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Download PDF by Pierre Wagner (eds.): Carnap’s Logical Syntax of Language

By Pierre Wagner (eds.)

ISBN-10: 0230235395

ISBN-13: 9780230235397

ISBN-10: 1349299669

ISBN-13: 9781349299669

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Extra info for Carnap’s Logical Syntax of Language

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Have to be defined according to the strictures of the syntactical method. The only basis for these definitions and the only presupposition is a definition of ‘direct consequence’ to be stated in the following form: “A1 60 is called a direct consequence of K1 61 in S if: (1) A1 and every expression of K1 has one of the following forms: . . ; and (2) A1 and K1 fulfil one of the following conditions: . ” The definition thus contains under (1) the formation rules and under (2) the transformation rules of S.

In material interpretation, the range of a sentence S1 in language S is ‘the class of all the possible cases in which S1 is true; in other words, it is the domain of possibilities left open by S1 ’ in the ‘object-domain with which S is concerned’ (LSL, p. 199). Or, as we would now say: the class of all the possible state-descriptions of the object-domain which make the sentence true. In his Introduction to Semantics, Carnap admits that the concept of range is ‘primarily a semantic L-concept’ and that it should be defined as such (1942, p.

In a footnote added to the 1965 edition of his Princeton Lectures, Gödel credits the general self-reference lemma to Carnap (Gödel 1934/1965, p. 63). The final paragraphs of Part III (§§37–40) give an outline of some further possible developments of Language II. They suggest ways of treating classes, cardinal numbers, real numbers, and physical concepts in the framework of this language. This clearly aims at showing some of the advantages of using a language such as Language II as a framework for science.

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Carnap’s Logical Syntax of Language by Pierre Wagner (eds.)

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