At the end of her last post, Armstrong raised the question of why we should be tempted to follow Leibniz’s way out of Della Rocca’s Dilemma if we reject key aspects of Leibniz’s way into the problem. The short answer, I think, is that the aspects of Leibniz’s way into the problem that are most problematic are not essential to his way out of Della Rocca’s Dilemma. Leibniz’s suspect commitment to relations being at least partially ontologically grounded in the divine intellect makes Della Rocca’s Dilemma more challenging, not less. Watching Leibniz juggle five balls makes it easier to see how we can juggle three.
I introduced the distinction between ontological and semantic grounding largely to explain the sense in which relations are and are not ideal for Leibniz. If we turn specifically to Della Rocca’s argument against the possibility of relata jointly grounding relations I don’t think that distinction is particularly important. What is important is the thought that at least some relational facts might be wholly grounded in their relata, that, for example, the fact that a and b co-exist might be wholly grounded in the existence of a and the existence of b. Borrowing notation that I learned from my colleague Selim Berker, we might express (what I’ll call) Leibniz’s Key Thought by saying that [p • q] <- [p], [q] where “[p]” is shorthand for “the fact that p,” and “[p] <- [q]” is shorthand for “[p] is fully grounded in [q].”
Although I think most contemporary philosophers accept Leibniz’s Key Thought, Della Rocca and Bradley would, I believe, demur. They think that [p], [q] cannot fully ground [p • q] on their own. Something more, in their view, is needed, namely, [p] and [q]’s standing in a certain relation, call it “R.” So, to fully ground [p • q], we’d need at least [p], [q] and R. But wait, they’ll say, [p], [q] and R also can’t fully ground [p • q] on their own. For the same reason as before, something more is needed, namely, their standing in some relation, call it “R’”. And so on. If one allows the first regress, obviously we’ll be off to the races. Either we will be committed to doubling back at some point, falling into a vicious circle, or we’ll be launched on an infinite regress. I think contemporary rationalists should follow Leibniz’s lead and nip the regress in the bud by accepting his Key Thought.
If I’ve understood her correctly, Armstrong sees Della Rocca’s argument against the possibility of relata jointly grounding relations slightly differently. Her suggestion is that, according to Della Rocca, “the coexistence of a and b requires the relation of partial grounding, which is itself grounded in the coexistence of a and b.” This suggestion, she thinks, generates an “additional fact in need of explanation … namely, why does the fact that a’s existence partially grounds a and b’s coexistence require appeal to both a and b?” But, as I think Armstrong would agree, if there is such a fact as a’s existence partially grounds a and b’s coexistence, it looks like it too can be grounded in a’s existence and b’s existence. Using Berker’s shorthand, and letting “[p] <- – – [q]” stand for “[p] is partially grounded in [q],” we can say [[p • q] <- – -[p]] <- [p], [q]. If Leibniz’s Key Thought is accepted, it will take care not only of Della Rocca’s Dilemma as I’ve interpreted it, but also as Armstrong has interpreted it. Either way, contemporary rationalists could do a whole lot worse than to follow Leibniz’s way out of Della Rocca’s Dilemma.
Thanks again to Armstrong for her careful reading and thoughtful comments. And thanks to Stewart Duncan for setting up our exchange.
[Posted on behalf of Jeff McDonough]