For Peter Lupu discussions with whom helped me clarify my thoughts on this topic.
0. What David Armstrong calls Truthmaker Maximalism is the thesis that every truth has a truthmaker. Although I find the basic truthmaker intuition well-nigh irresistible, I have difficulty with the notion that every truth has a truthmaker. Thus I question Truthmaker Maximalism.
1. Compare *Peter is tired* and *Every concretum is self-identical.* I will argue that propositions like the first have truthmakers while propositions like the second do not. (A declarative sentence enclosed in asterisks names the Fregean proposition expressed by the sentence. I will assume that the primary truthbearers are Fregean propositions. By definition, a truth is a true truthbearer.)
2. Intuitively, the first truth is in need of something external to it that 'makes' it true or determines it to be true, or serves as the ontological ground of its truth. By 'external to it,' I don't just mean that the truthmaker of a truth must be distinct from it: this condition is satisfied by a distinct proposition that entails it. What I mean is that the truthmaker must be both distinct from the truthbearer and not, like the truthbearer, a 'representational entity' where the latter term covers such items as sentences, contents of judgments, and Fregean propositions (the senses of context-free sentences in the indicative mood.) In other words, a truthmaker of a first-order truth such as *Peter is tired* must be outside the sphere of representations: it must be extralinguistic, extramental, and extra-propositional. Truthmakers, then, are 'in the world' in one sense of 'world.' They are ontological grounds of truth. Thus the truthmakers of propositions like *Peter is tired* cannot belong to the category of propositions. The ontological ground of such a proposition cannot be an entity within the sphere of propositions.
3. The truthmaker of *Peter is tired* cannot be a proposition; but it also cannot be utterly unlike a proposition. Consider Peter himself, that very concrete individual. It is clear that he could not be the truthmaker of *Peter is tired.* Granted, if Peter were not to exist, then the proposition in question could not be true. There are no truths about nonexistent objects. Truthmaker theory, as I understand and defend it, is anti-Meinongian. But although Peter's existence is a necessary condition of the truth of propositions about him, it is not the case that Peter's existence is a sufficient condition of the truth of contingent propositions about him. That Peter by himself cannot be the truthmaker of contingent propositions about him can be proven as follows.
Argument from Necessitation. Assume for reductio that Peter by himself can serve as truthmaker. Now, by Truthmaker Necessitarianism, whatever truthmakers are, they broadly logically necessitate the truth of their corresponding truthbearers. So if X is the truthmaker of *Peter is tired at t,* then there is no possible world in which X exists and *Peter is tired at t* is not true. But there are plenty of worlds in which Peter exists but *Peter is tired at t* is not true. So Peter by himself cannot be the truthmaker of *Peter is tired at t.*
Selection Argument. Consider any two true affirmative atomic contingent monadic propositions about Peter such as *Peter is tired at t* and *Peter is hungry at t.* If Peter by himself can serve as the truthmaker of one, then he can serve as the truthmaker of the other. But they obviously require numerically different truthmakers. So Peter is the truthmaker of neither of them. Although different truths can have the same truthmaker, this is not the case when both truths are atomic, even if both are about the same individual. The truthmakers of such atomic propositions as Peter is a philosopher and Peter is a violinist must be distinct and they must match up with, or select, their truthbearers. To do this, the truthmakers must have an internal structure isomorphic to the structure of the truthbearers. In other words, the truthmakers must be proposition-like despite their not being propositions. It follows that Peter by himself cannot be the truthmaker of atomic contingent propositions about him.
4. If Peter by himself cannot serve as truthmaker of the accidental predication *Peter is F*, then neither can F-ness by itself. The same goes for the set {Peter, F-ness}, the mereological sum (Peter + F-ness) and the ordered pair [Peter, F-ness]. For what is needed in addition to Peter and F-ness is a link in the truthmaker that corresponds to the copulative link in the proposition. After all, not every possible world in which both Peter and F-ness exists is a world in which Peter is F. There could be a world in which Peter exists and F-ness exists (by being instantiated by Paul) but in which Peter does not instantiate F-ness. I am assuming that F-ness is a universal, but not that F-ness is a transcendent universal (one that can exist uninstantiated). This is why concrete states of affairs are plausible candidates for the office of truthmaker.
5. But even if one balks at the admission of concrete states of affairs or facts, one will have to admit that Peter himself — assuming that this concrete individual is not assayed as a state of affairs! — cannot be the truthmaker of contingent propositions of the form *Peter is F.* Some will say that tropes can serve as truth makers. Fine, but they too have a proposition-like structure. If the trope Peter's-tiredness-at-t is the truthmaker of *Peter is tired at t,* then it is made true by an entity that has a proposition-like structure, a structure isomorphic to, and mirroring, the structure of the truthbearer.
