68 ideas
15357 | Philosophy is the most general intellectual discipline [Horsten] |
22024 | Fichte's subjectivity struggles to then give any account of objectivity [Pinkard on Fichte] |
15352 | A definition should allow the defined term to be eliminated [Horsten] |
15323 | Truth is a property, because the truth predicate has an extension [Horsten] |
15324 | Semantic theories of truth seek models; axiomatic (syntactic) theories seek logical principles [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] |
15340 | Tarski Bi-conditional: if you'll assert φ you'll assert φ-is-true - and also vice versa [Horsten] |
15354 | Tarski's hierarchy lacks uniform truth, and depends on contingent factors [Horsten] |
15345 | Semantic theories have a regress problem in describing truth in the languages for the models [Horsten] |
15350 | The Naïve 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] |
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] |
15367 | By adding truth to Peano Arithmetic we increase its power, so truth has mathematical content! [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] |
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] |
15331 | Kripke-Feferman has truth gaps, instead of classical logic, and aims for maximum strength [Horsten] |
15356 | Deflationism concerns the nature and role of truth, but not its laws [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] |
15368 | This deflationary account says truth has a role in generality, and in inference [Horsten] |
15344 | Deflationism skips definitions and models, and offers just accounts of basic laws of truth [Horsten] |
15325 | Inferential deflationism says truth has no essence because no unrestricted logic governs the concept [Horsten] |
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] |
22017 | Normativity needs the possibility of negation, in affirmation and denial [Fichte, by Pinkard] |
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] |
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] |
14086 | 'Modal' structuralism studies all possible concrete models for various mathematical theories [Linnebo] |
14087 | 'Set-theoretic' structuralism treats mathematics as various structures realised among the sets [Linnebo] |
14085 | 'Deductivist' structuralism is just theories, with no commitment to objects, or modality [Linnebo] |
14084 | Non-eliminative structuralism treats mathematical objects as positions in real abstract structures [Linnebo] |
14089 | Structuralism differs from traditional Platonism, because the objects depend ontologically on their structure [Linnebo] |
14083 | Structuralism is right about algebra, but wrong about sets [Linnebo] |
14090 | In mathematical structuralism the small depends on the large, which is the opposite of physical structures [Linnebo] |
15370 | Predicativism says mathematical definitions must not include the thing being defined [Horsten] |
14091 | There may be a one-way direction of dependence among sets, and among natural numbers [Linnebo] |
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] |
14088 | An 'intrinsic' property is either found in every duplicate, or exists independent of all externals [Linnebo] |
22018 | Necessary truths from basic assertion and negation [Fichte, by Pinkard] |
15372 | Some claim that indicative conditionals are believed by people, even though they are not actually held true [Horsten] |
22064 | Fichte's logic is much too narrow, and doesn't deduce ethics, art, society or life [Schlegel,F on Fichte] |
22032 | Fichte's key claim was that the subjective-objective distinction must itself be subjective [Fichte, by Pinkard] |
22020 | We only see ourselves as self-conscious and rational in relation to other rationalities [Fichte] |
22060 | The Self is the spontaneity, self-relatedness and unity needed for knowledge [Fichte, by Siep] |
22066 | Novalis sought a much wider concept of the ego than Fichte's proposal [Novalis on Fichte] |
22016 | The self is not a 'thing', but what emerges from an assertion of normativity [Fichte, by Pinkard] |
22019 | Consciousness of an object always entails awareness of the self [Fichte] |
22061 | Judgement is distinguishing concepts, and seeing their relations [Fichte, by Siep] |
15347 | A theory of syntax can be based on Peano arithmetic, thanks to the translation by Gödel coding [Horsten] |
22023 | Fichte's idea of spontaneity implied that nothing counts unless we give it status [Fichte, by Pinkard] |
22065 | Fichte reduces nature to a lifeless immobility [Schlegel,F on Fichte] |