By Pierre Wagner (eds.)
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Additional info for Carnap’s Logical Syntax of Language
E. there exists a sentence G of L such that T G and T ¬G. In other words, under the conditions just stated, there exists no method of formal derivation that deﬁnes a partition of the set of all the sentences of the language of theory T into sentences formally derivable from T on the one hand and sentences the negation of which is formally derivable from T on the other hand. ’ whenever it is actually the case that φ is formally derivable from T. Carnap’s concept of ‘consequence’ (Folge), although an essential tool of the ‘syntactical’ method, does not satisfy this property, and is therefore not termed a method of formal ‘derivation’ (Ableitung).
Even though Carnap considers the possibility of giving several interpretations to a calculus (LSL, p. 229) when be deﬁnes the concept ‘interpretation of a language’ in the context of general syntax (LSL, §62), he never resorts to any concept of an L-structure. Throughout LSL, he mentions what he calls the ‘material interpretation’ (inhaltliche Deutung)34 of the language he is considering, a clear indication that this language is interpreted. For example, after enumerating the primitive sentences of Language I, Carnap writes: ‘we shall now see that all primitive sentences when materially interpreted [bei inhaltlicher Deutung] are true’ (LSL, p.
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. 49 In the fourth part of LSL (on general syntax), when the concepts ‘true’ and ‘false’ are discussed in more detail, Carnap goes so far as to outline the procedure by which a predicate ‘true in S1 ’ (for some object-language S1 ) might be deﬁned in a metalanguage S2 .
Carnap’s Logical Syntax of Language by Pierre Wagner (eds.)