92 ideas
15357 | Philosophy is the most general intellectual discipline [Horsten] |
15447 | We shouldn't always follow where the argument leads! [Lewis on Plato] |
243 | It is foolish to quarrel with the mind's own reasoning processes [Plato] |
241 | We ought to follow where the argument leads us [Plato] |
21264 | Mortals are incapable of being fully rational [Plato] |
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] |
251 | Truth has the supreme value, for both gods and men [Plato] |
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] |
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] |
21259 | To grasp a thing we need its name, its definition, and what it really is [Plato] |
6171 | Beliefs are states of the head that explain behaviour, and also items with referential truth-conditions [McGinn] |
15372 | Some claim that indicative conditionals are believed by people, even though they are not actually held true [Horsten] |
21260 | Soul is what is defined by 'self-generating motion' [Plato] |
276 | My individuality is my soul, which carries my body around [Plato] |
15347 | A theory of syntax can be based on Peano arithmetic, thanks to the translation by Gödel coding [Horsten] |
249 | People who value beauty above virtue insult the soul by placing the body above it [Plato] |
265 | An action is only just if it is performed by someone with a just character and outlook [Plato] |
269 | Attempted murder is like real murder, but we should respect the luck which avoided total ruin [Plato] |
240 | It would be strange if the gods rewarded those who experienced the most pleasure in life [Plato] |
264 | The conquest of pleasure is the noblest victory of all [Plato] |
4332 | Virtue is a concord of reason and emotion, with pleasure and pain trained to correct ends [Plato] |
248 | A serious desire for moral excellence is very rare indeed [Plato] |
253 | Every crime is the result of excessive self-love [Plato] |
263 | The only worthwhile life is one devoted to physical and moral perfection [Plato] |
235 | Virtue is the aim of all laws [Plato] |
277 | The Guardians must aim to discover the common element in the four cardinal virtues [Plato] |
254 | Excessive laughter and tears must be avoided [Plato] |
266 | Injustice is the mastery of the soul by bad feelings, even if they do not lead to harm [Plato] |
242 | The best people are produced where there is no excess of wealth or poverty [Plato] |
256 | Virtue and great wealth are incompatible [Plato] |
245 | Totalitarian states destroy friendships and community spirit [Plato] |
239 | Education in virtue produces citizens who are active but obedient [Plato] |
1402 | Friendship is impossible between master and slave, even if they are made equal [Plato] |
262 | Men and women should qualify equally for honours on merit [Plato] |
236 | Sound laws achieve the happiness of those who observe them [Plato] |
259 | Justice is granting the equality which unequals deserve [Plato] |
257 | Mathematics has the widest application of any subject on the curriculum [Plato] |
238 | Children's games should channel their pleasures into adult activity [Plato] |
260 | Control of education is the key office of state, and should go to the best citizen [Plato] |
4331 | Education is channelling a child's feelings into the right course before it understands why [Plato] |
250 | The best way to educate the young is not to rebuke them, but to set a good example [Plato] |
275 | Creation is not for you; you exist for the sake of creation [Plato] |
273 | Movement is transmitted through everything, and it must have started with self-generated motion [Plato] |
8004 | In 'The Laws', to obey the law is to be obey god [Plato, by MacIntyre] |
21261 | Self-moving soul has to be the oldest thing there is [Plato] |
21258 | The only possible beginning for the endless motions of reality is something self-generated [Plato] |
21257 | Self-generating motion is clearly superior to all other kinds of motion [Plato] |
274 | Soul must be the cause of all the opposites, such as good and evil or beauty and ugliness [Plato] |
21263 | If all the motions of nature reflect calculations of reason, then the best kind of soul must direct it [Plato] |
278 | If astronomical movements are seen as necessary instead of by divine will, this leads to atheism [Plato] |
21265 | The heavens must be full of gods, controlling nature either externally or from within [Plato] |
21262 | There must be at least two souls controlling the cosmos, one doing good, the other the opposite [Plato] |