98 ideas
| 15357 | Philosophy is the most general intellectual discipline [Horsten] |
| 16325 | Analysis rests on natural language, but its ideal is a framework which revises language [Halbach] |
| 15352 | A definition should allow the defined term to be eliminated [Horsten] |
| 16292 | An explicit definition enables the elimination of what is defined [Halbach] |
| 16307 | Don't trust analogies; they are no more than a guideline [Halbach] |
| 15324 | Semantic theories of truth seek models; axiomatic (syntactic) theories seek logical principles [Horsten] |
| 16339 | Truth axioms prove objects exist, so truth doesn't seem to be a logical notion [Halbach] |
| 15323 | Truth is a property, because the truth predicate has an extension [Horsten] |
| 16330 | Truth-value 'gluts' allow two truth values together; 'gaps' give a partial conception of truth [Halbach] |
| 15374 | Truth has no 'nature', but we should try to describe its behaviour in inferences [Horsten] |
| 16324 | Any definition of truth requires a metalanguage [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] |
| 15348 | Propositions have sentence-like structures, so it matters little which bears the truth [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] |
| 15334 | The coherence theory allows multiple coherent wholes, which could contradict one another [Horsten] |
| 15336 | The pragmatic theory of truth is relative; useful for group A can be useless for group B [Horsten] |
| 15354 | Tarski's hierarchy lacks uniform truth, and depends on contingent factors [Horsten] |
| 15340 | Tarski Bi-conditional: if you'll assert φ you'll assert φ-is-true - and also vice versa [Horsten] |
| 15345 | Semantic theories have a regress problem in describing truth in the languages for the models [Horsten] |
| 16297 | Semantic theories avoid Tarski's Theorem by sticking to a sublanguage [Halbach] |
| 16337 | Disquotational truth theories are short of deductive power [Halbach] |
| 15332 | 'Reflexive' truth theories allow iterations (it is T that it is T that p) [Horsten] |
| 15346 | Axiomatic approaches to truth avoid the regress problem of semantic theories [Horsten] |
| 15361 | A good theory of truth must be compositional (as well as deriving biconditionals) [Horsten] |
| 15371 | An axiomatic theory needs to be of maximal strength, while being natural and sound [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] |
| 15367 | By adding truth to Peano Arithmetic we increase its power, so truth has mathematical content! [Horsten] |
| 16294 | Axiomatic truth doesn't presuppose a truth-definition, though it could admit it at a later stage [Halbach] |
| 16311 | To axiomatise Tarski's truth definition, we need a binary predicate for his 'satisfaction' [Halbach] |
| 16318 | Compositional Truth CT has the truth of a sentence depending of the semantic values of its constituents [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] |
| 16322 | CT proves PA consistent, which PA can't do on its own, so CT is not conservative over PA [Halbach] |
| 16305 | We know a complete axiomatisation of truth is not feasible [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] |
| 16314 | Theories of truth are 'typed' (truth can't apply to sentences containing 'true'), or 'type-free' [Halbach] |
| 15373 | Axiomatic approaches avoid limiting definitions to avoid the truth predicate, and limited sizes of models [Horsten] |
| 15330 | Friedman-Sheard theory keeps classical logic and aims for maximum strength [Horsten] |
| 16327 | Friedman-Sheard is type-free Compositional Truth, with two inference rules for truth [Halbach] |
| 16332 | The KF theory is useful, but it is not a theory containing its own truth predicate [Halbach] |
| 15331 | Kripke-Feferman has truth gaps, instead of classical logic, and aims for maximum strength [Horsten] |
| 16329 | Kripke-Feferman theory KF axiomatises Kripke fixed-points, with Strong Kleene logic with gluts [Halbach] |
| 16331 | The KF is much stronger deductively than FS, which relies on classical truth [Halbach] |
| 15325 | Inferential deflationism says truth has no essence because no unrestricted logic governs the concept [Horsten] |
| 15344 | Deflationism skips definitions and models, and offers just accounts of basic laws of truth [Horsten] |
| 15356 | Deflationism concerns the nature and role of truth, but not its laws [Horsten] |
