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 (TM). Alan Rhoda has recently come out in favor of TM in a penetrating weblog entry. After sketching my position, I will try to pinpoint my disagreement with Rhoda.
1) Compare *Peter is tired* and *Every cygnet is a swan.* I will argue that truths like the first need truthmakers while truths like the second do not. A declarative sentence enclosed in asterisks names the primary truthbearer expressed by the sentence when assertively uttered or, more generally, assertively tokened. A truthbearer is anything appropriately characterizable as either true or false when 'true' and 'false' are used in their sentential as opposed to their ontic senses. ('True friend' and 'false teeth' feature ontic senses of 'true' and 'false'.) Candidate truthbearers include assertively tokened sentences in the indicative mood, statements, asseverations, judgments, Fregean Gedanken, Bolzanian Saetze an sich and more. By definition, a truth is a true truthbearer, whatever truthbearers are taken to be.)
2) Intuitively, *Peter is tired,* being contingently true, both due to its dependence on the existence of Peter, and on Peter's accidentally possessing the property of being tired, 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. (An ontological ground is not the same as an empirical cause.) *Peter is tired* can't just be true. This is because its truth-value depends on the way the world is. It needs a truthmaker external to it. 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 (or other type of truthbearer) that entails *Peter is tired.* Entailment, however, is not truthmaking: entailment connects propositions to propositions; truthmaking connects extra-propositional entities (states of affairs for Armstrong) to propositions. What I mean when I say that a contingent truth needs something external to it to 'make' it true 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 assertively uttered sentences, judgments, Fregean thoughts/propositions (the senses of context-free sentences in the indicative mood), and whatever else counts as a truthbearer. In other words, a truthmaker of a contingent atomic truth such as *Peter is tired* must be outside the sphere of representations: it must be extralinguistic, extramental, and extra-propositional. Thus the truthmakers of propositions like *Peter is tired* cannot belong to the category of propositions. The ontological ground of a contingent proposition's being true 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 what does not exist. But although Peter or Peter's existence is a necessary condition of the truth of every true proposition about him, that very individual, it is not the case that Peter or Peter's existence is a sufficient condition of the truth of contingent propositions about him if these propositions are predications such as *Peter is tired.* (I am open to the suggestion that Peter himself suffices for the truth of *Peter exists.*) That Peter by himself cannot be the truthmaker of contingent predications about him can be proven or at least argued as follows.
Argument from Necessitation. Assume for reductio that Peter by himself can serve as truthmaker of contingent predications about him. 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.*
Argument from Selection. 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 that Peter is a philosopher and that 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. Extra-propositional but proposition-like! What may look like a 'bug' is a 'feature' of truthmaker theory. 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, as in middle-period Armstrong.
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 affair but as an individual — cannot be the truthmaker of contingent propositions of the form *Peter is F.* Some will say that tropes can serve as truthmakers. 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. We can call the first principle veritas sequitur esse (truth follows being). What it says is that a truth cannot be true unless there are one or more items it is about. Thus VSE requires that if Milo kicked Philo, this is true only if both Milo and Philo exist or have some mode of being other than existence. The truthmaker principle (TMP) goes beyond this in requiring the instantiation of the dyadic relation —kicks___ by Milo and Philo, in that order.
7) Consider now the analytic proposition *Every cygnet is a swan.* As analytic, it is true solely in virtue of the meanings of 'cygnet' and 'swan.' It is true ex vi terminorum. Its truth is not contingent on the existence of any cygnets. Why does it need a truthmaker? It certainly does not need anything external to it to make it true. 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, following Kant, 'analytic.' Clearly, nothing external to an analytic proposition is required to make it true. It follows that it cannot have a truthmaker. Or rather it follows if 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 truthmaker 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 (Kantian) sense. But I hear an objection coming.
8) "*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 of course 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.
9) Here is where Alan Rhoda will disagree:
Some philosophers say that truthmaking is asymmetric rather than anti-symmetric, but that is a mistake. Asymmetry disallows the possibility of self-grounding truthbearers. Anti-symmetry allows for that possibility. And this is something we should allow, because conceptually necessary propositions (e.g., all triangles have three sides) are their own truthmakers. If the proposition exists—whether it exists [as] a Platonic object, an idea in God’s mind, or something else—its very existence supplies a parcel of reality sufficient to explain and ground its own truth.
10) For me, truthmaking is an asymmetric relation whereas for Alan it is an antisymmetric relation. Thus I am maintaining that, for any x, y, if x makes-true y, then it is not the case that y makes-true x. This implies that no truthbearer is its own truthmaker or truth-ground. It implies that in no case is the truthmaker of a truth (a true truthbearer) that very truth. It implies that the truthmaker of a truth is in every case 'external' to that truth in the manner explained above.
Now a relation R is said to be antisymmetric just in case: for any x, y, if x stands in R to to y, and y stands in R to x, then x = y. The antisymmetry of 'makes-true' allows for cases in which a proposition (or other truthbearer) is its own truthmaker. Thus Every cygnet is a swan is its truthbearer that is its own truthmaker. This is Alan's position.
11) Here is a consideration in favor of my position. Truthmakers play an explanatory role. Now explanation is asymmetric: if x explains y, then it is not the case that y explains x. This holds for causal explanation, but also for metaphysical explanation or metaphysical grounding. It is the existence of Milo that metaphysically grounds the truth of Milo exists. And not the other way around. No one — I hope! — will say that that the truth of Philo's belief that Milo exists is what makes it the case that Milo exists or that Shlomo's sincere assertive utterance of 'Milo is sleeping' is what makes it the case that Milo is sleeping.
Now if truthmakers play an explanatory role, and metaphysical explanation is asymmetric, then no truthbearer is its own truthmaker. So in the case of analytic or conceptually necessary truths, we should say that they do not have and do not need truthmakers. To maintain this is to reject truthmaker maximalism.
It is worth noting that my position is consistent with saying that a truthbearer (whether a Platonic proposition, a divine thought, whatever) can serve as a truthmaker for a different truthbearer. The Platonic proposition expressed by '7 is prime,' for example, makes-true the general Platonic proposition that there are Platonic propositions.
Your move, Alan.
