A Leibnizian Way Out of the Rationalist’s Dilemma (Part 1)

[Comments on Jeffrey McDonough’s “Leibniz, Spinoza and an Alleged Dilemma for Rationalists” (Ergo 2015), by Chloe Armstrong]

 

Consider the following argument that starts with a Leibnizian view about relations:¹

1. Relations are ideal; they are not accidents that inhere jointly in their relata but exist insofar as they are apprehended or cognized by a mind comparing the relata.²
2. Coexistence is a relation.
3. Thus, the coexistence between distinct objects is ideal.
4. If coexistence between distinct objects is ideal, then no numerically distinct objects can coexist.
5. Therefore, no numerically distinct objects can coexist.

The conclusion of the argument endorses radical monism—the   denial that there exists a plurality of objects (including substances, attributes, and modes). This conclusion is unacceptable for Leibniz who maintains that there is a plurality of substances each with a multiplicity of states. (See, e.g., Monadology §§1-8.) Leibniz is in trouble if his analysis of relations undermines the existence of distinct objects. However, the problem runs deeper because Leibniz’s views about relations results from his commitment to the Principle of Sufficient Reason (PSR):

 

If an object x is in a certain state (or has a certain property or whatever), then there must be some thing or things in which the state is grounded, some thing or things in virtue of which the thing is in that state (McDonough 368).

The PSR, so formulated, requires that all states—including relations—be grounded. If the only way to ground relations is to affirm their ideality, then Leibniz’s commitment to the PSR seemingly entails radical monism. Michael Della Rocca (2012) summarizes: “Leibniz’s dilemma is this: EITHER give up the claim that there is a multiplicity of objects and that there are states of objects OR give up the claim that relations are grounded” (157).

 

Leibniz’s Way Out:

Jeffrey McDonough argues that Leibniz has a way out of this dilemma: the fact that coexistence is an ideal entity does not rule out the possibility of coexisting objects. The key is to distinguish two types grounding relations: ontological grounding and semantic or truth-making grounding. The ontological ground of a relation is that in virtue of which the relation exists (373). For example, the ontological ground of the relation of coexistence is an idea in God’s mind. Semantic or truth-making grounding explains why a statement or proposition is true, and, in the case of relations, it specifies the conditions under which a relational predicate holds (375). McDonough observes that the fact that the ontological ground of relations is ideal and mind-dependent does not thereby render the semantic ground of relations mind-dependent. Instead, the truth of relational predication might well be grounded in non-relational properties of each of the relata. In the case of coexistence, McDonough claims that the semantic ground of the relation is the existence of each of the relata. Put differently: coexistence is semantically grounded in existence. Thus, premise (4) of the above argument is false because coexistence is ontologically ideal but semantically real. If coexistence is a two-place relational predicate, Rxy, the fact that R picks out an ideal entity does not prevent Rab from being true as long as a and b each exist.

 

Semantic Grounding in Leibniz’s System:

I want to consider semantic grounding first with respect to Leibniz’s own system, and then with respect to Della Rocca’s more general way into the Rationalist’s Dilemma (which does not depend on uniquely Leibnizian views about the ideality of relations).

 

I’m particularly interested in the first issue, since it is not clear that we can successfully account for semantic grounding of coexistence in the Leibnizian system. This is because there are texts in which Leibniz not only identifies relations as dependent on God’s mind, but also seems to affirm that truth is similarly dependent:

 

The reality of relations is dependent on mind, as is that of truths; but they do not depend on the human mind, as there is a supreme intelligence which determines all of them from all time (New Essays 265).

God not only sees individual monads and the modifications of every monad whatsoever, but he also sees their relations, and in this consists the reality of relations and of truth (Notes for Leibniz to Des Bosses, 5 February 1712).

The above passages seem to assimilate the ideality of relations and the ideality of truth(s). If both the ontological and semantic grounds of coexistence are ideal, McDonough’s distinction between ontological and semantic grounds might not be viable for Leibniz.

 

This issue is also tied to the question of how to reconcile McDonough’s account of semantic grounding with Leibniz’s conceptual containment theory of truth. While it is very natural to ground the truth of coexistence of a and b in the existence of a and the existence of b, Leibniz famously maintains that truth is a matter of conceptual containment. Whether existence is contained in the complete concepts of substances is a controversial interpretive matter, but Leibniz does make it clear that the truth of other relations, such as Caesar having crossed the Rubicon, is true because the concept of having crossing the Rubicon is contained in Caesar’s concept. This suggests that—contra McDonough’s suggestion—the semantic ground for relations rests not in features of the relata themselves, but their concepts or notions.

 

I think, however, that reconciling the conceptual containment theory of truth with McDonough’s account will help explain how relational truths are semantically dependent on God’s mind, but not ideal in the same way as the ontological ground of relations. Perhaps relations are semantically grounded in both the existence of the relata and the concepts of the relata. For example, if God creates substances according to their complete concepts, then complete concepts semantically ground relations by (at least partially) grounding the relevant features of the substance that in turn ground the relation. In this sense truth is mind-dependent, but not ideal, because there is no individual entity corresponding to God’s idea of a relation in the world, but there are entities corresponding to complete concepts and those entities are the immediate ground of relational truths.

 

Both Della Rocca and McDonough stress that Della Rocca’s dilemma is not unique to Leibniz’s system, but confronts anyone committed to the PSR. That said, the above formulation of the problem depends on distinctive Leibnizian commitments including the ideality of relations. Why, then, should we take Leibniz’s way out if we reject key aspects of Leibniz’s way into the problem? I’ll take this question up in Part 2.

 

[Thanks to Stewart Duncan for inviting this post, and thanks to Jeff McDonough in advance for taking the time to respond.  In “Leibniz, Spinoza and an Alleged Dilemma for Rationalists” McDonough not only steers us through some of the most challenging aspects of Leibniz’s system, but also–amidst these opaque topics–develops the resources to engage the Rationalist’s Dilemma.   My comments reflect only a portion of McDonough’s enlightening and subtle discussion.]

Notes:

1. This is drawn from Jeffrey McDonough’s argument in “Leibniz, Spinoza and an Alleged Dilemma for Rationalists” (Ergo 2015). McDonough’s version is based on Michael Della Rocca’s discussion in “Violations of the Principle of Sufficient Reason (in Leibniz and Spinoza),” in Metaphysical Grounding: Understanding the Structure of Reality (Eds. Fabrice Correia and Benjamin Schnieder), Cambridge University Press: 2012, 139-164.

2. The sense in which relations are mind-dependent does not follow directly from Leibniz’s immaterialism. The distinction between ideal and real is one that Leibniz draws within his system. Relations are ideal in the sense that they are not states of the substances that they relate, but instead states that depend on a mind that understands the relevant features of the substances and compares them.

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