67 ideas
| 15357 | Philosophy is the most general intellectual discipline [Horsten] |
| 24032 | Clever scholars can obscure things which are obvious even to peasants [Descartes] |
| 24033 | Most scholastic disputes concern words, where agreeing on meanings would settle them [Descartes] |
| 24024 | The secret of the method is to recognise which thing in a series is the simplest [Descartes] |
| 24018 | One truth leads us to another [Descartes] |
| 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] |
| 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] |
| 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] |
| 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] |
| 24035 | Unity is something shared by many things, so in that respect they are equals [Descartes] |
| 24036 | I can only see the proportion of two to three if there is a common measure - their unity [Descartes] |
| 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] |
| 24029 | Among the simples are the graspable negations, such as rest and instants [Descartes] |
| 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] |
| 15391 | A substance is, roughly, a basic being or subject at the foundation of reality [Robb] |
| 15392 | If an object survives the loss of a part, complex objects can have autonomy over their parts [Robb] |
| 24030 | 3+4=7 is necessary because we cannot conceive of seven without including three and four [Descartes] |
| 15372 | Some claim that indicative conditionals are believed by people, even though they are not actually held true [Horsten] |
| 24019 | If we accept mere probabilities as true we undermine our existing knowledge [Descartes] |
| 24020 | We all see intuitively that we exist, where intuition is attentive, clear and distinct rational understanding [Descartes] |
| 24031 | When Socrates doubts, he know he doubts, and that truth is possible [Descartes] |
| 24025 | Clear and distinct truths must be known all at once (unlike deductions) [Descartes] |
| 24022 | Our souls possess divine seeds of knowledge, which can bear spontaneous fruit [Descartes] |
| 24034 | If someone had only seen the basic colours, they could deduce the others from resemblance [Descartes] |
| 24021 | The method starts with clear intuitions, followed by a process of deduction [Descartes] |
| 24027 | Nerves and movement originate in the brain, where imagination moves them [Descartes] |
| 24026 | Our four knowledge faculties are intelligence, imagination, the senses, and memory [Descartes] |
| 24028 | The force by which we know things is spiritual, and quite distinct from the body [Descartes] |
| 15347 | A theory of syntax can be based on Peano arithmetic, thanks to the translation by Gödel coding [Horsten] |
| 24023 | All the sciences searching for order and measure are related to mathematics [Descartes] |