Truthmaking and Correspondence – Two Sides of the Same Coin

What is the relation of truthmaker theory to the correspondence theory of truth?

In a paper by William Lane Craig and David Hunt that I’ve just finished responding to in a series of posts (1, 2, 3, 4, and 5), they assert that

It is … no part of the correspondence theory of truth that true propositions need to be grounded in reality. That is the theory of truth-makers, a controversial addendum to correspondence theory that has been defended by a minority of recent philosophers. (p. 66)

In other words, they claim that one can consistently be a correspondence theorist without being a truthmaker theorist.

Other philosophers see the matter differently. In the last post of that series I quote Marian David’s Stanford Encyclopedia of Philosophy (SEP) article on the correspondence theory of truth, in which he says that

truthmaker theory may be presented as a competitor to the correspondence theory or as a version of the correspondence theory. This depends considerably on how narrowly or broadly one construes “correspondence theory”, i.e., on terminological issues. Some advocates would agree with Dummett (1959, p. 14) who said that, although “we have nowadays abandoned the correspondence theory of truth”, it nevertheless “expresses one important feature of the concept of truth…: that a statement is true only if there is something in the world in virtue of which it is true”. Other advocates would follow Armstrong who tends to present his truthmaker theory as a liberal form of correspondence theory.

In other words, matters on this issue aren’t as clear and settled as Craig and Hunt seem to think.

In what follows I’m going to argue that Craig and Hunt are completely wrong about this. Correspondence theory (CT) and truthmaker theory (TM) necessarily go hand-in-hand. They are, in fact, two sides of the same coin.

Methodological preliminaries

As the David’s SEP article indicates, there is probably no such thing as the correspondence theory or the truthmaker theory. At least, there is no unique referent for these expressions if we focus on fully developed versions of each. The reason, of course, is because fully developed versions of CT and TM are going to have to say something substantive about what the relata of the correspondence and truthmaking relations are and what it means for such things to correspond and to make true in the relevant senses.

But suppose we focus instead on the minimal core of such theories? We can then identify the correspondence theory with what all fully developed correspondence theories have as their common essence. Likewise, we can identify the truthmaker theory with what all fully developed truthmaker theories have as their common essence. This, at any rate, is how I shall attempt to proceed.

What is the correspondence theory?

Striped to its bare essence, the correspondence theory (CT) says that the property being true is a kind of relation between (a) things of which truth can properly be predicated—we’ll follow the common practice of calling them truthbearers—and (b) things which, because they appropriately correspond to the truthbearers, are sufficient for rendering or making truthbearers true. We’ll follow the common practice of calling the latter things truthmakers. In these terms we can say that according to CT, the truth of a truthbearer consists in its correspondence to a truthmaker.

What is the truthmaker theory?

Stripped to its bare essence, the truthmaker theory (TM) says that truths need there to be something sufficient to make them true. Some versions of TM restrict this to say that only some truths need truthmakers, whereas other versions affirm that all truths need truthmakers. The latter thesis is known as truthmaker maximalism.

Truthmaker maximalism is controversial because there are some categories of truths (e.g., negative existentials, universal generalizations, truths about the past, etc.) for which many philosophers believe it is not possible, or at least not easy, to say what plausible truthmakers could be. And since we’re allegedly more convinced that the truths in question are true than than such truths could have truthmakers, so, it is argued, truthmaker maximalism must go.

I believe that objections to truthmaker maximalism are grossly overrated. (I won’t go into detail here since I’ve addressed these sorts of objections in a previous post.) Moreover, if, as the bare-bones correspondence theory posits, the truth of a truthbearer consists in its corresponding to a truthmaker, then to give up truthmaker maximalism is, ipso facto, to give up CT. It’s to say, contrary to CT, that it’s not the case that all truth consists in a relation of correspondence between truthbearers and truthmakers. It’s to say that some truths can be true without corresponding to anything. But CT is pretty intuitive and giving it up seems like a high price to pay. Moreover, there’s no pressing need to pay that price. All TM says is that for whatever truths one cares to countenance, one must posit an ontology rich enough to make, that is, to explain or ground those truths. If you find yourself with truths for which you can’t identify plausible truthmakers, then that’s a sign that your ontology—your theory about what sorts of things exist—is deficient.

