81 ideas
16325 | Analysis rests on natural language, but its ideal is a framework which revises language [Halbach] |
16292 | An explicit definition enables the elimination of what is defined [Halbach] |
9331 | How do we determine which of the sentences containing a term comprise its definition? [Horwich] |
16307 | Don't trust analogies; they are no more than a guideline [Halbach] |
6334 | The function of the truth predicate? Understanding 'true'? Meaning of 'true'? The concept of truth? A theory of truth? [Horwich] |
16339 | Truth axioms prove objects exist, so truth doesn't seem to be a logical notion [Halbach] |
16330 | Truth-value 'gluts' allow two truth values together; 'gaps' give a partial conception of truth [Halbach] |
16324 | Any definition of truth requires a metalanguage [Halbach] |
15647 | Truth definitions don't produce a good theory, because they go beyond your current language [Halbach] |
16293 | Traditional definitions of truth often make it more obscure, rather than less [Halbach] |
16301 | If people have big doubts about truth, a definition might give it more credibility [Halbach] |
6342 | Some correspondence theories concern facts; others are built up through reference and satisfaction [Horwich] |
6332 | The common-sense theory of correspondence has never been worked out satisfactorily [Horwich] |
15649 | In semantic theories of truth, the predicate is in an object-language, and the definition in a metalanguage [Halbach] |
16297 | Semantic theories avoid Tarski's Theorem by sticking to a sublanguage [Halbach] |
16337 | Disquotational truth theories are short of deductive power [Halbach] |
15655 | Should axiomatic truth be 'conservative' - not proving anything apart from implications of the axioms? [Halbach] |
15654 | If truth is defined it can be eliminated, whereas axiomatic truth has various commitments [Halbach] |
16326 | The main semantic theories of truth are Kripke's theory, and revisions semantics [Halbach] |
16299 | Gödel numbering means a theory of truth can use Peano Arithmetic as its base theory [Halbach] |
16340 | Truth axioms need a base theory, because that is where truth issues arise [Halbach] |
16305 | We know a complete axiomatisation of truth is not feasible [Halbach] |
16311 | To axiomatise Tarski's truth definition, we need a binary predicate for his 'satisfaction' [Halbach] |
16313 | A theory is 'conservative' if it adds no new theorems to its base theory [Halbach, by PG] |
16315 | The Tarski Biconditional theory TB is Peano Arithmetic, plus truth, plus all Tarski bi-conditionals [Halbach] |
16318 | Compositional Truth CT has the truth of a sentence depending of the semantic values of its constituents [Halbach] |
16322 | CT proves PA consistent, which PA can't do on its own, so CT is not conservative over PA [Halbach] |
16314 | Theories of truth are 'typed' (truth can't apply to sentences containing 'true'), or 'type-free' [Halbach] |
15648 | Instead of a truth definition, add a primitive truth predicate, and axioms for how it works [Halbach] |
16294 | Axiomatic truth doesn't presuppose a truth-definition, though it could admit it at a later stage [Halbach] |
15650 | Axiomatic theories of truth need a weak logical framework, and not a strong metatheory [Halbach] |
16327 | Friedman-Sheard is type-free Compositional Truth, with two inference rules for truth [Halbach] |
16331 | The KF is much stronger deductively than FS, which relies on classical truth [Halbach] |
16329 | Kripke-Feferman theory KF axiomatises Kripke fixed-points, with Strong Kleene logic with gluts [Halbach] |
16332 | The KF theory is useful, but it is not a theory containing its own truth predicate [Halbach] |
6335 | The redundancy theory cannot explain inferences from 'what x said is true' and 'x said p', to p [Horwich] |
23299 | Horwich's deflationary view is novel, because it relies on propositions rather than sentences [Horwich, by Davidson] |
6336 | No deflationary conception of truth does justice to the fact that we aim for truth [Horwich] |
6337 | The deflationary picture says believing a theory true is a trivial step after believing the theory [Horwich] |
6344 | Truth is a useful concept for unarticulated propositions and generalisations about them [Horwich] |
