Rudolf Carnap - Logical Syntax

Logical Syntax

Carnap's Logical Syntax of Language can be regarded as a response to Wittgenstein 's Tractatus.

Carnap elaborated and extended the concept of logical syntax proposed by Wittgenstein in the Tractatus (Section 3.325).

3.325. In order to avoid such errors we must make use of a sign-language that excludes them by not using the same sign for different symbols and by not using in a superficially similar way signs that have different modes of signification: that is to say, a sign-language that is governed by logical grammar—by logical syntax. ......

— Wittgenstein, Section 3.325, Tractatus

However, Wittgenstein stated that propositions cannot represent logical form.

4.121. Propositions cannot represent logical form: it is mirrored in them. What finds its reflection in language, language cannot represent. What expresses itself in language, we cannot express by means of language. Propositions show the logical form of reality. They display it.

— Wittgenstein, Section 4.121, Tractatus

Carnap disagreed. Wittgenstein proposed the idea of logical syntax. It is Carnap who designed, formulated and implemented the details of logical syntax in philosophical analysis. Carnap defined logical syntax as:

By the logical syntax of a language, we mean the formal theory of the linguistic forms of that language -- the systematic statement of the formal rules which govern it together with the development of the consequences which follow from these rules. A theory, a rule, a definition, or the like is to be called formal when no reference is made in it either to the meaning of the symbols (for examples, the words) or to the sense of the expressions (e.g. the sentences), but simply and solely to the kinds and order of the symbols from which the expressions are constructed.

— Carnap, Page 1, Logical Syntax of Language

In the U.S, the concept of logical syntax helped the development of natural language processing and compiler design (the Parrot virtual machine and LLVM).