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I'm baffled by one phrase in Tarski's papers: "the language which contains its own semantics".

Here is the passage:

The analysis of the antinomies mentioned shows, on the contrary, that the semantical concepts simply have no place in the language to which they relate, that the language which contains its own semantics, and within which the usual laws of logic hold, must inevitably be inconsistent. -- Alfred Tarski, Logic, Semantics, Metamathematics: Papers from 1923 to 1938 (1956)

This is at https://iep.utm.edu/par-log/.

As I see it, while it is unproblematic to have definitions of particular words of a language as part of this language, the idea that its semantics could be somehow included in it is just a misunderstanding of the notion of semantics.

Or does Tarski by "semantics of a language" just mean the definitions collectively of the words of this language?

Anyone understands what Tarski meant?

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    I'm not familiar with his writings, but Tarski invented the language/metalanguage distinction. This looks like his argument for how the semantics of a language should only be discussed in a metalanguage. Nov 11, 2023 at 10:56
  • He does not mean contains all of its own semantics. Semantics is what relates a language to its subject matter, and natural languages have devices to speak about their own sentences, making themselves into their subject matter. From context, he specifically has the truth predicate in mind. And a language which contains even just its own truth predicate must already be inconsistent (under classical logic).
    – Conifold
    Nov 11, 2023 at 11:27

1 Answer 1

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To my understanding, the key sentence is a few lines above.

... it has not always been kept in mind that the semantical concepts have a relative character, that they must always be related to a particular language … as though there was only one language in the world

What he says is simply that a specific language contains its own semantics, in the sense that concepts (ex. words) are mapped for every language in a different way. For example a translation of a word or a concept from one language to another does not have 1-1 equivalence of meaning.

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