43 ideas
3358 | Metaphysics focuses on Platonism, essentialism, materialism and anti-realism [Benardete,JA] |
3312 | There are the 'is' of predication (a function), the 'is' of identity (equals), and the 'is' of existence (quantifier) [Benardete,JA] |
3352 | Analytical philosophy analyses separate concepts successfully, but lacks a synoptic vision of the results [Benardete,JA] |
3329 | Presumably the statements of science are true, but should they be taken literally or not? [Benardete,JA] |
8623 | Proof reveals the interdependence of truths, as well as showing their certainty [Euclid, by Frege] |
13907 | If you pick an arbitrary triangle, things proved of it are true of all triangles [Euclid, by Lemmon] |
3326 | Set theory attempts to reduce the 'is' of predication to mathematics [Benardete,JA] |
3327 | The set of Greeks is included in the set of men, but isn't a member of it [Benardete,JA] |
3335 | The standard Z-F Intuition version of set theory has about ten agreed axioms [Benardete,JA, by PG] |
20100 | Classical liberalism seeks freedom of opinion, of private life, of expression, and of property [Micklethwait/Wooldridge] |
6297 | Euclid's geometry is synthetic, but Descartes produced an analytic version of it [Euclid, by Resnik] |
3332 | Greeks saw the science of proportion as the link between geometry and arithmetic [Benardete,JA] |
9603 | An assumption that there is a largest prime leads to a contradiction [Euclid, by Brown,JR] |
3330 | Negatives, rationals, irrationals and imaginaries are all postulated to solve baffling equations [Benardete,JA] |
3337 | Natural numbers are seen in terms of either their ordinality (Peano), or cardinality (set theory) [Benardete,JA] |
9894 | A unit is that according to which each existing thing is said to be one [Euclid] |
8738 | Postulate 2 says a line can be extended continuously [Euclid, by Shapiro] |
10302 | Euclid says we can 'join' two points, but Hilbert says the straight line 'exists' [Euclid, by Bernays] |
22278 | Euclid relied on obvious properties in diagrams, as well as on his axioms [Potter on Euclid] |
8673 | Euclid's parallel postulate defines unique non-intersecting parallel lines [Euclid, by Friend] |
10250 | Euclid needs a principle of continuity, saying some lines must intersect [Shapiro on Euclid] |
14157 | Modern geometries only accept various parts of the Euclid propositions [Russell on Euclid] |
1600 | Euclid's common notions or axioms are what we must have if we are to learn anything at all [Euclid, by Roochnik] |
3310 | If slowness is a property of walking rather than the walker, we must allow that events exist [Benardete,JA] |
12793 | Early pre-Socratics had a mass-noun ontology, which was replaced by count-nouns [Benardete,JA] |
3353 | If there is no causal interaction with transcendent Platonic objects, how can you learn about them? [Benardete,JA] |
3304 | Why should packed-together particles be a thing (Mt Everest), but not scattered ones? [Benardete,JA] |
3350 | Could a horse lose the essential property of being a horse, and yet continue to exist? [Benardete,JA] |
3309 | If a soldier continues to exist after serving as a soldier, does the wind cease to exist after it ceases to blow? [Benardete,JA] |
3351 | One can step into the same river twice, but not into the same water [Benardete,JA] |
3323 | Maybe self-identity isn't existence, if Pegasus can be self-identical but non-existent [Benardete,JA] |
3314 | Absolutists might accept that to exist is relative, but relative to what? How about relative to itself? [Benardete,JA] |
3306 | The clearest a priori knowledge is proving non-existence through contradiction [Benardete,JA] |
3345 | Appeals to intuition seem to imply synthetic a priori knowledge [Benardete,JA] |
3341 | Logical positivism amounts to no more than 'there is no synthetic a priori' [Benardete,JA] |
3344 | Assertions about existence beyond experience can only be a priori synthetic [Benardete,JA] |
3349 | If we know truths about prime numbers, we seem to have synthetic a priori knowledge of Platonic objects [Benardete,JA] |
20097 | The welfare state aims at freedom from want, and equality of opportunity [Micklethwait/Wooldridge] |
20099 | For communists history is driven by the proletariat [Micklethwait/Wooldridge] |
20098 | Fans of economic freedom claim that capitalism is self-correcting [Micklethwait/Wooldridge] |
20096 | Roman law entrenched property rights [Micklethwait/Wooldridge] |
3334 | Rationalists see points as fundamental, but empiricists prefer regions [Benardete,JA] |
3308 | In the ontological argument a full understanding of the concept of God implies a contradiction in 'There is no God' [Benardete,JA] |