Leibniz on the Empty Term ‘Nothing’

Filippo Costantini
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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).
莱布尼茨论“虚无”这个空词
本文讨论了莱布尼茨对一些关于实加法概念的逻辑论文中出现的“虚无”一词的处理方法。首先,本文认为术语应该被理解为一个空的(单数的)术语,并且有空术语的句子可以是真的(§2)。第二,它勾画出一个肯定的自由逻辑来描述空项的逻辑行为(§3)。解释这种方法避免了矛盾后威胁的引入‘虚无’这个词在现实之外微积分(§4),以及应该如何理解这种方法在莱布尼茨的哲学(§5),本文对这种方法的前景对莱布尼茨的思想的两个基本问题:无穷小的虚构性质(§6),和“没有”一词的出现证明上帝的存在,我们发现在新的论文(§7)。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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