65 ideas
15357 | Philosophy is the most general intellectual discipline [Horsten] |
5750 | Consistency is modal, saying propositions are consistent if they could be true together [Melia] |
15352 | A definition should allow the defined term to be eliminated [Horsten] |
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] |
15374 | Truth has no 'nature', but we should try to describe its behaviour in inferences [Horsten] |
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] |
15373 | Axiomatic approaches avoid limiting definitions to avoid the truth predicate, and limited sizes of models [Horsten] |
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] |
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] |
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] |
5737 | Predicate logic has connectives, quantifiers, variables, predicates, equality, names and brackets [Melia] |
5744 | First-order predicate calculus is extensional logic, but quantified modal logic is intensional (hence dubious) [Melia] |
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] |
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] |
5740 | Second-order logic needs second-order variables and quantification into predicate position [Melia] |
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] |
5741 | If every model that makes premises true also makes conclusion true, the argument is valid [Melia] |
15353 | The first incompleteness theorem means that consistency does not entail soundness [Horsten] |
15355 | Strengthened Liar: 'this sentence is not true in any context' - in no context can this be evaluated [Horsten] |
15364 | English expressions are denumerably infinite, but reals are nondenumerable, so many are unnameable [Horsten] |
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] |
15370 | Predicativism says mathematical definitions must not include the thing being defined [Horsten] |
5736 | No sort of plain language or levels of logic can express modal facts properly [Melia] |
5735 | Maybe names and predicates can capture any fact [Melia] |
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] |
5746 | The Identity of Indiscernibles is contentious for qualities, and trivial for non-qualities [Melia] |
5738 | We may be sure that P is necessary, but is it necessarily necessary? [Melia] |
5732 | 'De re' modality is about things themselves, 'de dicto' modality is about propositions [Melia] |
5739 | Sometimes we want to specify in what ways a thing is possible [Melia] |
5734 | Possible worlds make it possible to define necessity and counterfactuals without new primitives [Melia] |
5742 | In possible worlds semantics the modal operators are treated as quantifiers [Melia] |
5743 | If possible worlds semantics is not realist about possible worlds, logic becomes merely formal [Melia] |
5749 | Possible worlds could be real as mathematics, propositions, properties, or like books [Melia] |
5751 | The truth of propositions at possible worlds are implied by the world, just as in books [Melia] |
15372 | Some claim that indicative conditionals are believed by people, even though they are not actually held true [Horsten] |
5748 | We accept unverifiable propositions because of simplicity, utility, explanation and plausibility [Melia] |
15347 | A theory of syntax can be based on Peano arithmetic, thanks to the translation by Gödel coding [Horsten] |
13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |