81 ideas
| 12036 | Xenophanes began the concern with knowledge [Annas] |
| 12046 | Plato was the first philosopher who was concerned to systematize his ideas [Annas] |
| 7454 | Gassendi is the first great empiricist philosopher [Hacking] |
| 15357 | Philosophy is the most general intellectual discipline [Horsten] |
| 15352 | A definition should allow the defined term to be eliminated [Horsten] |
| 13838 | A decent modern definition should always imply a semantics [Hacking] |
| 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 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] |
| 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] |
| 13833 | 'Thinning' ('dilution') is the key difference between deduction (which allows it) and induction [Hacking] |
| 13834 | Gentzen's Cut Rule (or transitivity of deduction) is 'If A |- B and B |- C, then A |- C' [Hacking] |
| 13835 | Only Cut reduces complexity, so logic is constructive without it, and it can be dispensed with [Hacking] |
| 15329 | Nonclassical may accept T/F but deny applicability, or it may deny just T or F as well [Horsten] |
| 13845 | The various logics are abstractions made from terms like 'if...then' in English [Hacking] |
| 13840 | First-order logic is the strongest complete compact theory with Löwenheim-Skolem [Hacking] |
| 13844 | A limitation of first-order logic is that it cannot handle branching quantifiers [Hacking] |
| 15326 | Doubt is thrown on classical logic by the way it so easily produces the liar paradox [Horsten] |
| 13842 | Second-order completeness seems to need intensional entities and possible worlds [Hacking] |
| 15341 | Deduction Theorem: ψ only derivable from φ iff φ→ψ are axioms [Horsten] |
| 13837 | With a pure notion of truth and consequence, the meanings of connectives are fixed syntactically [Hacking] |
| 13839 | Perhaps variables could be dispensed with, by arrows joining places in the scope of quantifiers [Hacking] |
| 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] |
| 13843 | If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking] |
| 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] |
| 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] |
| 7447 | Probability was fully explained between 1654 and 1812 [Hacking] |
| 7448 | Probability is statistical (behaviour of chance devices) or epistemological (belief based on evidence) [Hacking] |
| 7449 | Epistemological probability based either on logical implications or coherent judgments [Hacking] |
| 15372 | Some claim that indicative conditionals are believed by people, even though they are not actually held true [Horsten] |
| 7450 | In the medieval view, only deduction counted as true evidence [Hacking] |
| 7451 | Formerly evidence came from people; the new idea was that things provided evidence [Hacking] |
| 7452 | An experiment is a test, or an adventure, or a diagnosis, or a dissection [Hacking, by PG] |
| 7459 | Follow maths for necessary truths, and jurisprudence for contingent truths [Hacking] |
| 15347 | A theory of syntax can be based on Peano arithmetic, thanks to the translation by Gödel coding [Horsten] |
| 3546 | 'Phronesis' should translate as 'practical intelligence', not as prudence [Annas] |
| 12037 | Euripides's Medea is a key case of reason versus the passions [Annas] |
| 3547 | Epicureans achieve pleasure through character development [Annas] |
| 3543 | Cyrenaics pursue pleasure, but don't equate it with happiness [Annas] |
| 12040 | Virtue is a kind of understanding of moral value [Annas] |
| 3541 | Ancient ethics uses attractive notions, not imperatives [Annas] |
| 3550 | Principles cover life as a whole, where rules just cover actions [Annas] |
| 3551 | Virtue theory tries to explain our duties in terms of our character [Annas] |
| 3552 | If excessively good actions are admirable but not required, then duty isn't basic [Annas] |
| 3542 | We should do good when necessary, not maximise it [Annas] |