If you believe all that, it’d be nice if one of truthmaking or in virtue of could be defined in terms of the other, so that we only have one primitive here rather than two. I think the prospects of defining truthmaking in terms of in virtue of are better than vice-versa, and I’d welcome thoughts on this.
How might one define the in virtue of relation that can hold between two true propositions in terms of the makes true relation that holds between a thing and a true proposition? Here are some of the obvious things that come to my mind, and why I don’t like them.
(1) p is true in virtue of q iff q makes p true
Okay, this one is obviously hopeless. For starters, if propositions are necessary existents, this entails that no contingent truth is true in virtue of anything. But even if propositions are contingent existents, presumably their existence is not contingent on them being true; they can exist and be false, and so this definition is still hopeless. Suppose 'X is wrong'
(2) p is true in virtue of q iff the truth of q makes p true
This solves the above problem, but at the cost of admitting weird entities. What type of entity is the truth of q? A truth trope: the particularized truth of the proposition q? Nasty.
(3) p is true in virtue of q iff the state of affairs that q makes p true
That might be okay if there were a state of affairs that p for every true proposition p. But there’s not.
(4) p is true in virtue of q iff (necessarily) whatever makes q true makes p true
No: it’s no part of the definition of truthmaking that every truth has a truthmaker, and we should allow for the possibility that one proposition is true in virtue of another even though neither have truthmakers, as well as the possibility that two propositions lack truthmakers but where one is not true in virtue of the other. And if every truth does have a truthmaker, the definition will entail the wrong result that
It doesn’t look to me like there’s a good way of defining in virtue of in terms of truthmaking; but I think truthmaking can be defined in terms of in virtue of. Truthmaker theory says that what is true is grounded in what there is: as I understand it, this is the claim that the totality of truths are ultimately true in virtue of just those truths that are concerned solely with ontology – that is, that any truth at all is ultimately true in virtue of some truth(s) concerning (solely) what there is.
Call the set containing all and only the brute propositions – that is, those that are not true in virtue of anything – BRUTUS. Consider also the set – call it EXISTS – of propositions whose entire content is that some thing, or some things, exist(s): call these propositions pure existence claims. (Pure existence claims will be expressible by sentences of the form ‘a exists’ or ‘the Xs exist’, where ‘a’ is a rigid designator and ‘the Xs’ a rigid plurally referring expression (i.e. it plurally refers in every possible world to the things that are actually the Xs if they exist, and it fails to refer if any of the actual Xs fail to exist.)
We can define truthmaking as follows.
(*) A proposition p is made true by X, or the Xs, just in case either (i) p belongs to BRUTUS & p belongs to EXISTS & p says that X (or the Xs) exist(s) or (ii) There is an x such that (p is true in virtue of x & x belongs to BRUTUS & x belongs to EXISTS & x says that X (or the Xs) exist(s)).
That is: a proposition is made true by some things, the Xs, if and only if it is the brutely true pure existence claim that the Xs exist or it is true in virtue of the brutely true pure existence claim that the Xs exist.
I’d welcome any thoughts on this. Especially if you think there’s a problem with the proposed definition of truthmaking in terms of in virtue of or if you think there’s a good way to define in virtue of in terms of truthmaking.