Intensional Semantics for Syllogistics: what Leibniz and Vasiliev Have in Common
DOI:
https://doi.org/10.12775/LLP.2022.006Słowa kluczowe
intensional semantics, Leibniz, multivalued logic, non-classical logic, imaginary logic, syllogistics, VasilievAbstrakt
This article deals with an alternative interpretation of syllogistics, different from the classical (extensional) one: an intensional one, in which subject and predicate are not associated with a set of individuals (the extension of the concept) but a set of attributes (the content of the concept). The authors of the paper draw attention to the fact that this approach was first proposed by Leibniz in works on logical calculus, which for a long time remained in the shadow of his other philosophical works. Currently, the intensional approach is gaining more and more popularity due to the development of non-classical logics, and the article will present several existing intensional formal syllogistic semantics.
The paper will also consider another historical approach to syllogistics, associated with the name of the Russian logician Nikolai Vasiliev, who is not only one of the founders of non-classical (non-Aristotelian logic) but also of a different intensional interpretation of such logic. The authors, along with the already known formalizations of Vasiliev’s ideas, present two new systems. One of them is a reconstruction of one type of imaginary logic with statements of three qualities: affirmative and two types of negative statements (with absolute and ordinary negation). The second system is the one that is adequate to semantics, in which instead of the four classical ones, only three types of statements are presented (two particular statements are replaced by one - accidental), and their significance is determined through the relation of the classical logical entailment. Both of them are interpreted intensionally.
The intensional approach in logic and, in particular, in syllogistics allows us to expand the class of accepted principles (which occurs due to the expansion of the class of correct moods of syllogisms).
Bibliografia
Aristotle, 1967, “Aristotle’s categories”, translated by J. L. Ackrill, in J. M. E. Moravcsik (ed.), Aristotle. Modern Studies in Philosophy, Palgrave Macmillan, London. DOI: https://doi.org/10.1007/978-1-349-15267-4_6
Glashoff, K., 2010, “An intensional Leibniz semantics for Aristotelian logic”, The Review of Symbolic Logic 3: 262–272. DOI: https://doi.org/10.1017/S1755020309990396
Kostiouk, T. P., and V. I. Markin, 1998, “Formal reconstruction of imaginary logic of N. A. Vasiliev” (in Russian), pages 154–159 in Modern Logic: Theory, History and Applications in Science. Proceedings of V Russian Scientific Conference, St. Petersburg: Publishing House of St. Petersburg State University.
Konkova, A. V., 2019, “Imaginary logic–2 as syllogistic theory” (in Russian), Logical Investigations 25 (2): 94–113. DOI: https://doi.org/10.21146/2074-1472-2019-25-2-94-113
Konkova, A. V., and V. I. Markin, 2020, “Syllogistics with two types of negation (reconstruction of one idea of N. A. Vasiliev)” (in Russian), Bulletin of the Moscow University, Series 7, Philosophy, 5, 7: 108–123.
Leibniz, G. W., and L. Couturat, 1903, “Opuscules Et Fragments Inédits de Leibniz Extraits des Manuscrits de la Bibliothèque Royale de Hanovre”, Paris: F. Alcan.
Leibniz, G. W., 1916, New Essays Concerning Human Understanding, translation by A. G. Langley, 2nd ed., Chicago, London: The Open Court Publishing Company.
Leibniz, G. W., 1989, “Two studies in the logical calculus”, in L. E. Loemker (ed.), Philosophical Papers and Letters. The New Synthese Historical Library (Texts and Studies in the History of Philosophy), vol. 2. Springer, Dordrecht. DOI: https://doi.org/10.1007/978-94-010-1426-7_27
Lenzen, W., 1983, “Zur extensionalen und “intensionalen” interpretationen der Leibnizschen logic”, Studia Leibnitiana: 129–148.
Markin, V. I., 2001, “Intensional semantics for traditional syllogistic” (in Russian), Logical Investigations 8: 82–91. DOI: https://doi.org/10.21146/2074-1472-2001-8-0-82-91
Markin, V. I., 2016 “Interpretation of categorical propositions in termsof relevant entailment” (in Russian), Logical Investigations 22 (1): 70–81. DOI: https://doi.org/2074-1472-2016-22-1-70-81
Shalack, V. I., 2015, “Syntactic interpretation of categorical attributive propositions” (in Russian), Logical Investigations 21 (1): 60–78. DOI: https://doi.org/2074-1472-2015-21-1-60-78
Van Rooij, R., 2014, “Leibnizian intensional semantics for syllogistic reasoning”, 2014, oages 179-194 in H. Wansing et al. (eds.), Recent Trends in Philosophical Logic, Springer. DOI: https://doi.org/10.1007/978-3-319-06080-4_13
Vasiliev, N. A., 1989, Imaginary Logic. Selected Works, Moscow: Nauka.
Zaitsev, D., 2017, “Generalized Vasiliev-style propositions”, in: V. Markin and D. Zaitsev (eds.), The Logical Legacy of Nikolai Vasiliev and Modern Logic, Synthese Library, Studies in Epistemology, Logic, Methodology, and Philosophy of Science, vol. 387, Springer. DOI: https://doi.org/10.1007/978-3-319-66162-9_11
Zaitsev, D. V., and V. I. Markin, 1999, “Imaginary logic–2. Reconstruction of one of the variants of the famous logical system of N. A. Vasiliev” (in Russian), pages 134–142 in Proceedings of the Scientific research seminar of the Logical Center of the Institute of Philosophy of the Russian Academy of Sciences, Vol. 13.
Pobrania
Opublikowane
Jak cytować
Numer
Dział
Licencja
Prawa autorskie (c) 2022 Antonina Konkova, Maria Legeydo
Utwór dostępny jest na licencji Creative Commons Uznanie autorstwa – Bez utworów zależnych 4.0 Międzynarodowe.
Statystyki
Liczba wyświetleń i pobrań: 1503
Liczba cytowań: 0
