Semiotics in Poland 1984–1969 pp 273-283 | Cite as

# Normal and Non-Normal Classes Versus the Set-Theoretical and the Mereological Concept of Class

Studies in the Concept of Class (II)

Chapter

## Abstract

We shall concern ourselves here with the transition from the current concept of class to the distributive (set-theoretical) and the collective (mereological) concept of class. This transition is linked to the concepts of normal and non-normal class. Preliminary remarks on that issue have already been made in Sec. 8.

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## Notes

- 1.This is a continuation of the preceding paper by the same authors. It also assumes a knowledge of that paper on the part of the reader.Google Scholar
- 2.Note that the tentative reconstructions of Russell’s antinomy, as carried out in Sec. 6, refer to the existential axiom (3.1). The symbolisms adopted there (
*k*_{1}=*K*(*KN*_{1}),*k*_{2}=*K*(*KN*_{2}),*q*=*K*(*KN*),*q*^{*}=*K*(*non-KNN*)) include implicit assumptions of the existence of the respective classes*K*(*KN*_{1}),*K*(*KN*_{2}),*K*(*KN*),*K*(*non-KNN*) in accordance with (3.1).Google Scholar - 3.Note that the axiom of extensionality:
*x*is*KL*∧*y*is*KL*∧*El*(*x*) =*El*(*y*) →*x*=*y*, follows easily from (2.2) and hence is a theorem for the current interpretation of the concepts of class and element.Google Scholar - 4.We are using abbreviated symbolism here: for
*a*and*b*we should write*Id*(*a*) and*Id*(*b*), respectively (cf. footnote^{3}to the first paper by the same authors).Google Scholar - 5.This is the situation described by (7.8) in Sec. 7 we have:
*c*is*KN*(*C*) ∧*c*is*KNN*(*c*).Google Scholar - 6.S. Lesniewski,
*Podstawy ogólnej teorii mnogości*(The Foundation of General Set Theory), I, Moscow 1916, and *O podstawach matematyki’ (On the Foundations of Mathematics),*Przeglqd Filozoficzny*, 30-34, Warsaw 1927–1934.Google Scholar

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© PWN — Polish Scientific Publishers — Warszawa 1979