|Truth-functions: truth-functions map truth-values onto other truth-values. In two-valued logic, the two available truth values are "true" or "false" (t/f). The disjunction (A or B) now maps (t or t), (t or f) and (f or t) onto t, and (f or f) onto f. Non-truth-functional semantics differ from truth-functional semantics in that they also take other meanings of the logical links ("and", "or", "if then") into account, for example, expressions such as "nevertheless," "though," "still", whose propositional content corresponds to the "and", but which bring a certain additional expressive force into play. See also truth-functional semantics, truth-conditional semantics, semantics, propositional content._____________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 142
Truth Functions/Statement Calculus/Bivalence/Functor/Lukasiewicz: in a bivalent system only four different functions can be formed with one argument - namely, if φ forms a functor with one argument, then the following cases can occur:
(1) φ0 = 0 and φ1 = 0 ( "Fp" falsum, wrong)
(2) φ0 = 0 and φ1 = 1 (φp is equivalent to p)
(3) φ0 = 1 and φ1 0 = : (Negation)
(4) φ0 = 1 and φ1 = 1: "Vp" (verum, true).
Possibility/N.B.: the "Mp" must be identical to one of these four cases. Problem: each of the theses (1), (2), and (18) now excludes certain cases.(1)
1. J. Lukasiewicz, Philosophische Bemerkungen zu mehrwertigen Systemen des Aussagenkalküls, CR Varsovie Cl. III, 23, 51-77_____________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.
Logik Texte Berlin 1983