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Leibniz on the Empty Term ‘Nothing’

Filippo Costantini    Università Ca’ Foscari Venezia, Italia    

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abstract

This paper discusses Leibniz’s treatment of the term ‘nihil’ that appears in some logical papers about the notion of Real Addition. First, the paper argues that the term should be understood as an empty (singular) term and that sentences with empty terms can be true (§2). Second, it sketches a positive free logic to describe the logical behaviour of empty terms (§3). After explaining how this approach avoids a contradiction that threatens the introduction of the term ‘nihil’ in the Real Addition calculus (§4), and how this approach should be understood within Leibniz’s philosophy (§5), the paper assesses the prospects of such an approach with regard to two fundamental issues in Leibniz’s thought: the fictional nature of infinitesimals (§6), and the occurrence of the term ‘nothing’ in the proof of the existence of God that we find in the New Essays (§7).

Published
Dec. 15, 2021
Accepted
Aug. 31, 2021
Submitted
July 12, 2021
Language
EN

Keywords: Real AdditionMereologyEmpty termsNothingnessPositive Free LogicLeibniz

Copyright: © 2021 Filippo Costantini. This is an open-access work distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction is permitted, provided that the original author(s) and the copyright owner(s) are credited and that the original publication is cited, in accordance with accepted academic practice. The license allows for commercial use. No use, distribution or reproduction is permitted which does not comply with these terms.