My handout for the seminar yesterday is here – the paper we were discussing is here (subscription required). We were glad to have Cian Dorr drop in for the discussion – he really livened up what might have turned into an hour and a half of Gonzalo teaching everybody about how truthmakers work!
My take on the contribution which Gonzalo’s paper makes to the big-picture debate over truthmakers is as follows. Conceptions of truthmaking which appeal only to entailment, or to necessitation, get things importantly wrong. The way to fix up the account of truthmaking is to appeal to a metaphysical ‘in virtue of’ relation. Truthmaking is not mere sufficiency for the truth of a proposition. However, this undermines much of the appeal that truthmaker theory had for some of its original proponents – it does not, after all, allow us to avoid primitive metaphysical ‘grounding’ or ‘dependence’ relations. Still, it does not make truthmaker theory altogether useless – it just undermines the idea that it is a panacea for all ills in foundational metaphysics.
With those general thoughts out of the way, here are a few more straightforward conclusions to come out of the discussion:
– The view that Gonzalo settles on has fairly strong commitments to propositions. In the notation used in the paper, <P>, <P & P>, <P & P & P>… all come out as distinct propositions. This is because they can be made true in different ways – take P to be ‘there is a chair’. Then my chair and your chair can make true <P & P> jointly. My chair and your chair can make true <P> separately, but they can’t make it true jointly. Gonzalo wants to underwrite this with a view of propositions as internally structured entities.
– However, <P>, <P v P>, <P v P v P>… do not have to be taken as distinct propositions for the account to go through. This suggests a minimalist account of propositions compatible with Gonzalo’s truthmaker account as follows: propositions are identical iff, necessarily, they are made true by the same entities. So <P>, <P v P>, etc, come out as different names for a single proposition, while <P>, <P & P>, <P & P & P>… come out as distinct propositions. Why might we be attracted to this minimalist view of propositions? We might think we have a better grip on existence, and on the ‘in virtue of’ relation, than we do of that of a proposition. This view holds the promise of an explanatory account of what a proposition is in terms only of truthmaking and necessity.
– However, there are several pretty major problems with the minimalist view. One is that, if we take the truthmaker for a=a to be a itself, then the <a exists> comes out as the same as <a=a>, making a a necessary existent. Unless you’re Tim Williamson, this is a bad result. Another problem is that all necessary falsehoods would come out either as the same null proposition, or as not propositions at all – none of them have any truthmakers. I’m still tempted by the view though, and would be interested to hear any further objections to it.