Abstract
The present paper proposes a comparative analysis of two standpoints on the existence and nature of universals hold by Stanisław Leśniewski and Bolesław Sobociński. We consider first the nominalistic argumentation of Leśniewski formalized by Sobocińki and described in the correspondence with J. M. Bocheński in 1956. Sobociński’s formalization revealed a fundamental pragmatic weakness of the reconstructed argumentation which was also mentioned by Sobociński. He himself was aware of the difficulties connected with an adequate interpretation of the crucial axiom, whose acceptance Leśniewski imputed to supporters of all theories of universals. Finally, the problem of the existence and nature of universals was elaborated by Sobociński also in a separate typescript “Uwagi w sprawie powszechników” (Remarks on universals). The view formulated by Sobociński comes from a combination of the methodology of deductive systems and the conceptualist standpoint. From the philosophical perspective Sobociński’s idea is both interesting and original, but it remained unknown to philosophers and logicians in general. For these reason we describe it and compare it with Leśniewski’s approach. We use in this description epistemological notions of R. Suszko. Our analysis enables to speak about universals in sense of Leśniewski, which are described by some universal in sense of Sobociński.
Research was carried out within the project Logic, Concepts, and Communication (LogiCCom, IP-2014-09-9378) financed by Croatian Science Foundation (HRZZ).
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Notes
- 1.
The historical presentation of all the discussion is shown by M. Grygianiec in [5].
- 2.
Such a role was played by the work “Sprawa istnienia przedmiotów idealnych” (The problem of the existence of ideal objects) [6] and by fragments devoted to Leśniewski’s argumentations from “Elementy teorii poznania, logiki formalnej i metodologii nauk” (Elements of cognitive theory, formal logic, and methodology of science) [7], which elicited replies from R. Ingarden and K. Ajdukiewicz. A report on this discussion can be found in [5, pp. 110–113].
- 3.
Such intentions can be found in the text of Sobociński’s letters. R. Murawski names Sobociński “an expert on logical problems” who has collaborated with all members of the Cracow Circle (J. M. Bocheński, J. Salamucha, F. Drewnowski). He participated in all of the meetings of the Circle, but he did not published any works related to the philosophical topics considered by the Circle [11, pp. 360–361].
- 4.
Under the subsequent symbolic expressions we quote Leśniewski’s original words from [9] (only variables are changed).
- 5.
Sobociński uses quotation marks here.
- 6.
The actual aim of the proof is discussed by K. Ajdukiewicz in his remarks on T. Kotarbiński’s report on Leśniewski’s idea [1, p. 227]. If someone accepts A1 (as an axiom), then the argument justifies implication Z1 → A7, and not the thesis of the non-existence of universals.
- 7.
Sobociński might have confused the dates of the argumentations of 1913 and 1927.
- 8.
This formula is equivalent to the definition of universal assumed in Luschei’s formalization of Leśniewski’s argument (cf. [10, p. 309]).
- 9.
Let us notice that although the thesis of EO is \(\neg \exists x (x\varepsilon \bigwedge )\), also \(\exists x (x \subset \bigwedge )\). The fact that \(x\subset \bigwedge \) is only equivalent to the fact that: ¬∃z(zεx)—we can say that in this situation x is an empty object.
- 10.
We owe this conception to M. Łyczak.
- 11.
In the further part of the text he will add that the effect of abstraction depends also on “our knowledge and other external circumstances”.
- 12.
For any sentential functor, an expression created by this functor and any sentence, should also have a logical value.
- 13.
In 1946, only a few days before Sobociński left Poland forever, the young Suszko visited him in Warsaw. Many years later Suszko told Professor Mieczysław Omyła about that only meeting with Sobociński, saying that they discussed logic. We do not know what problems they discussed during that meeting. Although the similarities between the approaches described by us may be accidental, to us it seems to be interesting also in the context of that meeting.
- 14.
- 15.
The notion of the adequacy of axioms was distinguished by Sobociński from the notions of the adequacy and completeness of theories. We assume the following simplification of his explanation: (1) a set of formulas expressed in a language of a given theory is adequate when the set of all the theses of a given theory can be deduced from that set of formulas (cf. [14, pp. 56–57]); (2) independence is understood as such a property of a set of axioms that none of its elements can be deduced on the grounds of a specific theory from other axioms.
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Acknowledgements
We would like to express our gratitude to Professor M. Omyła for his advice concerning R. Suszko’s epistemological analysis, and to M. Łyczak for valuable seminar discussions. Fragments of Sobociński’s and Suszko’s texts were translated by Marcin Kuczok.
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Świętorzecka, K., Porwolik, M. (2018). Bolesław Sobociński on Universals. In: Garrido, Á., Wybraniec-Skardowska, U. (eds) The Lvov-Warsaw School. Past and Present. Studies in Universal Logic. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-65430-0_42
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