15357 | Philosophy is the most general intellectual discipline |

15352 | A definition should allow the defined term to be eliminated |

10882 | Predicative definitions only refer to entities outside the defined collection |

15323 | Truth is a property, because the truth predicate has an extension |

15324 | Semantic theories of truth seek models; axiomatic (syntactic) theories seek logical principles |

15342 | Tarski proved that any reasonably expressive language suffers from the liar paradox |

15374 | Truth has no 'nature', but we should try to describe its behaviour in inferences |

15348 | Propositions have sentence-like structures, so it matters little which bears the truth |

15333 | Modern correspondence is said to be with the facts, not with true propositions |

15337 | The correspondence 'theory' is too vague - about both 'correspondence' and 'facts' |

15334 | The coherence theory allows multiple coherent wholes, which could contradict one another |

15336 | The pragmatic theory of truth is relative; useful for group A can be useless for group B |

15354 | Tarski's hierarchy lacks uniform truth, and depends on contingent factors |

15340 | Tarski Bi-conditional: if you'll assert φ you'll assert φ-is-true - and also vice versa |

15345 | Semantic theories have a regress problem in describing truth in the languages for the models |

15332 | 'Reflexive' truth theories allow iterations (it is T that it is T that p) |

15346 | Axiomatic approaches to truth avoid the regress problem of semantic theories |

15350 | The Naďve Theory takes the bi-conditionals as axioms, but it is inconsistent, and allows the Liar |

15351 | Axiomatic theories take truth as primitive, and propose some laws of truth as axioms |

15361 | A good theory of truth must be compositional (as well as deriving biconditionals) |

15371 | An axiomatic theory needs to be of maximal strength, while being natural and sound |

15373 | Axiomatic approaches avoid limiting definitions to avoid the truth predicate, and limited sizes of models |

15367 | By adding truth to Peano Arithmetic we increase its power, so truth has mathematical content! |

15330 | Friedman-Sheard theory keeps classical logic and aims for maximum strength |

15331 | Kripke-Feferman has truth gaps, instead of classical logic, and aims for maximum strength |

15325 | Inferential deflationism says truth has no essence because no unrestricted logic governs the concept |

15344 | Deflationism skips definitions and models, and offers just accounts of basic laws of truth |

15356 | Deflationism concerns the nature and role of truth, but not its laws |

15368 | This deflationary account says truth has a role in generality, and in inference |

15358 | Deflationism says truth isn't a topic on its own - it just concerns what is true |

15359 | Deflation: instead of asserting a sentence, we can treat it as an object with the truth-property |

15329 | Nonclassical may accept T/F but deny applicability, or it may deny just T or F as well |

15326 | Doubt is thrown on classical logic by the way it so easily produces the liar paradox |

15341 | Deduction Theorem: ψ only derivable from φ iff φ→ψ are axioms |

15328 | A theory is 'non-conservative' if it facilitates new mathematical proofs |

15349 | It is easier to imagine truth-value gaps (for the Liar, say) than for truth-value gluts (both T and F) |

15366 | Satisfaction is a primitive notion, and very liable to semantical paradoxes |

10884 | A theory is 'categorical' if it has just one model up to isomorphism |

15353 | The first incompleteness theorem means that consistency does not entail soundness |

15355 | Strengthened Liar: 'this sentence is not true in any context' - in no context can this be evaluated |

15364 | English expressions are denumerably infinite, but reals are nondenumerable, so many are unnameable |

10883 | Cantor's Continuum Hypothesis says there is a gap between the natural and the real numbers |

10885 | Computer proofs don't provide explanations |

10881 | The concept of 'ordinal number' is set-theoretic, not arithmetical |

15360 | ZFC showed that the concept of set is mathematical, not logical, because of its existence claims |

15369 | Set theory is substantial over first-order arithmetic, because it enables new proofs |

15370 | Predicativism says mathematical definitions must not include the thing being defined |

15338 | We may believe in atomic facts, but surely not complex disjunctive ones? |

15362 | If 'Italy is large' lacks truth, so must 'Italy is not large'; but classical logic says it's large or it isn't |

15363 | In the supervaluationist account, disjunctions are not determined by their disjuncts |

15372 | Some claim that indicative conditionals are believed by people, even though they are not actually held true |

15347 | A theory of syntax can be based on Peano arithmetic, thanks to the translation by Gödel coding |