Philosophy Dictionary of ArgumentsHome | |||
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Type theory: Restriction of formal systems to a type of reference that prevents symbols of one level (of one type) from referring to symbols of the same level (of the same type). This is intended to avoid paradoxes arising from the self-referentiality of the symbols or expressions used. Original proposals for type theories come from B. Russell (B. Russell, Mathematical logic as based on the theory of types, in American Journal of Mathematics 30 (1908), pp. 222-262). See also Self-reference, Circularity, Paradoxes, Russell's paradox, Stages, Branched type theory. _____________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. | |||
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Rudolf Carnap on Type Theory - Dictionary of Arguments
I 81f E.g. a, b are bodies, the sentences " a is quadrangular", "b is red is true or false, in any case sensefull. Furthermore, the sentences "square is a spatial property" and "red is a color" be true." In contrast, the series of words "a is a spatial property", " quadrangular is red", "color is a spatial property " should be neither true, nor false but meaningless, mere pseudo-propositions. ((s) So do not: "a is a feature".) Such pseudo-propositions can be avoided if a term (property) of n-th level is based only to such of (n-1) th stage. It follows that the assumption that if a certain property is applied to itself , it can be neither true nor false, but always is pointless. >Sense, >Senseless, >Truth value gaps._____________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 [Concept/Author], [Author1]Vs[Author2] or [Author]Vs[term] resp. "problem:"/"solution:", "old:"/"new:" and "thesis:" is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition. |
Ca I R. Carnap Die alte und die neue Logik In Wahrheitstheorien, G. Skirbekk (Hg), Frankfurt 1996 Ca II R. Carnap Philosophie als logische Syntax In Philosophie im 20.Jahrhundert, Bd II, A. Hügli/P.Lübcke (Hg), Reinbek 1993 Ca IV R. Carnap Mein Weg in die Philosophie Stuttgart 1992 Ca IX Rudolf Carnap Wahrheit und Bewährung. Actes du Congrès International de Philosophie Scientifique fasc. 4, Induction et Probabilité, Paris, 1936 In Wahrheitstheorien, Gunnar Skirbekk, Frankfurt/M. 1977 Ca VI R. Carnap Der Logische Aufbau der Welt Hamburg 1998 CA VII = PiS R. Carnap Sinn und Synonymität in natürlichen Sprachen In Zur Philosophie der idealen Sprache, J. Sinnreich (Hg), München 1982 Ca VIII (= PiS) R. Carnap Über einige Begriffe der Pragmatik In Zur Philosophie der idealen Sprache, J. Sinnreich (Hg), München 1982 |