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Full Idea
People have not been aware that the language about which we speak need by no means coincide with the language in which we speak. ..But the language which contains its own semantics must inevitably be inconsistent.
Gist of Idea
A language containing its own semantics is inconsistent - but we can use a second language
Source
Alfred Tarski (The Establishment of Scientific Semantics [1936], p.402)
Book Ref
Tarski,Alfred: 'Logic, Semantics, Meta-mathematics' [Hackett 1956], p.402
A Reaction
It seems that Tarski was driven to propose the metalanguage approach mainly by the Liar Paradox.
| 13335 | Semantics is the concepts of connections of language to reality, such as denotation, definition and truth [Tarski] |
| 13336 | A language containing its own semantics is inconsistent - but we can use a second language [Tarski] |
| 13337 | A language: primitive terms, then definition rules, then sentences, then axioms, and finally inference rules [Tarski] |
| 13338 | '"It is snowing" is true if and only if it is snowing' is a partial definition of the concept of truth [Tarski] |
| 13339 | A sentence is satisfied when we can assert the sentence when the variables are assigned [Tarski] |
| 13340 | Satisfaction is the easiest semantical concept to define, and the others will reduce to it [Tarski] |
| 13341 | Using the definition of truth, we can prove theories consistent within sound logics [Tarski] |