In Part 1, I raised some questions about how to understand semantic grounding as a response to the Rationalist’s Dilemma within Leibniz’s system. In this post, I will explore the notion of semantic grounding as a response to the dilemma as it arises for adherents to the PSR more generally.
According to McDonough’s solution, relations are semantically grounded in their relata jointly and still satisfy the PSR. In particular, McDonough thinks that the relation of coexistence is unproblematically grounded in the existence of its relata:
If one has an explanation for the fact that my dog exists, and one has an explanation for the fact that my cat exists, then ipsis factis one has an explanation for the fact that both my dog and cat exist…what is harder to imagine is [Leibniz] agreeing with the intuition that, say, having explained the fact that one substance exists and the fact that another substance exists, there should remain an additional fact still standing in need of explanation, namely, the fact that both substances exist (McDonough 379).
However, Della Rocca offers an argument against the possibility of relata jointly grounding relations. This argument is part of what makes Della Rocca’s dilemma worrisome for those that accept the PSR but reject Leibniz’s views on the ideality of relations (or substance-accident ontology for that matter). Della Rocca argues that the coexistence of objects cannot be grounded in the existence of those objects as follows:
…in order for a relation between a and b to hold, the relation must be partially grounded in a (and also partially grounded in b). Call this relation of partial grounding (between a and R) R’. So R holds in part because R’ holds. Why does R’, the relation of partial grounding between a and R, hold? There’s a relation, R’, of partial grounding between a and R only because a coexists with b. Call the relation of coexistence R”…Now in virtue of what do a and b co-exist, i.e. in virtue of what does the relation, R”, of coexistence hold? Just as R’ obtains in part because a and b coexist, so too R” obtains because a and b coexist…so R” holds in part because R” holds…And here we reach a circular explanation of a relation (Della Rocca 149).
The key move in the above argument is that grounding the coexistence of a and b requires the relation of partial grounding, which is itself grounded in the coexistence of a and b. McDonough, as we saw above, thinks that coexistence can be semantically grounded in existence, because it’s unlikely that “there should remain an additional fact still standing in need of explanation, namely, the fact that both substances exist.” It is, however, worth revisiting this issue precisely because Della Rocca does not think that coexistence directly appeals to the coexistence of both a and b. Instead, the relation of partial grounding generates appeals to the coexistence of a and b. My point is that the additional fact in need of explanation is a fact about grounding—namely, why does the fact that a’s existence partially grounds a and b’s coexistence require appeal to both a and b?
Perhaps Della Rocca is emphasizing the partial aspect of this relation. In order for it to be true that a partially grounds the coexistence of a and b, b must also partially ground coexistence. So the conditions under which a partially grounds a and b’s coexistence depends upon both a and b existing, or their coexistence.
On the one hand, I’m not sure I’m doing Della Rocca’s objection justice for, when reframed this way, it is still difficult to see why the partial grounding relation requires appeal to coexistence. The partial grounding relation itself is not so specific as to involve the other objects involved in partial grounding. Thus, to my mind, a’s existing partially grounds the coexistence of a and b in the same way that a’s existing partially grounds the coexistence of a and c, in the same way it would partially ground the coexistence of a, b, and c.
On the other hand, it is also true that a’s existence does not partially ground a and b’s coexistence without b’s existence. This, at least for me, gives Della Rocca’s worry some bite. But what this suggests is that a’s partial grounding depends on b’s existence, and thus only derivatively on the coexistence of a and b. So we have reason to think that a’s partial grounding relation too depends on a’s existence and b’s existence. This is consistent with what McDonough says about semantic grounding: not only is coexistence grounded in existence, but also the partial grounding of coexistence is grounded in existence. What is surprising, perhaps, is that a’s partial grounding depends upon b’s existence, but as long as it does not depend on their coexistence it is not circular.
Della Rocca’s argument above focuses on circularity, but he also raises an infinite regress worry—a Bradley-style regress—whereby the relation between x and y is grounded in a further relation which is grounded in other relations which are themselves grounded in other relations and so on (151). The relation of partial grounding is itself partially grounded thus there is the possibility for an infinite regress of grounding relations. While Leibniz seems opposed to an ontological regress of relations (see Mugnai 2010) it is less clear whether he would object to a semantic regress. Because the issue here is rooted in the ontological aspect of relations I have focused more on the circularity worry. However, if partial grounding can be grounded in existence, then even if there are an infinite number of semantic grounding relations as long as the ground for each is not itself a relation there is not a vicious semantic regress.
I’ll leave it to the reader to determine the gravity of Della Rocca’s objection, and the viability of my recommendations using McDonough’s resources. But, as I’ve rendered it, I think that Della Rocca’s objections raise the following important questions for developing a notion of semantic grounding:
- Do semantically grounded relations generate further truths about grounding?
- If grounding is a relation, are its instances semantically grounded?
- Is coexistence the (partial?) ground of the grounding relation for coexistence?
Della Rocca, Michael (2012). “Violations of the Principle of Sufficient Reason in Leibniz and Spinoza.” In Fabrice Correia and Benjamin Schnieder (Eds.), Metaphysical Grounding, Understanding the Structure of Reality (139-164). Cambridge University Press.
McDonough, Jeffrey (2015). “An Alleged Dilemma for Rationalists.” Ergo, 2, 367-392.
Mugnai, Massimo (2010). “Leibniz and ‘Bradley’s Regress.’” The Leibniz Review, 20, 1-12.