REALE · Reassessing Leibniz's conception of number and the infinite
Horizon 2020 — Marie Skłodowska-Curie Actions
- Duration
- 2021-01-01 → 2023-12-31
- EU contribution
- €237,768
- Participants
- 2
- Scheme
- MSCA-IF
Lines connect the coordinator with its partners.
Results in brief
Reassessing Leibniz's conception of number and the infinite
The project aims at reconstructing Leibniz’s conception of number and his mathematical notion of infinite in light of his mereological theory (i.e. the theory of the parthood relation) of quantity. The project is articulated into three main parts: the study of Leibniz’s mereological calculus and its philosophical implications; the study of Leibniz’s theory of quantity, its metaphysical applications, and its connection with the notion of number, in particular real numbers; the role of infinity in his conception of the foundation of mathematics. The topic is particularly relevant for the promise of reassessing Leibniz's conception of the fundamental mathematical concepts beyond those related to the infinitesimal calculus. it aims at providing a richer understating of Leibniz's role in the history of philosophy and mathematics. The first objective is to provide a formalization of Leibniz’s mereological calculus and to study its logical properties. In particular, contemporary mereological is exploited to assess, from a logical point of view, the straighten and the weakness of Leibniz's fremework. The second objective is to clarify Leibniz's theory of quantity and the notion of number. After reconstructing the rules and operations that regulate the notion of quantity, and after explaining Leibniz's ideas concerning the problem of estimating quantities of different natures (estimating forces, lengths, volumes, etc.), the project shows how the concept of number (more specifically, positive relation number) is derived from this theory. The third objective is to investigate the view of the mathematical infinite in the light of the first two objectives. Particular attention is devoted to the relation between the distinction between the potential and the actual infinite and the reasons why Leibniz endorsed both of them. Moreover, it is shown how the mereological framework justifies Leibniz’s premises in his argument against the infinite number.
Data: CORDIS, © European Union
Project objective
The overall aim of the project is to investigate a neglected, though highly significant, topic in Leibniz’s thought: his general conception of number in light of his mereological theory. Special attention will be given to how this mereological background affects Leibniz’s conception of the infinite, and in particular his denial of the existence of an infinite number. In this way, the project will reshape the standard view according to which Leibniz’s rejection of infinite number is simply based on a faulty argument. On the contrary, the project’s ambition is to bring out – from Leibniz’s reflection on this topic – a (mereological) foundational theory for mathematics that can be seen as an alternative with regard to the standard set theoretical one. This topic has the potential to bridge the gulf now existing between an important mereological foundation of mathematics, as the Leibnizian’ one, with contemporary approaches – made in the 20th century by Lesniesky and his school on one side, and David Lewis’s Parts of Classes, on the other side – which exploit mereology to provide a less ontologically committed foundations for mathematics then set theory. The project can thus fill a gap in Leibniz’s scholarship and, at the same time, shed light on these contemporary attempts, and possibly revive some of their key aspects.
Original text from CORDIS.
Participants
Links
Data: CORDIS, © European Union