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Full Idea
If a classical language is expressively weakened - for example, by dispensing with negation - then it can contain its own truth predicate.
Gist of Idea
A weakened classical language can contain its own truth predicate
Source
Anil Gupta (Truth [2001], 5.2)
Book Ref
'Blackwell Guide to Philosophical Logic', ed/tr. Goble,Lou [Blackwell 2001], p.101
A Reaction
Thus the Tarskian requirement to move to a metalanguage for truth is only a requirement of a reasonably strong language. Gupta uses this to criticise theories that dispense with the metalanguage.
Related Ideas
Idea 16295 Tarski proved that truth cannot be defined from within a given theory [Tarski, by Halbach]
Idea 14796 Independent truth (if there is any) is the ultimate result of sufficient enquiry [Peirce]
| 14965 | Truth rests on Elimination ('A' is true → A) and Introduction (A → 'A' is true) [Gupta] |
| 14964 | The Liar reappears, even if one insists on propositions instead of sentences [Gupta] |
| 14968 | A weakened classical language can contain its own truth predicate [Gupta] |
| 14969 | Strengthened Liar: either this sentence is neither-true-nor-false, or it is not true [Gupta] |