March 7, 2017

Carnap's Logical Syntax of Language by Pierre Wagner

By Pierre Wagner

This volumes goal is to supply an advent to Carnaps ebook from a historic and philosophical viewpoint, each one bankruptcy targeting one particular factor. The publication should be of curiosity not just to Carnap students yet to all these attracted to the heritage of analytical philosophy.

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Carnap's Logical Syntax of Language

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In §39, Carnap consider the special case of the real numbers: The usual axioms of the arithmetic of real numbers need not be set up here in the form of new primitive sentences. These axioms – and hence the theorems derivable from them – are demonstrable in Language II. (LSL, p. 148) The inclusion of ‘0’ and ‘l ’ among the logical symbols, and of axioms of arithmetic among the logical rules of Language I and Language II, should also be contrasted with Carnap’s earlier view on logic and mathematics.

Sm in Language I’ is defined on the basis of primitive sentences (Grundsätze) and of rules of inference (Schlußregeln) (LSL, p. 29). Primitive sentences are not given directly but through schemata, because no sentential variables are available in Language I. Schemata for the sentential calculus, the bounded quantifiers, identity, arithmetic, and the K-operator are laid down in §11 (LSL, p. 30) in such a way that mathematical primitive sentences are not distinguished from the ones we would call ‘logical’.

Other numerals (zz), predicates (pr), or functors (fu) can be introduced through definitions. 55 ‘Derivation [Ableitung] of a sentence Sn with premisses S1 . . Sm in Language I’ is defined on the basis of primitive sentences (Grundsätze) and of rules of inference (Schlußregeln) (LSL, p. 29). Primitive sentences are not given directly but through schemata, because no sentential variables are available in Language I. Schemata for the sentential calculus, the bounded quantifiers, identity, arithmetic, and the K-operator are laid down in §11 (LSL, p.

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