The first year has been dedicated to the first objective. The research has been focused on Leibniz’s mereology as a formal calculus. Moreover, I have also deal with the philosophical problems arising form this calculus. In particular, I worked on Leibniz’s papers on Real Addition (the Plus-Minus Calculus) where Leibniz develops his mereological calculus. The analysis of Leibniz’s mereology has also exploited the other logical papers by Leibniz (in particular the Generales Inquisitiones) and some more mathematical works where Leibniz defines a number of important concepts (such as that of similarity, congruence, equality and homogeneity) which are at the heart of his notion of part. This study has been supplemented with a continuous study of contemporary mereology, with the aim of evaluating Leibniz’s achievement with regard to contemporary mereological formal systems.
This research has produced the following papers:
1. Leibniz’s on the Empty Term Nothing;
2. Composition as identity and the logical roots of Leibniz’s nominalism;
3. Leibniz’s Mereology: a Logical Reconstruction.
The second year has been dedicated to the second objective concerning the notions of quantity and numbers. The theory of quantity, which is based on mereological notions, gives us the general background to analysis the concept of number. I worked on the notion of quantity both from a mathematical point of view (reconstructing a formal theory of quantity) and from a metaphysical point of view (where I worked I on the role of the notion of quantity in Leibniz’s philosophy more generally). I have also analyzed the way in which Leibniz’s introduce the notion of quantity in the 1680s via a procedure that is reminiscent of definitions by abstractions.
This research has produced the following papers:
4. Quantity as Limit: Leibniz on the Metaphysics of Quantity; a paper devoted to the metaphysical interpretation of the notion of quantity in Leibniz’s philosophy.
5. Definitions by Abstraction and Leibniz's Notion of Quantity: a paper devoted to the abstractionist way in which quantity and other cognate notions are introduced by Leibniz in the 1680s.
6. From Measure to Numbers. Leibniz on Real Numbers. On the justification of real numbers in Leibniz via his own theory of measure.
The third year has been dedicated to the third objective of the project concerning the notion of infinite. First, I focused on the mathematical notion of infinite and I argued that his theory of measure clarifies Leibniz's position on the topic. In order for this theory to always provide an exact determination of ratios between magnitudes, when it deals with infinite sequences, these sequences must be considered actual, and not merely potential infinities (otherwise we would not have any exact measure, but only an approximation). Second, I focus on the metaphysical notion of infinite showing, once again, that the theory of measure plays a central role also in this context, especially with regard to Leibniz's rejection of the existence of a soul of the world.
The research has produced the following papers:
7.Estimating quantities. On how much of a thing there is.
8.There is no anima mundi. Leibniz's Argument against the Soul of the World.
