Leśniewski’s Concept of Names as Class Names

Zuzana Rybaříková

Abstract


Stanisław Leśniewski developed a system of logic and foundations of mathematics that considerably differs from Russell and Whitehead’s system. The difference between these two approaches to logic is significant primarily in the case of Leśniewski’s calculus of names, Ontology, and the concept of names that it contains. Russell’s theory of descriptions played a much more important role than Leśniewski’s concept of names in the history of philosophy. In response to that, several researchers aimed to approximate Leśniewski’s concept of names to Russell’s theory. There are several such attempts. This paper presents an interpretation that was suggested by Arthur Prior. Prior interpreted Leśniewskian names as class names. This interpretation was rejected by such prominent Leśniewskian scholars as Peter Simons or Rafal Urbaniak. According to Simons, class names oppose Leśniewski’s ontological views. Urbaniak claimed that Prior’s interpretation of Leśniewskian names as class names is unclear. The aim of this paper is to demonstrate that from the formal point of view, Prior’s interpretation could be justified.

Keywords


Stanisław Leśniewski; Arthur N. Prior; theory of descriptions; Leśniewski’s concept of names; Leśniewski’s Ontology

https://doi.org/10.5817/pf19-2-1904

Full Text:

PDF (Czech)

References

Show references Hide references

Geach, P. T. – Kenny, A. J. P. (1971): Editorial Note, in Prior, A. N. Objects of Thought, Clarendon Press 1971, vii–ix.

Ishimoto, A. (1977): A Propositional Fragment of Leśniewski's Ontology, Studia Logica 36(4), 285–299, dostupné na: .

Jadczak, R. (1993): Stanisław Leśniewski a Szkoła Lwowsko-Warszawska, Analecta 2/2(4), 29–38, dostupné na: .

Lejewski, C. (1954-1968): Letters from Lejewski to Prior, nevydané dopisy dostupné v Priorově pozůstalosti v Bodleyově knihovně v Oxfordu, box 2.

Lejewski, C. (1954a): Lejewski to Prior from 30. 11. 1954, nevydaný dopis dostupný v Priorově pozůstalosti v Bodleyově knihovně v Oxfordu, box 2.

Lejewski, C. (1954b): Logic and Existence, The British Journal for the Philosophy of Science 5(18), 104–119, dostupné na: .

Lejewski, C. (1977): Systems of Leśniewski's Ontology with the Functor of Weak Inclusion as the Only Primitive Term, Studia Logica 36(4), 323–349, dostupné na: .

Lejewski, C. (1984): On Leśniewski Ontology, in Srzednicki, J. T. J. – Rickey, V. F. (eds.) Leśniewski’s Systems: Ontology and Mereology, Kluwer Academic Publisher, 123–148.

Leśniewski, S. (1992a): On the Foundations of Mathematics, in Leśniewski, S. Collected Works I, Surma S.J. – Srzednicki J. T. J. – Barnett J. D. – Rickey V. F. (eds.), Kluwer Academic Publisher, 174–382.

Leśniewski, S. (1992b): Fundamentals of a New System of the Foundations of Mathematics, in Leśniewski, S. Collected Works II, Surma S.J. – Srzednicki J. T. J. – Barnett J. D. – Rickey V. F. (eds.), Kluwer Academic Publisher, 410–605.

Leśniewski, S. (1992c): On the Foundations of Ontology, in Leśniewski, S. Collected Works II, Surma S.J. – Srzednicki J. T. J. – Barnett J. D. – Rickey V. F. (eds.), Kluwer Academic Publisher, 606–628.

Ludlow, P. (2013): Descriptions, in Zalta, E. N. (ed.) The Stanford Encyclopedia of Philosophy. (Fall 2013 Edition) [online], 2004-03-02, rev. 2013-06-25 [navštíveno 2017-11-8], dostupné na: .

Miéville, D. (2009): Leśniewski, Negation, and the Art of Logical Subtlety, in Lapointe S et al (eds.) The Golden Age of Polish Philosophy: Kazimierz Twardowski’s Philosophical Legacy, Springer, 113–120.

Prior, A. N. (1955): English and Ontology, British Journal for the Philosophy of Science 6(21), 64–65, dostupné na: < https://doi.org/10.1093/bjps/VI.21.64>.

Prior, A. N. (1955-1956): Definitions, Rules and Axioms, Proceedings of the Aristotelian Society 56, 199–216, dostupné na: .

Prior, A. N. (1957): Time and Modality, Clarendon Press.

