humans that exist are humans that do not exist in the actual world. Nonetheless, in those worlds that there are humans is made true by the various (non-actual)
humans that exist in those worlds. While we can speak truly when speaking counterfactually about truthmakers, the important point to remember is that truthmaking theorists are
interested ultimately in what actually exists—truthmaking is first and foremost an ontological project. We certainly can describe what exists in non-actual possible worlds, but doing so is of no immediate help to determining our ontology, understood as the study of what (actually)
exists.
105I beg my reader to let us set aside for the moment the worrisome questions about fiction that call our attention
Despite their differences, the modal reading of truth-conditions interacts in interesting ways with truthmaking. On the Lewisian view, when we ask after the truth-condition of a sentence, we are directed to a space of possible worlds. Similarly, when we ask after the truthmaker for a sentence, we also need to consider a space of possible worlds, for truthmaking is an irreducibly modal notion.106 How do these two inquiries intersect? In general, the actual world always will belong to the set of possible worlds given by any particular truth’s truth-condition. So will all the possible worlds in which the truth’s
truthmakers exist. Consider again the true sentence ‘There are humans’. The truth-condition for ‘There are humans’ is given by the set of all possible worlds in which ‘There are humans’ is true (that is, the set of all possible worlds in which there are humans). So any possible world that includes a human being belongs to that set. Call that set ‘S’. Since ‘There are humans’ is true (true in the actual world), our world W@ is a member of S. I am one of the several billion truthmakers for ‘There are humans’. I (or one of my counterparts) also exist in many possible worlds. Since I am essentially human, in each and every world in which I exist, ‘There are humans’ is true. So every world in which I exist is a member of S. The same goes for every other truthmaker for ‘There are humans’. So if we take the set of (actual world) truthmakers for ‘There are humans’, and then define a set of possible worlds that includes all the worlds where at least one of the (actual world) truthmakers for ‘There are humans’ exists, we will have a subset of S. In the present case, we in fact have a proper subset. For also included in S are possible worlds where the only humans that exist are ones that do not exist in the actual world. The world where Batman is the only human belongs to S, as does the one with only Billy Budd. The idea here is that there are possible worlds where a sentence is true, and yet none of its (actual world) truthmakers exist. That is not to say that in that world the
106See Fox 1987 and Merricks 2007: 11-14 for why truthmaker theory requires an account of
truth lacks a truthmaker. Billy Budd is a truthmaker for that there are humans in the worlds
(but only in those worlds) where he exists. Billy Budd is no truthmaker for that there are humans, but he would have been had the world been graced with the existence of the lovable
but unjustly doomed seaman.
Now let us generalize. Identify the truth-conditions of some sentence s with the set of
possible worlds S that includes all and only those worlds where s is true. Suppose s is in fact
true, and has some truthmakers, collected together in the set T. The set of possible worlds U in which at least one member of T exists is a subset, possibly a proper subset, of S. There are some cases where U and S will be coextensive. Consider the true sentence ‘Asay exists’. S is here given by the space of worlds where I exist. I of course am the truthmaker for ‘Asay exists’. Hence I appear to exhaust T.107 The set of worlds in which at least one member of T (i.e., me) exists just is the set of worlds where ‘Asay exists’ is true. So here U and S are the same. But in many cases, U will be a proper subset of S because there are “merely possible” but non-actual potential truthmakers for many actual truths (like Batman for thatthere are humans). Also note that if we were maximalists (such that, necessarily, all truths have
truthmakers), the truth-conditions of a sentence will give the space of possible worlds in which that sentence has a truthmaker. For any world in which some sentence s has a
truthmaker is a world in which s is true. Any such world will belong therefore to the set of
worlds given by the truth-condition of s. But as we just saw, some of the possible worlds
given by the meaning of a sentence are of little interest to truthmaking. Truthmaker theorists are “actual-world chauvinists”, to borrow Armstrong’s phrase (1989a: 56). They want to
107It might be thought that there are other truthmakers for ‘Asay exists’. For example, there is the mereological
sum of myself and Cuba. So add that to T. Still, T will generate the same U, for there are no worlds where the mereological sum of myself and Cuba exists, but I do not. To generate a distinct U, we would need a truthmaker for ‘Asay exists’ that is wholly separate from me, and I fail to see what that could be.
know what exists in the actual world. That some merely possible thing makes true some sentence in another distant possible world is of no matter to real ontology. To find truthmakers, we must look to the actual world.108
The foregoing shows how the notion of truthmaking and the notion of truth-
conditions come apart in fundamental ways. In essence, the former is an ontological notion,