6. It seems to me that I have just definitively established that the truthmakers of accidental atomic predications like 'Peter is a philosopher' cannot be concrete individuals lacking a proposition-like structure. I have also made it clear that we should not confuse the principle that there are no truths about nonexistent objects with the truthmaker principle.
7. We now turn to *Every concrete object is self-identical.* On Truthmaker Maximalism, every truth has a truthmaker. The proposition just cited is true, indeed necessarily true, but what could be its truthmaker? Consider a possible world W in which only abstract objects exist. The proposition cited, being true in all worlds, is true in W. But there are no concrete objects in W, and a fortiori no facts having them as constituents. The proposition cited would seem to be a truth that cannot have a truthmaker in every world in which it exists and is nonetheless true.
8. Consider the analytic proposition *Every cygnet is a swan.* As analytic, it is true solely in virtue of the meanings of 'cygnet' and 'swan.' The concept cygnet includes the concept swan, so that, by sheer analysis of the subject concept, one can arrive at the truth in question. That's why we call it 'analytic.' Clearly, nothing external to an analytic proposition is required to make it true. It follows that it cannot have a truthmaker. For we saw in #2 above that a truthmaker of a first-order truthbearer is an entity that is external to the truthbearer and resident in the realm of reality beyond the sphere of representations broadly construed.
Does this not decisively refute maximalism? There are plenty of analytic truths, but none of them has or can have a truthmaker. For if you say that an analytic truth needs a truthmaker, then you are saying that it needs something external to it to 'synthesize,' to bring together, subject and predicate concepts. But analytic truths are precisely not synthetic in that sense. But I hear an objection coming.
"*Every cygnet is a swan* does have a truthmaker, namely, the fact that cygnet includes swan." This is a confused response. There would not be a analytic truthbearer at all if cygnet did not include swan. The very existence of the proposition *Every cygnet is a swan* requires that the first concept include the second. So there is no need of an ontological ground of the truth of this proposition. One could say that in the analytic case the truthbearer is its own truthmaker. But it is better to say that in the analytic case there cannot be a truthmaker as 'truthmaker' was defined in #2 above.
Here is a second argument. *Every cygnet is a swan* is necessarily true, true in all possible worlds. So it it is true in those worlds in which there are no material objects. Let W be one of those worlds. Now if the proposition in question had a truthmaker, it would have to be some chunk or chunks of material reality. This is because the proposition is about material objects, and cygnets and swans are material objects. Since there are no material objects in W, and since the proposition is true in W (because it it true in every world), the proposition does not have a truthmaker in W. Not having a truthmaker in one world, it doesn't have a truthmaker in any world.
9. What about *Peter is self-identical*? Although this is a contingent truth, because not true in all worlds, it is an essential predication, true in every world in which Peter exists. Peter exists in some but not all worlds, but in the worlds in which he exists he is self-identical. It is therefore very tempting to say that Peter by himself is the truthmaker of *Peter is self-identical.* Generalizing the temptation, we can say that for every essential property F-ness of Peter, the truthmaker of *Peter is F* is just Peter himself. For by the definition of 'essential property,' Peter cannot fail to instantiate each of his essential properties in every world in which he exists. If there are n distinct essential properties of Peter, then there are n disinct propositions about him, but all have the same truthmaker, Peter himself.
10. If concrete individuals are allowed as truthmakers of some propositions, then, given that concrete individuals cannot be the truthmakers of some other propositions, the ones expressed by accidental predications, we have to ask whether 'truthmaking' picks out the same relation in both types of case.
Some writers seem to think that the mere existence of the truthmaker logically suffices to make the corresponding truthbearer true. Thus:
TMP1: Necessarily, if *T exists,* then *p* is true.
(Note that 'Necessarily, if T, then *p* is true' makes no sense: a nonproposition cannot stand in an entailment relation.)
TMP1 clearly works for the 'essential' cases. But it does not fit the 'accidental' cases very well. It makes sense to say that the mere existence of Peter makes true *Peter is human.* But how could the mere existence of the fact of Peter's being tired make true the corresponding proposition? It is not the mere existence of this fact (concrete state of affairs) that functions as truthmaker, but its existence PLUS its proposition-like structure. Otherwise, the fact in question could not 'select' *Peter is tired* as opposed to *Peter is hungry.*
The truthmakers of these two propositions do not differ in point of existence, nor do they differ in point of their individual constituent, Peter. So if truthmaking is a matter of the mere existence of the truthmaker, then either truthmaker could make true either proposition. And that can't be right. So we try:
TMP2: Necessarily, if *T exists* and *T is structurally isomorphic to *p**, then *p* is true.
The trouble with this latter principle is that it cannot accommodate the 'essential' cases for the simple reason that concrete individuals lack proposition-like structure.
The upshot is that 'truthmaking' has no one univocal sense: it is being used to pick our two very different relations. Is that a problem? We will have to pursue this in a separate post.
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