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Single Idea 15354

[filed under theme 3. Truth / F. Semantic Truth / 1. Tarski's Truth / a. Tarski's truth definition ]

Full Idea

According to the Tarskian hierarchical conception, truth is not a uniform notion. ...Also Kripke has emphasised that the level of a token of the truth predicate can depend on contingent factors, such as what else has been said by a speaker.

Gist of Idea

Tarski's hierarchy lacks uniform truth, and depends on contingent factors

Source

Leon Horsten (The Tarskian Turn [2011], 04.5)

Book Ref

Horsten,Leon: 'The Tarskian Turn' [MIT 2011], p.55

The 46 ideas from 'The Tarskian Turn'

15324 Semantic theories of truth seek models; axiomatic (syntactic) theories seek logical principles [Horsten]
15323 Truth is a property, because the truth predicate has an extension [Horsten]
15325 Inferential deflationism says truth has no essence because no unrestricted logic governs the concept [Horsten]
15329 Nonclassical may accept T/F but deny applicability, or it may deny just T or F as well [Horsten]
15326 Doubt is thrown on classical logic by the way it so easily produces the liar paradox [Horsten]
15328 A theory is 'non-conservative' if it facilitates new mathematical proofs [Horsten]
15330 Friedman-Sheard theory keeps classical logic and aims for maximum strength [Horsten]
15331 Kripke-Feferman has truth gaps, instead of classical logic, and aims for maximum strength [Horsten]
15332 'Reflexive' truth theories allow iterations (it is T that it is T that p) [Horsten]
15334 The coherence theory allows multiple coherent wholes, which could contradict one another [Horsten]
15333 Modern correspondence is said to be with the facts, not with true propositions [Horsten]
15337 The correspondence 'theory' is too vague - about both 'correspondence' and 'facts' [Horsten]
15336 The pragmatic theory of truth is relative; useful for group A can be useless for group B [Horsten]
15338 We may believe in atomic facts, but surely not complex disjunctive ones? [Horsten]
15340 Tarski Bi-conditional: if you'll assert φ you'll assert φ-is-true - and also vice versa [Horsten]
15341 Deduction Theorem: ψ only derivable from φ iff φ→ψ are axioms [Horsten]
15344 Deflationism skips definitions and models, and offers just accounts of basic laws of truth [Horsten]
15345 Semantic theories have a regress problem in describing truth in the languages for the models [Horsten]
15346 Axiomatic approaches to truth avoid the regress problem of semantic theories [Horsten]
15347 A theory of syntax can be based on Peano arithmetic, thanks to the translation by Gödel coding [Horsten]
15348 Propositions have sentence-like structures, so it matters little which bears the truth [Horsten]
15349 It is easier to imagine truth-value gaps (for the Liar, say) than for truth-value gluts (both T and F) [Horsten]
15350 The Naďve Theory takes the bi-conditionals as axioms, but it is inconsistent, and allows the Liar [Horsten]
15351 Axiomatic theories take truth as primitive, and propose some laws of truth as axioms [Horsten]
15352 A definition should allow the defined term to be eliminated [Horsten]
15353 The first incompleteness theorem means that consistency does not entail soundness [Horsten]
15354 Tarski's hierarchy lacks uniform truth, and depends on contingent factors [Horsten]
15355 Strengthened Liar: 'this sentence is not true in any context' - in no context can this be evaluated [Horsten]
15356 Deflationism concerns the nature and role of truth, but not its laws [Horsten]
15358 Deflationism says truth isn't a topic on its own - it just concerns what is true [Horsten]
15357 Philosophy is the most general intellectual discipline [Horsten]
15359 Deflation: instead of asserting a sentence, we can treat it as an object with the truth-property [Horsten]
15360 ZFC showed that the concept of set is mathematical, not logical, because of its existence claims [Horsten]
15361 A good theory of truth must be compositional (as well as deriving biconditionals) [Horsten]
15363 In the supervaluationist account, disjunctions are not determined by their disjuncts [Horsten]
15362 If 'Italy is large' lacks truth, so must 'Italy is not large'; but classical logic says it's large or it isn't [Horsten]
15364 English expressions are denumerably infinite, but reals are nondenumerable, so many are unnameable [Horsten]
15366 Satisfaction is a primitive notion, and very liable to semantical paradoxes [Horsten]
15367 By adding truth to Peano Arithmetic we increase its power, so truth has mathematical content! [Horsten]
15368 This deflationary account says truth has a role in generality, and in inference [Horsten]
15369 Set theory is substantial over first-order arithmetic, because it enables new proofs [Horsten]
15370 Predicativism says mathematical definitions must not include the thing being defined [Horsten]
15371 An axiomatic theory needs to be of maximal strength, while being natural and sound [Horsten]
15372 Some claim that indicative conditionals are believed by people, even though they are not actually held true [Horsten]
15373 Axiomatic approaches avoid limiting definitions to avoid the truth predicate, and limited sizes of models [Horsten]
15374 Truth has no 'nature', but we should try to describe its behaviour in inferences [Horsten]