Philosophy Now Forum

Alistair MacFarlane thinks through the life of a godfather of logic.

https://philosophynow.org/issues/111/Al ... _1901-1983

Many thanks for the excellent and the concise article on Tarski. It seems to me, though, that there is no need for a meta-language. which is only required because of the adherence to a syntactic/semantic approach. This is fine for context-free languages, such as the Turing/Church model and it derivation; however, natural language swims in a sea of context.

General utterances about a concept can be interpreted through a repertoire of specialised ones. So, /I am martin, what are you called/ is supported by the name repertoire:
/i do not know my name/my name is X/what is my name/i do not have a name/
The associated train of thought, which can be constructed by an autopoietic repertoire, is followed via the felicity of these supporting concepts. An underlying repertoire deals with things like repetition/disambiguation. A more in depth example can be found in http://hrcak.srce.hr/file/191133

The downside is that this approach is incomplete, but this is also reflected in natural language: I may speak English, and the language of the medical profession may be in English, but it may be beyond me. However, with an unlimited set of concepts, a practical set of repertoires can be achieved. For a demonstration of this approach, please see https://www.youtube.com/watch?v=HsJyrdtk0GM

Tarski's work in logic may be entirely rigorous and consistent, but it can only apply in some abstract domain. Even if it is applied to words there is no assurance that those words have a logical connection with the real world of facts.

The article says that: "Truth is a correspondence between a belief and the way the world is". While I am not going to argue against that, I will say that this is not a logically rigorous correspondence; it cannot be proven by any logical means.

While Tarski's work is undoubtedly important for logic, its philosophical implications are limited to an abstract domain.