84 ideas
15357 | Philosophy is the most general intellectual discipline [Horsten] |
12027 | There must be a plausible epistemological theory alongside any metaphysical theory [Forbes,G] |
15352 | A definition should allow the defined term to be eliminated [Horsten] |
10882 | Predicative definitions only refer to entities outside the defined collection [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] |
12005 | The symbol 'ι' forms definite descriptions; (ιx)F(x) says 'the x which is such that F(x)' [Forbes,G] |
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] |
12010 | Is the meaning of 'and' given by its truth table, or by its introduction and elimination rules? [Forbes,G] |
15328 | A theory is 'non-conservative' if it facilitates new mathematical proofs [Horsten] |
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] |
10884 | A theory is 'categorical' if it has just one model up to isomorphism [Horsten] |
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] |
10885 | Computer proofs don't provide explanations [Horsten] |
10881 | The concept of 'ordinal number' is set-theoretic, not arithmetical [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] |
15338 | We may believe in atomic facts, but surely not complex disjunctive ones? [Horsten] |
12023 | Vagueness problems arise from applying sharp semantics to vague languages [Forbes,G] |
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] |
12017 | In all instances of identity, there must be some facts to ensure the identity [Forbes,G] |
12024 | If we combined two clocks, it seems that two clocks may have become one clock. [Forbes,G] |
11885 | Only individual essences will ground identities across worlds in other properties [Forbes,G, by Mackie,P] |
12014 | An individual essence is a set of essential properties which only that object can have [Forbes,G] |
12015 | Non-trivial individual essence is properties other than de dicto, or universal, or relational [Forbes,G] |
12013 | Essential properties depend on a category, and perhaps also on particular facts [Forbes,G] |
13804 | A property is essential iff the object would not exist if it lacked that property [Forbes,G] |
13805 | Properties are trivially essential if they are not grounded in a thing's specific nature [Forbes,G] |
12012 | Essential properties are those without which an object could not exist [Forbes,G] |
13808 | A relation is essential to two items if it holds in every world where they exist [Forbes,G] |
13806 | Trivially essential properties are existence, self-identity, and de dicto necessities [Forbes,G] |
13807 | A property is 'extraneously essential' if it is had only because of the properties of other objects [Forbes,G] |
12025 | Artefacts have fuzzy essences [Forbes,G] |
12022 | Same parts does not ensure same artefact, if those parts could constitute a different artefact [Forbes,G] |
13809 | One might be essentialist about the original bronze from which a statue was made [Forbes,G] |
12020 | An individual might change their sex in a world, but couldn't have differed in sex at origin [Forbes,G] |
11888 | Identities must hold because of other facts, which must be instrinsic [Forbes,G, by Mackie,P] |
12003 | De re modal formulae, unlike de dicto, are sensitive to transworld identities [Forbes,G] |
12028 | De re necessity is a form of conceptual necessity, just as de dicto necessity is [Forbes,G] |
13810 | The source of de dicto necessity is not concepts, but the actual properties of the thing [Forbes,G] |
12008 | Unlike places and times, we cannot separate possible worlds from what is true at them [Forbes,G] |
12009 | The problem with possible worlds realism is epistemological; we can't know properties of possible objects [Forbes,G] |
12007 | Possible worlds are points of logical space, rather like other times than our own [Forbes,G] |
12011 | Transworld identity concerns the limits of possibility for ordinary things [Forbes,G] |
12016 | The problem of transworld identity can be solved by individual essences [Forbes,G] |
12004 | Counterpart theory is not good at handling the logic of identity [Forbes,G] |
12021 | Haecceitism attributes to each individual a primitive identity or thisness [Forbes,G] |
12029 | We believe in thisnesses, because we reject bizarre possibilities as not being about that individual [Forbes,G] |
15372 | Some claim that indicative conditionals are believed by people, even though they are not actually held true [Horsten] |
15347 | A theory of syntax can be based on Peano arithmetic, thanks to the translation by Gödel coding [Horsten] |
22745 | Pherecydes said the first principle and element is earth [Pherecydes, by Sext.Empiricus] |
5883 | Pherecydes was the first to say that the soul is eternal [Pherecydes, by Cicero] |