15656 | Deflationists say truth merely serves to express infinite conjunctions [Halbach] |
16338 | Deflationism says truth is a disquotation device to express generalisations, adding no new knowledge [Halbach] |
16316 | Deflationists say truth is just for expressing infinite conjunctions or generalisations [Halbach] |
16317 | The main problem for deflationists is they can express generalisations, but not prove them [Halbach] |
16319 | Compositional Truth CT proves generalisations, so is preferred in discussions of deflationism [Halbach] |
16320 | Some say deflationism is axioms which are conservative over the base theory [Halbach] |
16335 | In Strong Kleene logic a disjunction just needs one disjunct to be true [Halbach] |
16334 | In Weak Kleene logic there are 'gaps', neither true nor false if one component lacks a truth value [Halbach] |
15657 | To prove the consistency of set theory, we must go beyond set theory [Halbach] |
16309 | Every attempt at formal rigour uses some set theory [Halbach] |
16333 | The underestimated costs of giving up classical logic are found in mathematical reasoning [Halbach] |
15652 | We can use truth instead of ontologically loaded second-order comprehension assumptions about properties [Halbach] |
6339 | Logical form is the aspects of meaning that determine logical entailments [Horwich] |
15651 | Instead of saying x has a property, we can say a formula is true of x - as long as we have 'true' [Halbach] |
16310 | A theory is some formulae and all of their consequences [Halbach] |
16341 | Normally we only endorse a theory if we believe it to be sound [Halbach] |
16344 | Soundness must involve truth; the soundness of PA certainly needs it [Halbach] |
16342 | You cannot just say all of Peano arithmetic is true, as 'true' isn't part of the system [Halbach] |
16347 | Many new paradoxes may await us when we study interactions between frameworks [Halbach] |
16336 | The liar paradox applies truth to a negated truth (but the conditional will serve equally) [Halbach] |
16321 | The compactness theorem can prove nonstandard models of PA [Halbach] |
16343 | The global reflection principle seems to express the soundness of Peano Arithmetic [Halbach] |
16312 | To reduce PA to ZF, we represent the non-negative integers with von Neumann ordinals [Halbach] |
16308 | Set theory was liberated early from types, and recent truth-theories are exploring type-free [Halbach] |
16345 | That Peano arithmetic is interpretable in ZF set theory is taken by philosophers as a reduction [Halbach] |
16346 | Maybe necessity is a predicate, not the usual operator, to make it more like truth [Halbach] |
8431 | Problems with Goodman's view of counterfactuals led to a radical approach from Stalnaker and Lewis [Horwich] |
9333 | A priori belief is not necessarily a priori justification, or a priori knowledge [Horwich] |
9342 | Understanding needs a priori commitment [Horwich] |
9332 | Meaning is generated by a priori commitment to truth, not the other way around [Horwich] |
9341 | Meanings and concepts cannot give a priori knowledge, because they may be unacceptable [Horwich] |
9334 | If we stipulate the meaning of 'number' to make Hume's Principle true, we first need Hume's Principle [Horwich] |
9339 | A priori knowledge (e.g. classical logic) may derive from the innate structure of our minds [Horwich] |
2798 | Probability of H, given evidence E, is prob(H) x prob(E given H) / prob(E) [Horwich] |
2799 | Bayes' theorem explains why very surprising predictions have a higher value as evidence [Horwich] |
6338 | We could know the truth-conditions of a foreign sentence without knowing its meaning [Horwich] |
6340 | There are Fregean de dicto propositions, and Russellian de re propositions, or a mixture [Horwich] |
16298 | We need propositions to ascribe the same beliefs to people with different languages [Halbach] |
6341 | Right translation is a mapping of languages which preserves basic patterns of usage [Horwich] |
6005 | Animals are dangerous and nourishing, and can't form contracts of justice [Hermarchus, by Sedley] |
8432 | Analyse counterfactuals using causation, not the other way around [Horwich] |