|Heterology/Grelling/Nelson/Berka: Let φ(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.
φ 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. (K. Berka / L. Kreiser Logic-Texte Berlin 1983, p 382 (German)).
See also paradoxes, predicates, reference._____________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.
Peter Geach on Heterology - Dictionary of Arguments
Heterological/Heterology/Geach: E.g. ""is an obscene term" is heterological" - should have the same meaning (same meaning, synonym) as ""is an obscene expression" is not an obscene expression" (correct). - Problem: this definition ""is heterological" is heterologous" would be synonym with ""is heterological "is not heterological" - contradiction.
Grellings Paradox/(s): a general term "is not applicable to itself" is not applicable to itself.
(1) "heterological" lacks the property for which it stands, namely the absence of the property for which it stands, namely ... recourse. - Ryle: no property is ever mentioned.
(2) "... lacks the property for which "heterological" stands.
(1) is an extension of "heterological", and just true of those words, of which (2) is not true Grelling's paradox. (1) is not at all ambiguous - otherwise it would always have to refer to the same property in all events of (1), e.g. "French"....
Solution/Geach: "the property for which it stands" never denotes any specifiable property. - Various heterological epithets stand for different properties._____________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. Translations: Dictionary of Arguments 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.
Logic Matters Oxford 1972