There are other objections to TM that are independent of truthmaker maximalism. (I discuss such objections here and here.) But to the extent they succeed they do so by weighing TM down with extraneous requirements that go beyond its bare essence.

When restricted to their bare essences, CT entails truthmaker maximalism, and therefore entails TM.

How should we understand the relation between CT and TM?

I believe there is very good reason to affirm both CT and TM. But there is a nontrivial question about how their relation should be understood. David, in his SEP article, states the difficulty this way:

Talk of truthmaking and truthmakers goes well with the basic idea underlying the correspondence theory; hence, it might seem natural to describe, e.g., a traditional fact-based correspondence theory as maintaining that the truthmakers are facts and that truthmaking is correspondence. However, the assumption that the correspondence relation can be regarded as a species (or precisification) of the truthmaking relation is dubious. Correspondence appears to be a symmetric relation (if x corresponds to y, then y corresponds to x), whereas it is usually taken for granted that truthmaking is an asymmetric relation, or at least not a symmetric one. It is hard to see how a symmetric relation could be a species (or precisification) of an asymmetric or non-symmetric relation.

What David points out here is that truthmaking and correspondence are different relations because they have incompatible relational properties. Correspondence is a symmetric relation, whereas truthmaking is non-symmetric. (More exactly, truthmaking is anti-symmetric. A relation R between a and b is anti-symmetric just in case if aRb then it is not the case that bRa, except possibly in the case where a=b.)

But if we can’t simply identify truthmaking with correspondence, how then are they related?

I believe the answer is quite simple. What both relations have in common is that they have truthbearers and truthmakers as their relata. I characterize these as follows:

• A truthbearer is anything of which truth values may aptly be predicated.
• A truthmaker is anything which, in virtue of its existence, necessitates and explains the truth of any corresponding truthbearers.

As my characterization of truthmakers makes clear, truthmaking is an explanatory relation. It answers the question “Why is this truthbearer true?” Answer: Because there exists a truthmaker to which it corresponds. Truthmaking is anti-symmetric because it is explanatory. Some things explain themselves, but not everything does or can. The mere existence of an analytically necessary proposition like <All triangles have three sides> is enough to explain its truth. In such a case, the truthbearer is its own truthmaker. But the mere existence of a synthetic proposition doesn’t explain it’s truth. Such propositions are logically contingent. If they are true, they are true in virtue of something outside the proposition. They cannot be their own truthmakers. For example, <The cat is on the mat> requires for its truth (a) that there be a cat, (b) that there be a mat, and (c) that the cat and mat in question are spatially related such that the cat is on the mat.

In contrast, correspondence is a semantic relation. Is answers the question “Why is this truthmaker adequate to make this truthbearer true?” Answer: Because the intelligible content of the truthmaker contains the intelligible content of the truthbearer. Both truthbearers and truthmakers have content. The content of a truthbearer is what it presents as being the case. This content is intelligible because it can be formulated as a proposition. <The cat is on the mat>, for example, presents it as being the case that a certain cat is physically on a certain mat. The content of a truthmaker is the totality of its constituents related as they are to each other. A truthmaker presents itself, namely, the very totality that it is, as being the case. This content is intelligible to the extent that it can be represented propositionally. Correspondence between a truthbearer and a truthmaker obtains when the intelligible content of the truthmaker (propositionally represented) contains the intelligible content of the truthbearer. It may contain other content besides, but it cannot contain less. The relation is symmetric because, once we exclude as irrelevant any excess content in the truthmaker, the relevant intelligible content in each case is exactly the same.

Conclusion

CT and TM are correlative. They are two sides of the same coin. All true truthbearers have truthmakers, and correspondence determines which truthmakers are capable of making which truthbearers true.

EDIT 2015.02.11: I have modified the paragraph before the conclusion to emphasize that it is the intelligible content of truthmakers that matters. The point is to distinguish intelligible or propositionally representable content from other sorts of content that cannot exist in truthbearers in the same way as in truthmakers. My dog Zoey is a truthmaker for <Zoey exists>. Her constituents include things like blood, bones, and fur. That’s part of her physical content. But that content can’t be part of <Zoey exists>. The proposition obviously doesn’t contain any fur! We can, however, represent her physical constituents and their relations propositionally. We can conceive of there being a complete description of Zoey. Such a description must, if it is complete, include the fact that she exists.