| 15368 | This deflationary account says truth has a role in generality, and in inference [Horsten] |
| 15358 | Deflationism says truth isn't a topic on its own - it just concerns what is true [Horsten] |
| 15359 | Deflation: instead of asserting a sentence, we can treat it as an object with the truth-property [Horsten] |
| 16338 | Deflationism says truth is a disquotation device to express generalisations, adding no new knowledge [Halbach] |
| 16317 | The main problem for deflationists is they can express generalisations, but not prove them [Halbach] |
| 16316 | Deflationists say truth is just for expressing infinite conjunctions or generalisations [Halbach] |
| 16320 | Some say deflationism is axioms which are conservative over the base theory [Halbach] |
| 16319 | Compositional Truth CT proves generalisations, so is preferred in discussions of deflationism [Halbach] |
| 15329 | Nonclassical may accept T/F but deny applicability, or it may deny just T or F as well [Horsten] |
| 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] |
| 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] |
| 15326 | Doubt is thrown on classical logic by the way it so easily produces the liar paradox [Horsten] |
| 15341 | Deduction Theorem: ψ only derivable from φ iff φ→ψ are axioms [Horsten] |
| 15328 | A theory is 'non-conservative' if it facilitates new mathematical proofs [Horsten] |
| 16310 | A theory is some formulae and all of their consequences [Halbach] |
| 15349 | It is easier to imagine truth-value gaps (for the Liar, say) than for truth-value gluts (both T and F) [Horsten] |
| 15366 | Satisfaction is a primitive notion, and very liable to semantical paradoxes [Horsten] |
| 16344 | Soundness must involve truth; the soundness of PA certainly needs it [Halbach] |
| 16341 | Normally we only endorse a theory if we believe it to be sound [Halbach] |
| 16342 | You cannot just say all of Peano arithmetic is true, as 'true' isn't part of the system [Halbach] |
| 15353 | The first incompleteness theorem means that consistency does not entail soundness [Horsten] |
| 16347 | Many new paradoxes may await us when we study interactions between frameworks [Halbach] |
| 15355 | Strengthened Liar: 'this sentence is not true in any context' - in no context can this be evaluated [Horsten] |
| 16336 | The liar paradox applies truth to a negated truth (but the conditional will serve equally) [Halbach] |
| 15364 | English expressions are denumerably infinite, but reals are nondenumerable, so many are unnameable [Horsten] |
| 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] |
| 15360 | ZFC showed that the concept of set is mathematical, not logical, because of its existence claims [Horsten] |
| 15369 | Set theory is substantial over first-order arithmetic, because it enables new proofs [Horsten] |
| 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] |
| 15370 | Predicativism says mathematical definitions must not include the thing being defined [Horsten] |
| 16345 | That Peano arithmetic is interpretable in ZF set theory is taken by philosophers as a reduction [Halbach] |
| 15338 | We may believe in atomic facts, but surely not complex disjunctive ones? [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] |
| 15363 | In the supervaluationist account, disjunctions are not determined by their disjuncts [Horsten] |
| 16346 | Maybe necessity is a predicate, not the usual operator, to make it more like truth [Halbach] |
| 15372 | Some claim that indicative conditionals are believed by people, even though they are not actually held true [Horsten] |
| 9312 | Consciousness is reductively explained either by how it represents, or how it is represented [Kriegel/Williford] |
| 9315 | Red tomato experiences are conscious if the state represents the tomato and itself [Kriegel/Williford] |
| 9313 | Experiences can be represented consciously or unconsciously, so representation won't explain consciousness [Kriegel/Williford] |
| 9316 | How is self-representation possible, does it produce a regress, and is experience like that? [Kriegel/Williford] |
| 9314 | Unfortunately, higher-order representations could involve error [Kriegel/Williford] |
| 15347 | A theory of syntax can be based on Peano arithmetic, thanks to the translation by Gödel coding [Horsten] |
| 16298 | We need propositions to ascribe the same beliefs to people with different languages [Halbach] |