Normal and Non-Normal Classes in Current Language1
Russell’s antinomy of the class of normal classes, i.e., the class of those classes which are not their own elements, emerged when the current concept of class was being given more precision. It is this current concept of class which is blamed for Russell’s antinomy.
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- 1.The problems to be discussed and the main theses of the present paper come from Z. Kraszewski. R. Suszko’s contribution is confined to the proposal that everyday language should be identified with the formalism of the logic of statements and the logic of terms, and to certain suggestions concerning the arrangement of the material.Google Scholar
- 2.For a limited version of a formalism of the logic of terms see A. Morawiec, ‘Podstawy logiki nazw’ (Foundations of the Theory of Names), Studia Logica, XII, 1961.Google Scholar
- 3.It may be assumed that the argument A in K (A) is always a subjective complement (a general term). While adopting this position we also admit terms in the form of K (a), where a is a proper name (an individual term): we can consider K (a) to be an abbreviation for K (Id (a)), where Id is the relative predicate ‘identical with’; in that case the term ‘Id(a)’ is a subjective complement.Google Scholar
- 4.The relative terms mentioned previously are thus interpreted in a weak sense, in which a whole is its own part (fragment, component, element).Google Scholar
- 5.It is obvious, by virtue of (2.3), that every KN is KL and that every KNN is KL.Google Scholar
- 6.We have disregarded here the fourth, combinatorily possible, definition of normal and non-normal classes, namely KNN3 = KL and non-KN, KN3 = KL and non-KNN. This case seems to be totally unintuitive.Google Scholar
- 7.Certain examples in this paragraph have had to be modified, because the use of articles in English renders some of the original Polish formulations pointless. (Tr.)Google Scholar