16325 | Analysis rests on natural language, but its ideal is a framework which revises language |

16292 | An explicit definition enables the elimination of what is defined |

16307 | Don't trust analogies; they are no more than a guideline |

16330 | Truth-value 'gluts' allow two truth values together; 'gaps' give a partial conception of truth |

16339 | Truth axioms prove objects exist, so truth doesn't seem to be a logical notion |

15647 | Truth definitions don't produce a good theory, because they go beyond your current language |

16293 | Traditional definitions of truth often make it more obscure, rather than less |

16301 | If people have big doubts about truth, a definition might give it more credibility |

16324 | Any definition of truth requires a metalanguage |

16296 | Tarski's Theorem renders any precise version of correspondence impossible |

15649 | In semantic theories of truth, the predicate is in an object-language, and the definition in a metalanguage |

16297 | Semantic theories avoid Tarski's Theorem by sticking to a sublanguage |

16337 | Disquotational truth theories are short of deductive power |

16318 | Compositional Truth CT has the truth of a sentence depending of the semantic values of its constituents |

16311 | To axiomatise Tarski's truth definition, we need a binary predicate for his 'satisfaction' |

16299 | Gödel numbering means a theory of truth can use Peano Arithmetic as its base theory |

16340 | Truth axioms need a base theory, because that is where truth issues arise |

16305 | We know a complete axiomatisation of truth is not feasible |

16322 | CT proves PA consistent, which PA can't do on its own, so CT is not conservative over PA |

16313 | A theory is 'conservative' if it adds no new theorems to its base theory |

16315 | The Tarski Biconditional theory TB is Peano Arithmetic, plus truth, plus all Tarski bi-conditionals |

16314 | Theories of truth are 'typed' (truth can't apply to sentences containing 'true'), or 'type-free' |

15648 | Instead of a truth definition, add a primitive truth predicate, and axioms for how it works |

15650 | Axiomatic theories of truth need a weak logical framework, and not a strong metatheory |

15655 | Should axiomatic truth be 'conservative' - not proving anything apart from implications of the axioms? |

15654 | If truth is defined it can be eliminated, whereas axiomatic truth has various commitments |

16294 | Axiomatic truth doesn't presuppose a truth-definition, though it could admit it at a later stage |

16326 | The main semantic theories of truth are Kripke's theory, and revisions semantics |

16327 | Friedman-Sheard is type-free Compositional Truth, with two inference rules for truth |

16329 | Kripke-Feferman theory KF axiomatises Kripke fixed-points, with Strong Kleene logic with gluts |

16331 | The KF is much stronger deductively that FS, which relies on classical truth |

16332 | The KF theory is useful, but it is not a theory containing its own truth predicate |

15656 | Deflationists say truth merely serves to express infinite conjunctions |

16338 | Deflationism says truth is a disquotation device to express generalisations, adding no new knowledge |

16316 | Deflationists say truth is just for expressing infinite conjunctions or generalisations |

16317 | The main problem for deflationists is they can express generalisations, but not prove them |

16320 | Some say deflationism is axioms which are conservative over the base theory |

16319 | Compositional Truth CT proves generalisations, so is preferred in discussions of deflationism |

16335 | In Strong Kleene logic a disjunction just needs one disjunct to be true |

16334 | In Weak Kleene logic there are 'gaps', neither true nor false if one component lacks a truth value |

15657 | To prove the consistency of set theory, we must go beyond set theory |

16309 | Every attempt at formal rigour uses some set theory |

16333 | The underestimated costs of giving up classical logic are found in mathematical reasoning |

15652 | We can use truth instead of ontologically loaded second-order comprehension assumptions about properties |

15651 | Instead of saying x has a property, we can say a formula is true of x - as long as we have 'true' |

16310 | A theory is some formulae and all of their consequences |

16323 | The object language/ metalanguage distinction is the basis of model theory |

16342 | You cannot just say all of Peano arithmetic is true, as 'true' isn't part of the system |

16341 | Normally we only endorse a theory if we believe it to be sound |

16344 | Soundness must involve truth; the soundness of PA certainly needs it |

16347 | Many new paradoxes may await us when we study interactions between frameworks |

16336 | The liar paradox applies truth to a negated truth (but the conditional will serve equally) |

16321 | The compactness theorem can prove nonstandard models of PA |

16343 | The global reflection principle seems to express the soundness of Peano Arithmetic |

15653 | We can add Reflexion Principles to Peano Arithmetic, which assert its consistency or soundness |

16312 | To reduce PA to ZF, we represent the non-negative integers with von Neumann ordinals |

16308 | Set theory was liberated early from types, and recently truth-theories are exploring type-free |

16345 | That Peano arithmetic is interpretable in ZF set theory is taken by philosophers as a reduction |

16346 | Maybe necessity is a predicate, not the usual operator, to make it more like truth |

16298 | We need propositions to ascribe the same beliefs to people with different languages |