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Full Idea
In semantic theories of truth (Tarski or Kripke), a truth predicate is defined for an object-language. This definition is carried out in a metalanguage, which is typically taken to include set theory or another strong theory or expressive language.
Gist of Idea
In semantic theories of truth, the predicate is in an object-language, and the definition in a metalanguage
Source
Volker Halbach (Axiomatic Theories of Truth (2005 ver) [2005], 1)
Book Ref
'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [plato.stanford.edu], p.2
A Reaction
Presumably the metalanguage includes set theory because that connects it with mathematics, and enables it to be formally rigorous. Tarski showed, in his undefinability theorem, that the meta-language must have increased resources.
Related Idea
Idea 15650 Axiomatic theories of truth need a weak logical framework, and not a strong metatheory [Halbach]
| 19188 | We can't use a semantically closed language, or ditch our logic, so a meta-language is needed [Tarski] |
| 19189 | The metalanguage must contain the object language, logic, and defined semantics [Tarski] |
| 23297 | The language to define truth needs a finite vocabulary, to make the definition finite [Davidson] |
| 23288 | When Tarski defines truth for different languages, how do we know it is a single concept? [Davidson] |
| 19323 | 'Snow is white' depends on meaning; whether snow is white depends on snow [Etchemendy] |
| 15345 | Semantic theories have a regress problem in describing truth in the languages for the models [Horsten] |
| 16297 | Semantic theories avoid Tarski's Theorem by sticking to a sublanguage [Halbach] |
| 15649 | In semantic theories of truth, the predicate is in an object-language, and the definition in a metalanguage [Halbach] |
| 19120 | Semantic theories need a powerful metalanguage, typically including set theory [Halbach/Leigh] |