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

Studies in the Concept of Class (II)
  • Zdzisiaw Kraszewski
  • Roman Suszko
Chapter
Part of the Synthese Library book series (SYLI, volume 119)

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. 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. 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 (k1 = K (KN1), k2 = K (KN2), q = K (KN),q* = K (non-KNN)) include implicit assumptions of the existence of the respective classes K (KN1),K (KN2), K (KN), K (non-KNN) in accordance with (3.1).Google Scholar
  3. 3.
    Note that the axiom of extensionality: x is KLy is KLEl (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. 4.
    We are using abbreviated symbolism here: for a and b we should write Id (a) and Id (b), respectively (cf. footnote3 to the first paper by the same authors).Google Scholar
  5. 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. 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

Copyright information

© PWN — Polish Scientific Publishers — Warszawa 1979

Authors and Affiliations

  • Zdzisiaw Kraszewski
  • Roman Suszko

There are no affiliations available

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