Truth-maker theory attempts to view the relation between truth and being as more than merely global supervenience. The idea is that we can take a particular truth – for example the true proposition that there is some cheese – and ask what element of actual being takes particular responsibility for it. In simple cases the question is easy to answer; in our example it is the world’s cheese. In more complicated cases – for example the (presumably) true proposition that energy is conserved – the question is much harder to answer.
The question is posed in various ways: as the question of what grounds what (Schaffer?), as the question of what makes what true (eg Armstrong?), and as the question of what determines what (?). The disparate terminology conceals some key common ground. Truth-maker theorists tend to agree that truthmakers necessitate the truth of their associated propositions, and they tend to agree that every true proposition has a truthmaker.
This agreement is enough to guarantee the supervenience of truth on being, as endorsed by Bigelow, Lewis, and many others since. But by itself it is not enough to satisfy the Australian school of truth-maker theorists, because it is compatible with the only kind of supervenience being the monistic kind, where the actual world is the truthmaker for every contingent true proposition. As I understand it, this is Schaffer’s view; but it seems to be regarded as not doing proper justice to the motivations behind truthmaker theory.
Graham Oddie at the Philosophical Society in Oxford yesterday suggested an alternative, but still revisionary, treatment of truthmakers. By combining the view with a theory of propositions according to which they amount to ascriptions of genuine properties, such that there are no negative propositions, Oddie reduces the scale of the task faced by the truthmaker theorist. His suggestion is that truthmakers correspond to commensurate actual sufficers; that is, roughly, that they element of being that is proportionate – ‘commensurate’ – to the truth they make.
One way of being a commensurate actual suffice is to be a minimal actual sufficer; that is, some event such that, necessarily, if it obtains then the proposition is true, but such that no part of it is such that, necessarily, if it obtains then the proposition is true. Restall has a nice example which shows that minimal actual sufficers can’t be the whole story – no fusion of electrons can be a minimal actual sufficer for the proposition that there is a denumerable infinity of electrons. (Oddie had a suggestion for dealing with this which I won’t discuss here.)
The thing that struck me about the position developed was how similar the notion of truth-making which emerges is to the notions of truth-causing and truth-explaining. In the recent literatures on causation and on explanation, the idea that a cause should be proportionate to the effect and the idea that an explanans should be proportionate to the explanandum are commonplace. These notions of proportionality are often cashed out using counterfactuals, for example by Yablo and by Menzies and List.
The difference is that Oddie’s account uses an indicative conditional to characterize sufficiency – if the truthmaker obtains then the proposition is true – and something like a minimality condition to characterize proportionality. In contrast, Menzies and List use subjunctive conditionals both to characterize sufficiency and to characterize proportionality – if the cause were to occur, the effect would occur, and if the cause were not to occur, the effect would not occur. (To get this to work, they drop the strong centering assumption from a Lewisian counterfactual semantics. But it seems possible that there are ways to combine their view with an account of counterfactuals which preserves strong centring, for example by using counterfactuals prefaced by a generic operator in the analysis of sufficiency and proportionality, rather than just the bare counterfactuals.)
Applying these subjunctive conditionals to ascribing responsibility for truth gives interesting results. Let’s try saying that an event is responsible for the truth of a proposition where a) if the event were to obtain, the proposition would be true and b) if the event were not to obtain, the proposition would not have been true. A non-minimal sufficer will not comply with the second of these conditions: the closest worlds where the non-minimal suffice does not obtain is one where another sufficer obtains instead, so non-minimal sufficers will not be proportionate.
If we adopt this account of proportionality both for causation and for ascribing responsibility for truth, the resulting picture is a picture of truth-causing.
Consider the example ‘there is some cheese’, and see how the conditionals work out in this case. For any cheesy event, if that event were to obtain then the proposition would be true. So any cheesy event satisfies the first condition. But it is hard to see what event could satisfy the second condition. A truth-causer for ‘there is some cheese’ would have to be such that, if it were to not obtain, then ‘there is some cheese’ would be false. But even the totality of the world’s cheese seems not to meet this condition. Had the totality of the world’s cheese not existed, presumably some other cheese might have existed instead.
So we get the surprising result that the cause of the truth of ‘there is some cheese’ is neither any particular piece of cheese, nor the totality of the world’s cheese. Are there any other candidates for the cause of this truth? The totality of the world’s cows are neither sufficient nor proportionate; the totality of cows could have existed without there being any cheese (if there were nobody around to milk them), and there could have been cheese even without the totality of cows (if there were other cows around instead). So it looks like nothing actual is the cause of the truth of ‘there is some cheese’.
Contrast this result with singular propositions. The cause of the truth of ‘Oddie exists’ is Oddie. Were there to be an Oddie-ish event, ‘Oddie exists’ would be true; were there not to be an Oddie-ish event, ‘Oddie exists’ would not be true. So singular propositions do have truth-causers – the referent of the singular term.
So maximalism fails for truth-causers: some truths (those that are general rather than particular) are true without there being any particular actual thing or things which causes their truth. So Oddie should resist assimilating commensurate actual sufficers to commensurate causes, and using the account of commensurateness appropriate to causation.
It remains to be seen whether any non-counterfactual account of proportionality can be given which allows us to retain maximality for truth-makers. Oddie’s proposal is that proportionality amounts to a disjunction of minimality and recursively-defined smallness; perhaps it can be made to work, but it doesn’t look as elegant as the counterfactual account of proportionality available in the case of causation.