Abstract:

Leibniz famously claims that the world is governed by two complete sets of laws of corporeal nature, one mechanical and one final–causal. Some readers have thought this mere bluff (e.g. Bennett 2005), but Jeffrey McDonough (2008; 2022) has argued persuasively that Leibniz is committed to two complete and equipotent sets of laws that are nonetheless harmonious.
Granting that Leibniz really does seek complete and equipotent sets of laws, I argue that these two realms of law are not in harmony. I structure my argument around the following conditional:

(1) If mechanistic and final-causal laws diverge, and
(2) if mechanistic and final-causal laws are both construed as objective, then
(C) there is a conflict between Leibniz’s realms of mechanistic and final–causal law.

As I see it, defenders of harmony between Leibniz’s two realms do not dispute this conditional. Rather, they deny either (1) or (2). For example, McDonough has urged that (1) need not be true, but more recently has focused on denying (2). Laws of nature are mere “ideal abstractions,” on this view, and the world can be represented by arbitrarily many ideal abstractions (2022, 52; cf. 2008, 681; Rutherford 1995, 217).

I will first support (1) by arguing that these two sets of laws diverge in their dictates about asymmetric dependence between parts and wholes. Leibniz’s account of mechanistic law takes properties of material wholes to be determined by their parts. By contrast, his paradigm laws in optics proceed from whole to part. For Leibniz, parts and wholes stand in a conditioning or grounding relation. This relation is antisymmetric, so parts and wholes cannot be mutually conditioning. Thus Leibniz ought to treat this as a case of nomic conflict, rather than mere overdetermination.

In support of (2), I then argue that even if laws of nature in Leibniz are abstract or ideal entities, he is committed to realism about the content of laws, which means that genuine laws cannot contradict one another. Realism follows from his assertions that laws of phenomena are well–founded. They are both metaphysical and logical consequences of more basic laws of monads, which are harmonized in a single law of the actual world in its totality. This law fully metaphysically determines all facts about the phenomenal world, so for any phenomenal fact, it must be determinate whether parts ground wholes or wholes ground parts. And because of the logical consequence relation between the law of the world and the laws of mechanics, negating the laws of mechanics (because they contradict final– causal laws) entails by modus tollens the negation of the law of the actual world itself.