In a 1687 letter to Arnauld, Leibniz draws on an argument against mind-body causation that is reminiscent of one from Spinoza’s Ethics. According to this argument, mind-body causation is impossible because of the lack of proportion between thoughts and motions. This paper aims to shed light on Leibniz’s use of Spinoza’s argument by reconstructing both its internal structure and its development in Leibniz’s later works. In particular, the reconstruction focuses on the new version of this argument that Leibniz adopts against Stahl’s vitalism as well as on the change that this new version reveals in Leibniz’s attitude towards occasionalism. The possible influence of Cordemoy is also taken into consideration. The epistemological and metaphysical issues surrounding this argument are an essential part of the history of Leibniz’s psycho-physical parallelism.

This paper deals with the metaphysics of the notion of quantity in the philosophy of Leibniz, and its aim is to defend the following bi-conditional: for any object x, x has a certain quantity if and only if x has a (metaphysical) limit or a bound. The direction from left to right is justified in §3, while in §4 I develop an argument to justify the direction from right to left. Since the bi-conditional links the metaphysical notion of limit to the mathematical notion of quantity (and in this way it links Leibniz’s metaphysics with his conception of Mathesis Universalis), it allows the use of metaphysics to clarify the features of the mathematical notion of quantity. This task is accomplished in §5 and §6. Finally, §7 discusses a possible objection.

In these remarks on Ohad Nachtomy’s account of Leibniz’s philosophy of the infinite in his recent book, Living Mirrors, I focus on his suggestion that living creatures be interpreted as exemplifying the second of the three degrees of infinity that Leibniz articulates in 1676, as things which are infinite in their own kind. For the infinity characterizing created substances cannot be the highest degree, which is reserved by Leibniz for the divine substance, while Nachtomy sees the lowest degree as applicable only to “entia rationis such as numbers and relations”. Against this, I argue that the lowest or syncategorematic infinite applies to any multiplicity or magnitude that is greater than any assignable, so that something further can always be added; whereas the second degree applies to the divine attributes or perfections, which are maximal in that nothing further of that kind can be added.