On the Definability of Leśniewski’s Copula ‘is’ in Some Ontology-Like Theories

• Autorzy: Marcin Łyczak , Andrzej Pietruszczak
• Języki publikacji: EN

Abstrakty

EN

We formulate a certain subtheory of Ishimoto’s [1] quantifier-free fragment of Leśniewski’s ontology, and show that Ishimoto’s theory can be reconstructed in it. Using an epimorphism theorem we prove that our theory is complete with respect to a suitable set-theoretic interpretation. Furthermore, we introduce the name constant 1 (which corresponds to the universal name ‘object’) and we prove its adequacy with respect to the set-theoretic interpretation (again using an epimorphism theorem). Ishimoto’s theory enriched by the constant 1 is also reconstructed in our formalism with into which 1 has been introduced. Finally we examine for both our theories their quantifier extensions and their connections with Leśniewski’s classical quantified ontology.

Słowa kluczowe

EN

elementary ontology; quantifier-free fragment of ontology; ontology-like theories; copula ‘is’; calculus of names; Leśniewski's ontology; subtheories of Leśniewski’s ontology

• Wydawca: Wydawnictwo Uniwersytetu Łódzkiego
• Czasopismo: Bulletin of the Section of Logic
• Rocznik: 2018
• Tom: 47
• Numer: 4

Daty

wydano

2018-12-30

Twórcy

autor

Marcin Łyczak

• Cardinal Stefan Wyszyński University, Institute of Philosophy, Department of Logic

autor

Andrzej Pietruszczak

• Nicolaus Copernicus University in Toru´n, Department of Logic

Bibliografia

• A. Ishimoto, A propositional fragment of Leśniewski’s ontology, Studia Logica 36 (1977), pp. 285–299.
• B. Iwanuś, On Leśniewski’s elementary ontology, Studia Logica 31 (1973), pp. 73–119. Reprint: pages 165–215 in [9].
• A. Pietruszczak, Bezkwantyfikatorowy rachunek nazw. Systemy i ich metateoria (Quantifier-free Calculus of Names. Systems and their Metatheory), Wydawnictwo Adam Marszałek, Toruń 1991.
• A. Pietruszczak, Standardowe rachunki nazw z funktorem Leśniewskiego (Standard calculus of name with Leśniewski’s copula), Acta Universitatis Nicolai Copernici, Logika I (1991), pp. 5–29.
• A. Pietruszczak, O teoriach pierwszego rzędu związanych z elementarnym fragmentem ontologii Leśniewskiego (About first-order theories connected with elementary fragment of Leśniewski’s ontology), pages 127–168 in J. Perzanowski and A. Pietruszczak (eds.), Logika & Filozofia Logiczna 1996–1998, Wydawnictwo Naukowe UMK, Toruń 2000.
• H. Rasiowa and R. Sikorski, The Mathematics of Metamathematics, PWN, Warszawa 1970.
• J. Słupecki, S. Leśniewski’s calculus of names, Studia Logica 3 (1955), pp. 7–72. Reprint: pages 59–122 in [9].
• B. Sobociński, O kolejnych uproszczeniach aksomatyki »ontologji« Prof. St. Leśniewskiego (On the successive simplifications of the axiom of professor Leśniewski’s »ontology«), pages 145–160 in Fragmenty Filozoficzne. Księga pamiątkowa ku uczczeniu 15-lecia pracy nauczycielskiej w Uniwersytecie Warszawskim Prof. Tadeusza Kotarbińskiego, Warszawa, 1934. English translation by Z. Jordan in S. McCall (ed.), Polish Logic 1920–1939, Clarendon Press, Oxford, 1967.
• J. Srzednicki et al. (eds.), Leśniewski’s Systems. Ontology and Mereology, Martinus Nijhoff Publishers and Ossolineum, The Hage, Boston and Wrocław, 1984.
• M. Takano, A semantical investigation into Leśniewski’s axiom of his ontology, Studia Logica 44, 1 (1985), pp. 71–77.

Identyfikatory

DOI

10.18778/0138-0680.47.4.02