By Pierre Wagner
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Additional resources for Carnap's Logical Syntax of Language
416–18). ), Carnap deﬁnes ‘analytic in Language II’ (LSL, §34d), a concept also based on the notion of evaluation introduced in §34c. At that point, he comes so close to a deﬁnition of truth that the reader may wonder why he did not actually give one. In the special case of a logical language (Language II with no descriptive symbols), Carnap’s deﬁnition of ‘analytic in II’ is a deﬁnition of ‘true in II’. But Language I and Language II are descriptive languages (LSL, p. 101 and pp. 181–2) with synthetic sentences.
66 Formally, the concept of P-rules results from the syntactical deﬁnitions of ‘L-consequence’ and ‘P-consequence’ given in §51 (LSL, p. 181), which are the basis for further syntactical deﬁnitions (L-language, P-language, L-content, P-content . ), the most important of which is probably the deﬁnition of ‘analytic’. An analytic (or L-valid) sentence is deﬁned as an L-consequence of the null class (whereas valid sentences are consequences 36 Carnap’s Logical Syntax of Language of the null class, and P-valid sentences are valid sentences which are not L-valid).
An analytic (or L-valid) sentence is deﬁned as an L-consequence of the null class (whereas valid sentences are consequences 36 Carnap’s Logical Syntax of Language of the null class, and P-valid sentences are valid sentences which are not L-valid). Intuitively, the difference between P-valid and L-valid sentences is that an L-valid sentence remains valid under all possible substitutions of descriptive expressions. 68 One of the most challenging tasks of the book (from a technical point of view) is undertaken in the following paragraphs (§§53–8) where Carnap offers syntactical deﬁnitions of terms such as ‘predicate’, ‘functor’, ‘variable’, ‘sentential function’, ‘universal operator’, ‘existential operator’, ‘connective’, ‘negation’, ‘conjunction’, ‘numerical expression’, ‘numeral’, ‘arithmetic’, and ‘real number’.
Carnap's Logical Syntax of Language by Pierre Wagner