Prior, A. N. (1965): Existence in Lesniewśki and in Russell, Studies in Logic and the Foundations of Mathematics 40, 149–155, dostupné na: .

Prior, A. N. (1971): Objects of Thought, Clarendon Press.

Quine, W. V. O. (2006): Existence a kvantifikace, in Peregrin, J. (ed.) Logika 20. století: mezi filosofií a matematikou: výbor textů k moderní logice, Filosofia, 453–471.

Russell, B. (1967): Popisy, in Russell B., Logika, jazyk a věda, Svoboda, 38–50.

Russell, B. (2001): Poznání založené na obeznámenosti a poznání založené na deskripci, Filosofický časopis 49 (5), 754–770.

Rickey, V. F. (1975): Creative Definitions in Propositional Calculi, Notre Dame Journal of Formal Logic 14 (2), 273–293, dostupné na: < https://doi.org/10.1305/ndjfl/1093891710>.

Rickey, V. F. (1998a): A Survey of Leśniewski’s Logic, in Srzednicki, J. T. J. – Stachniak, Z. (eds.) Leśniewski's Systems: Protothetic, Kluwer Academic Publisher, 23–42.

Rickey, V. F. (1998b): Axiomatic Inscriptional Syntax. Part II: The Syntax of Protothetic, in Srzednicki, J. T. J. – Stachniak, Z. (eds.) Leśniewski's Systems: Protothetic, Kluwer Academic Publisher, 217–288.

Sagal, P. T. (1973): On How Best to Make Sense of Lesniewski’s Ontology, Notre Dame Journal of Formal Logic 14 (2), 259–262, , dostupné na: .

Simons, P. (1982): On Understanding Leśniewski, History and Philosophy of Logic 3(2), 1982, č. 2, s. 165–191, dostupné na: .

Simons, P. (1998): Nominalism in Poland, in Srzednicki, J. T. J. – Stachniak, Z. (eds.) Leśniewski's Systems: Protothetic, Kluwer Academic Publisher, 1–22.

Simons, P. (2015): Stanisław Leśniewski, in Zalta EN (ed.) The Stanford Encyclopedia of Philosophy (Winter 2015 Edition) [online], 2005-11-27, rev. 2015-11-10 [navštíveno 2017-11-8], dostupné na: .

Słupecki, J. (1984): S. Leśniewski’s Calculus of Names, in Srzednicki, J. T. J. – Rickey, V. F. (eds.) Leśniewski’s Systems: Ontology and Mereology, Kluwer Academic Publisher, 59–122.

Słupecki, J. (1998): St. Lesniewski's Protothetics, in Srzednicki, J. T. J. – Stachniak, Z. (eds.) Leśniewski's Systems: Protothetic, Kluwer Academic Publisher, 85–152.

Sobociński, B. (1953-1965): Letters from Sobocinski to Prior, nevydané dopisy dostupné v Priorově pozůstalosti v Bodleyově knihovně v Oxfordu, box 3.

Sobociński, B. (1998a): An Investigation of Protothetic, in Srzednicki, J. T. J. – Stachniak, Z. (eds.) Leśniewski's Systems: Protothetic, Kluwer Academic Publisher, 69–83.

Sobociński, B. (1998b): On the Single Axioms of Protothetic, in Srzednicki, J. T. J. – Stachniak, Z. (eds.) Leśniewski's Systems: Protothetic, Kluwer Academic Publisher, 153–217.

Surma, P. (2012): Poglądy filozoficzne Jana Łukasiewicza a logiki wielowartościowe, Semper, Varšava.

Tarski, A. (1998): On the Primitive Term of Logistic, in Srzednicki, J. T. J. – Stachniak, Z. (eds.) Leśniewski's Systems: Protothetic, Kluwer Academic Publisher, 43–68.

Urbaniak, R. (2008): Leśniewski and Russell’s Paradox: Some Problems, History and Philosophy of Logic 29 (2), 115–146,

dostupné na: < https://doi.org/10.1080/01445340701550817>.

Urbaniak, R. (2014): Leśniewski’s System of Logic and Foundations of Mathematics, Springer.

Woleński, J. (1985): Filozoficzna szkoła Lwowsko-Warszawska, Państwowe wydawnictwo naukowe.

Woleński, J. (1999): Reism and Leśniewski’s Ontology, in Woleński, J. Essays in the history of logic and logical philosophy, Jagiellonian University Press 1999, 13–21.




Copyright (c) 2019 author


Published by the Department of Philosophy, Faculty of Arts, Masaryk University, Brno, Czech Republic.
ISSN: 1212-9097