Logic Language

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

By Pierre Wagner (eds.)

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Extra info for Carnap’s Logical Syntax of Language

Example text

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).

Here, Carnap’s distance from any kind of foundationalist epistemology becomes palpable. In the framework of the logic of science and in agreement with the principle of tolerance, Carnap states the defining rules of a proposed language – in this case, Language II – and uses concepts provided by the syntactical method in order to prove properties that result from the choice of these rules. The method of logical syntax provides tools for the logic of science in the context of the principle of tolerance: ‘[.

What follows is a series of definitions for d-terms (derivable, proof, demonstrable, refutable, decidable . ) in §47 and for c-terms (consequence, valid, contravalid, determinate, incompatible, dependent, content, equipollent, synonymous . ) in §§48–9. 62 A crucial step is taken in §50 where Carnap attempts nothing less than a general definition of ‘logical’. We now realize that this is an enormous task on which logicians have worked hard to this day and which is still much discussed in the philosophy of logic.

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