On the Definability of Leśniewski’s Copula ‘is’ in Some Ontology-Like Theories
Marcin Łyczak; Andrzej Pietruszczak
Bulletin of the Section of Logic (2018)
- Volume: 47, Issue: 4
- ISSN: 0138-0680
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topMarcin Łyczak, and Andrzej Pietruszczak. "On the Definability of Leśniewski’s Copula ‘is’ in Some Ontology-Like Theories." Bulletin of the Section of Logic 47.4 (2018): null. <http://eudml.org/doc/295579>.
@article{MarcinŁyczak2018,
abstract = {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.},
author = {Marcin Łyczak, Andrzej Pietruszczak},
journal = {Bulletin of the Section of Logic},
keywords = {elementary ontology; quantifier-free fragment of ontology; ontology-like theories; copula ‘is’; calculus of names; Leśniewski's ontology; subtheories of Leśniewski’s ontology},
language = {eng},
number = {4},
pages = {null},
title = {On the Definability of Leśniewski’s Copula ‘is’ in Some Ontology-Like Theories},
url = {http://eudml.org/doc/295579},
volume = {47},
year = {2018},
}
TY - JOUR
AU - Marcin Łyczak
AU - Andrzej Pietruszczak
TI - On the Definability of Leśniewski’s Copula ‘is’ in Some Ontology-Like Theories
JO - Bulletin of the Section of Logic
PY - 2018
VL - 47
IS - 4
SP - null
AB - 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.
LA - eng
KW - elementary ontology; quantifier-free fragment of ontology; ontology-like theories; copula ‘is’; calculus of names; Leśniewski's ontology; subtheories of Leśniewski’s ontology
UR - http://eudml.org/doc/295579
ER -
References
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- 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.
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- 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.
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- 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.
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