Thursday, July 23, 2009

Truthmakers

It is fairly standard to say that the truthmaker of a proposition p is what makes p be true. But suppose we accept a non-deflationary theory of truth on which the claim that p is true is distinct from the claim that p, and is the attribution of the property of truth to p. Now let p be the proposition that there are horses. Then, any horse (or maybe the sum of them all) is a truthmaker for p, or so it is pretty standard to think. But while a horse makes there be horses, a horse is not enough to make it be true that there are horses, since the latter claim involves something other than a horse, namely the proposition p. So, we need to distinguish between making there be horses and making it true that there are horses. A horse suffices for the former task. But for the latter task, we need a horse, p, and whatever relations and properties are involved in the attribution of truth to p (e.g., an instance of a correspondence relation). (I am grateful to Dan Johnson for helping me get clear on what this latter task involves.)

We now have a linguistic question. Is the "truthmaker" of p just a horse, or a horse, p and whatever else is needed? Since "truthmaker" is entirely a stipulative term of art, nothing deeply significant rides on this question, but the question does have two aspects: the sociological question of just how the word "truthmaker" has been used by philosophers, and the question of which way of using the word gets at a more fundamental concept. Say that a "truthmaker(1)" is the concept that goes with the answer "a horse" and a "truthmaker(2)" is the concept that goes with the answer that also includes p. Then there is a natural way of defining truthmakers(2) in terms of truthmakers(1). The truthmaker(2) of p is identical to the truthmaker(1) of the proposition that p is true. One might try to define a truthmaker(1) in terms of taking a truthmaker(2) and subtracting the proposition and the relation, but that definition will be messy and difficult to give. So, it seems that the truthmaker(1) is the more fundamental of the two concepts. Moreover, sociologically, I think "truthmaker(1)" is the right reading of how "truthmaker" has been used, because as a matter of fact most users of truthmakers don't include the proposition and the correspondence relation in the truthmaker.

But now we see that unless we have a deflationary theory of truth, the term "truthmaker", understood as truthmaker(1), is a bit of a misnomer. For the truthmaker of p isn't what makes p be true. It is only a part of what makes p be true: makes p be true is not just the truthmaker(1) but also p and how its related to the truthmaker(1).

It may, of course, turn out that deflationary theories of truth are correct. But unless deflationary theories are established to be true, as much of our theorizing as possible should be compatible with non-deflationary theories as well, and so we should be sensitive to the difference between the condition that p and the condition that p is true.

Two other areas where the distinction could matter are these: (1) Is it a part of our concept of knowledge that if x knows p, then p is true, or should we rather say that if x knows p, then p? (2) Should we require it to be a part of omniscience that for all p, God knows p if p is true, or that for all p, God knows p iff p? With a bivalent logic and an acceptance of Schema (T) as a necessary truth, the answers are going to be necessarily extensionally equivalent. But conceptually there may be a difference, and how we answer (1) and (2) may affect some of our intuitions.

Such sensitivity will also be important when we consider non-bivalent logic, even if we only consider them to dismiss them. For instance, suppose we deny that contingent propositions about the future are true or false, but accept excluded middle. Then if we understand omniscience as implying that God knows p if p is true, God can be omniscient without knowing contingent propositions about the future. But if we understand omniscience as implying that God knows p if p, then omniscience requires God to know some contingent propositions about the future, even if none such are true.

4 comments:

Jonathan D. Jacobs said...

One way to think of truthmak*ing* is that it is an internal relation between a representation and the *truthmaker*. If you have both the proposition and the truthmaker, then you have the one related to the other by truthmaking relation.

But, one could then add, internal relations are not additions of being, so there really isn't a truthmaking relation, there's just bits of the world and the representations.

I'm not sure how this relates to deflationary and non-deflationary theories of truth. In fact, a lot of truthmakers think of truthmaking theory as a way to avoid offering a theory of truth and just go on and do metaphysics. It would be interesting if it turned out, as you seem to argue, that you can't do that—that a conception of truthmaking and theories of truth are not independent.

Alexander R Pruss said...

There still is a difference between the truthmaker of p and of True(p), even on this solution: the truthmaker of True(p) includes p.
If one thinks all and only true propositions have truthmakers, it's hard to avoid saying that "True(p) iff there is a truthmaker for p" is a theory of truth, with all the consequent puzzles. ("(p)(x)(x is not a truthmaker for p or this sentence does not express p)")

enigMan said...

Hi Alex,

I would not dismiss bivalent logic, being a Presentist. It seems to me that the ordinary concept of truth is basically as Aristotle said, i.e. saying of what is (not) that it is (not). That is, it is a correspondance of our words (or propositional thoughts) with reality. So the truthmaker is naturally the relevant bit of reality. But we might call other stuff true, and then there would be other reasons why it was rightly called true.

Say I suppose that S will be P, and then S is P, and so I take myself to have been right earlier. If S might not have been P, then under Presentism it was indefinite (rather than true) that S would be P, at that earlier time. So bivalent logic captures that correspondance with reality under Presentism. There is even so a sense of 'true' in which what I supposed was true earlier. I was, after all, saying of what was actually to be that it would actually be.

But that latter correspondance is only with the artificial 'actual world' of possible 4-D worlds semantics (if Presentism is true). What makes it true (if it is indeed properly true) at the earlier time is then not only what was actually to be, but also our conventions about calling stuff true with hindsight. Nonetheless, the most basic sort of truthmaker, the one with the most metaphysical (rather than conventional) significance, is the (1) one...

suppose we deny that contingent propositions about the future are true or false, but accept excluded middle [...] if we understand omniscience as implying that God knows p if p, then omniscience requires God to know some contingent propositions about the future, even if none such are true.

So God knows that S will P if S will P, but why should it be the case that S will P before S does P, if S might not P at that earlier time?

enigMan said...

Thinking out loud, Alanyser takes 'S will P' to be false if S might not P. I have not seen the point of taking 'will' to always mean 'will definitely'; but it now occurs to me that it may be a good approach if we do take omniscience to mean that God knows p if p, perhaps...