Is Leibnizian calculus embeddable in first order logic?
| Autor: | Piotr Błaszczyk, Karin U. Katz, Mikhail G. Katz, Thomas Mormann, David Sherry, Vladimir Kanovei, Taras Kudryk |
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| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
Computer science
History and Overview (math.HO) Infinitesimal 050905 science studies 01 natural sciences 03B10 26E35 01A45 History and Philosophy of Science Computer Science::Logic in Computer Science FOS: Mathematics Calculus medicine 0101 mathematics Relation (history of concept) Calculus (medicine) Philosophy of science Multidisciplinary Mathematics - History and Overview 010102 general mathematics 05 social sciences Mathematics - Logic medicine.disease First-order logic Focus (linguistics) Ontology 0509 other social sciences Logic (math.LO) |
| Popis: | To explore the extent of embeddability of Leibnizian infinitesimal calculus in first-order logic (FOL) and modern frameworks, we propose to set aside ontological issues and focus on procedural questions. This would enable an account of Leibnizian procedures in a framework limited to FOL with a small number of additional ingredients such as the relation of infinite proximity. If, as we argue here, first order logic is indeed suitable for developing modern proxies for the inferential moves found in Leibnizian infinitesimal calculus, then modern infinitesimal frameworks are more appropriate to interpreting Leibnizian infinitesimal calculus than modern Weierstrassian ones. Keywords: First order logic; infinitesimal calculus; ontology; procedures; Leibniz; Weierstrass; Abraham Robinson 22 pages, to appear in Foundations of Science |
| Databáze: | OpenAIRE |
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