Leibniz on the Empty Term ‘Nothing’
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 po...
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| Format: | Article |
| Language: | English |
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Fondazione Università Ca’ Foscari
2021-12-01
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| Series: | JoLMA |
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| Online Access: | http://doi.org/10.30687/Jolma/2723-9640/2021/02/001 |
| _version_ | 1797464608364036096 |
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| author | Costantini, Filippo |
| author_facet | Costantini, Filippo |
| author_sort | Costantini, Filippo |
| collection | DOAJ |
| description |
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).
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| first_indexed | 2024-03-09T18:10:36Z |
| format | Article |
| id | doaj.art-298c75b82ffa415a8492f257386e9e4a |
| institution | Directory Open Access Journal |
| issn | 2723-9640 |
| language | English |
| last_indexed | 2024-03-09T18:10:36Z |
| publishDate | 2021-12-01 |
| publisher | Fondazione Università Ca’ Foscari |
| record_format | Article |
| series | JoLMA |
| spelling | doaj.art-298c75b82ffa415a8492f257386e9e4a2023-11-24T09:10:09ZengFondazione Università Ca’ FoscariJoLMA2723-96402021-12-012210.30687/Jolma/2723-9640/2021/02/001journal_article_6191Leibniz on the Empty Term ‘Nothing’Costantini, Filippo0Università Ca’ Foscari Venezia, Italia 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). http://doi.org/10.30687/Jolma/2723-9640/2021/02/001Empty terms. Leibniz. Mereology. Nothingness. Positive Free Logic. Real Addition |
| spellingShingle | Costantini, Filippo Leibniz on the Empty Term ‘Nothing’ JoLMA Empty terms. Leibniz. Mereology. Nothingness. Positive Free Logic. Real Addition |
| title | Leibniz on the Empty Term ‘Nothing’ |
| title_full | Leibniz on the Empty Term ‘Nothing’ |
| title_fullStr | Leibniz on the Empty Term ‘Nothing’ |
| title_full_unstemmed | Leibniz on the Empty Term ‘Nothing’ |
| title_short | Leibniz on the Empty Term ‘Nothing’ |
| title_sort | leibniz on the empty term nothing |
| topic | Empty terms. Leibniz. Mereology. Nothingness. Positive Free Logic. Real Addition |
| url | http://doi.org/10.30687/Jolma/2723-9640/2021/02/001 |
| work_keys_str_mv | AT costantinifilippo leibnizontheemptytermnothing |