|Paradoxes: are contradictions within formally correct statements or sets of statements that lead to an existence assumption, which initially seemed plausible, to be withdrawn. Paradoxes are not errors, but challenges that may lead to a re-formulation of the prerequisites and assumptions, or to a change in the language, the subject domain, and the logical system. See also Russellian paradox, contradictions, range, consistency._____________Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments. |
|Berka I 382
Heterology/Grelling/Nelson/Berka: Let j (M) be the word that refers to the concept defined by M.
M is an element of the subset M* of the set of all sets M.
j refers to the allocation, by which the elements of F (a set equivalent to M*) are allocated to the elements of M*.
This word is either element of M or not.
Def autological is the word when it is element of M. I.e. the word has the concept that it refers to, as a feature.
heterological is the word, if it is not member of the set M.
Antinomy/Grelling - the word "heterological" is in turn either autological or heterological.
a) Assume that it is autological, then it is member of the class defined by the notion that refers to itself, it is therefore heterological, contrary to the assumption.
b) Assume it is autological, then it is not member of the set, which refers to itself, it is therefore not heterological, again contrary to the assumption.(1)
1. K. Grelling/L. Nelson, Bemerkungen zu den Paradoxien von Rzussell und Burali-Forti, Abh. Fries. Sch, N. F. II, H. 3 (1908), 301-324; Abgedruckt in: Nelson, L , Beiträge zur Philosophie der Logik und Mathematik, Frankfurt/M. 1959, 59-86_____________Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution. The note [Author1]Vs[Author2] or [Author]Vs[term] is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition.
K. Grelling/L. Nelson, Bemerkungen zu den Paradoxien von Rzussell und Burali-Forti, Abh. Fries. Sch, N. F. II, H. 3 (1908), 301-324; Abgedruckt in: Nelson, L , Beiträge zur Philosophie der Logik und Mathematik, Frankfurt/M. 1959, 59-86
Logik Texte, K. Berka/L. Kreiser, Berlin 1986
Logik Texte Berlin 1983