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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]
| 11215 | Notable definitions have been of piety (Plato), God (Anselm), number (Frege), and truth (Tarski) [Gupta] |
| 11216 | If definitions aim at different ideals, then defining essence is not a unitary activity [Gupta] |
| 11217 | Chemists aim at real definition of things; lexicographers aim at nominal definition of usage [Gupta] |
| 11220 | Ostensive definitions look simple, but are complex and barely explicable [Gupta] |
| 11218 | Stipulative definition assigns meaning to a term, ignoring prior meanings [Gupta] |
| 11221 | A definition can be 'extensionally', 'intensionally' or 'sense' adequate [Gupta] |
| 11222 | The ordered pair <x,y> is defined as the set {{x},{x,y}}, capturing function, not meaning [Gupta] |
| 11223 | Definitions usually have a term, a 'definiendum' containing the term, and a defining 'definiens' [Gupta] |
| 11224 | Traditional definitions are general identities, which are sentential and reductive [Gupta] |
| 11226 | Traditional definitions need: same category, mention of the term, and conservativeness and eliminability [Gupta] |
| 11225 | A definition needs to apply to the same object across possible worlds [Gupta] |
| 11227 | The 'revision theory' says that definitions are rules for improving output [Gupta] |
| 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] |