A topological interpretation of three Leibnizian principles within the functional extensions
Three philosophical principles are often quoted in connection with Leibniz: "objects sharing the same properties are the same object" (Identity of indiscernibles), "everything can possibly exist, unless it yields contradiction" (Possibility as consistency), and "the ideal el...
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| Format: | Article |
| Language: | English |
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Logical Methods in Computer Science e.V.
2018-07-01
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| Series: | Logical Methods in Computer Science |
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| Online Access: | https://lmcs.episciences.org/4156/pdf |
| _version_ | 1827322770017484800 |
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| author | Marco Forti |
| author_facet | Marco Forti |
| author_sort | Marco Forti |
| collection | DOAJ |
| description | Three philosophical principles are often quoted in connection with Leibniz:
"objects sharing the same properties are the same object" (Identity of
indiscernibles), "everything can possibly exist, unless it yields
contradiction" (Possibility as consistency), and "the ideal elements correctly
determine the real things" (Transfer). Here we give a precise
logico-mathematical formulation of these principles within the framework of the
Functional Extensions, mathematical structures that generalize at once
compactifications, completions, and elementary extensions of models. In this
context, the above Leibnizian principles appear as topological or algebraic
properties, namely: a property of separation, a property of compactness, and a
property of directeness, respectively. Abiding by this interpretation, we
obtain the somehow surprising conclusion that these Leibnizian principles may
be fulfilled in pairs, but not all three together. |
| first_indexed | 2024-04-25T01:34:09Z |
| format | Article |
| id | doaj.art-16943ec73b7543c3a5f8fa9c85a31abe |
| institution | Directory Open Access Journal |
| issn | 1860-5974 |
| language | English |
| last_indexed | 2024-04-25T01:34:09Z |
| publishDate | 2018-07-01 |
| publisher | Logical Methods in Computer Science e.V. |
| record_format | Article |
| series | Logical Methods in Computer Science |
| spelling | doaj.art-16943ec73b7543c3a5f8fa9c85a31abe2024-03-08T10:02:03ZengLogical Methods in Computer Science e.V.Logical Methods in Computer Science1860-59742018-07-01Volume 14, Issue 310.23638/LMCS-14(3:5)20184156A topological interpretation of three Leibnizian principles within the functional extensionsMarco FortiThree philosophical principles are often quoted in connection with Leibniz: "objects sharing the same properties are the same object" (Identity of indiscernibles), "everything can possibly exist, unless it yields contradiction" (Possibility as consistency), and "the ideal elements correctly determine the real things" (Transfer). Here we give a precise logico-mathematical formulation of these principles within the framework of the Functional Extensions, mathematical structures that generalize at once compactifications, completions, and elementary extensions of models. In this context, the above Leibnizian principles appear as topological or algebraic properties, namely: a property of separation, a property of compactness, and a property of directeness, respectively. Abiding by this interpretation, we obtain the somehow surprising conclusion that these Leibnizian principles may be fulfilled in pairs, but not all three together.https://lmcs.episciences.org/4156/pdfmathematics - logiccomputer science - logic in computer sciencemathematics - general topology03a05, 03h05, 03e65 |
| spellingShingle | Marco Forti A topological interpretation of three Leibnizian principles within the functional extensions Logical Methods in Computer Science mathematics - logic computer science - logic in computer science mathematics - general topology 03a05, 03h05, 03e65 |
| title | A topological interpretation of three Leibnizian principles within the functional extensions |
| title_full | A topological interpretation of three Leibnizian principles within the functional extensions |
| title_fullStr | A topological interpretation of three Leibnizian principles within the functional extensions |
| title_full_unstemmed | A topological interpretation of three Leibnizian principles within the functional extensions |
| title_short | A topological interpretation of three Leibnizian principles within the functional extensions |
| title_sort | topological interpretation of three leibnizian principles within the functional extensions |
| topic | mathematics - logic computer science - logic in computer science mathematics - general topology 03a05, 03h05, 03e65 |
| url | https://lmcs.episciences.org/4156/pdf |
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