78 ideas
15357 | Philosophy is the most general intellectual discipline [Horsten] |
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] |
15346 | Axiomatic approaches to truth avoid the regress problem of semantic theories [Horsten] |
15371 | An axiomatic theory needs to be of maximal strength, while being natural and sound [Horsten] |
15332 | 'Reflexive' truth theories allow iterations (it is T that it is T that p) [Horsten] |
15361 | A good theory of truth must be compositional (as well as deriving biconditionals) [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] |
15879 | The Square of Opposition has two contradictory pairs, one contrary pair, and one sub-contrary pair [Harré] |
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] |
15891 | Traditional quantifiers combine ordinary language generality and ontology assumptions [Harré] |
15878 | Some quantifiers, such as 'any', rule out any notion of order within their range [Harré] |
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] |
15363 | In the supervaluationist account, disjunctions are not determined by their disjuncts [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] |
15874 | Scientific properties are not observed qualities, but the dispositions which create them [Harré] |
15884 | Laws of nature remain the same through any conditions, if the underlying mechanisms are unchanged [Harré] |
15372 | Some claim that indicative conditionals are believed by people, even though they are not actually held true [Horsten] |
15880 | In physical sciences particular observations are ordered, but in biology only the classes are ordered [Harré] |
15869 | Reports of experiments eliminate the experimenter, and present results as the behaviour of nature [Harré] |
15881 | We can save laws from counter-instances by treating the latter as analytic definitions [Harré] |
15882 | Since there are three different dimensions for generalising laws, no one system of logic can cover them [Harré] |
15887 | 'Grue' introduces a new causal hypothesis - that emeralds can change colour [Harré] |
15888 | The grue problem shows that natural kinds are central to science [Harré] |
15889 | It is because ravens are birds that their species and their colour might be connected [Harré] |
15890 | Non-black non-ravens just aren't part of the presuppositions of 'all ravens are black' [Harré] |
15885 | The necessity of Newton's First Law derives from the nature of material things, not from a mechanism [Harré] |
15868 | Idealisation idealises all of a thing's properties, but abstraction leaves some of them out [Harré] |
15347 | A theory of syntax can be based on Peano arithmetic, thanks to the translation by Gödel coding [Horsten] |
7258 | The forefather of modern intuitionism is Richard Price [Price,R, by Dancy,J] |
15886 | Science rests on the principle that nature is a hierarchy of natural kinds [Harré] |
15864 | Classification is just as important as laws in natural science [Harré] |
15865 | Newton's First Law cannot be demonstrated experimentally, as that needs absence of external forces [Harré] |
15862 | Laws can come from data, from theory, from imagination and concepts, or from procedures [Harré] |
15870 | Are laws of nature about events, or types and universals, or dispositions, or all three? [Harré] |
15871 | Are laws about what has or might happen, or do they also cover all the possibilities? [Harré] |
15876 | Maybe laws of nature are just relations between properties? [Harré] |
15860 | We take it that only necessary happenings could be laws [Harré] |
15872 | Must laws of nature be universal, or could they be local? [Harré] |
15867 | Laws describe abstract idealisations, not the actual mess of nature [Harré] |
15892 | Laws of nature state necessary connections of things, events and properties, based on models of mechanisms [Harré] |
15875 | In counterfactuals we keep substances constant, and imagine new situations for them [Harré] |