Agent Smith wrote: ↑Mon Apr 03, 2023 7:03 am
I believe Tarski and I are on the same page in certain respects. His views, are as usual, natural, as natural as trees are I suppose. There's a very good chance that we can say something nasty about Tarski, philosophically/logically, and his proof. This has always been so, is, always will be. I for one can't see why not Tarski and ... his ... proof? By the way, it isn't quite clear to me whether Tarski was simply commenting, remarking, or doing what some of you claim he's doing.
You can read his actual two-page proof right here:
https://liarparadox.org/Tarski_275_276.pdf
I used to think that Tarski's Object language / Metalanguage was great when
the Object language is natural language such as English and the Meta language
is natural language formalized in something like higher order logic.
https://plato.stanford.edu/entries/tars ... #ObjLanMet
The following formal system does not need the Object Language / Meta language
dichotomy. Self contradictory expressions can simply be rejected as non-truth bearers
in the following system.
Introducing the foundation of correct reasoning
Just like with syllogisms conclusions a semantically necessary consequence of their premises
Semantic Necessity operator: ⊨□
(a) Some expressions of language L are stipulated to have the semantic property of Boolean true.
Like Prolog Facts except every natural language expression can be encoded.
(b) Some expressions of language L are a semantically necessary consequence of others.
Like Prolog Rules except every natural language expression can be encoded.
P is a subset of expressions of language L // one or more elements of (a) and/or (b)
T is a subset of (a)
Provable(P,X) means P ⊨□ X
True(T,X) means X ∈ (a) or T ⊨□ X
False(T,X) means T ⊨□ ~X