34 ideas
| 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] |
| 4261 | The Lottery Paradox says each ticket is likely to lose, so there probably won't be a winner [Bonjour, by PG] |
| 6297 | Euclid's geometry is synthetic, but Descartes produced an analytic version of it [Euclid, by Resnik] |
| 9603 | An assumption that there is a largest prime leads to a contradiction [Euclid, by Brown,JR] |
| 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] |
| 9476 | If dispositions are more fundamental than causes, then they won't conceptually reduce to them [Bird on Lewis] |
| 8425 | For true counterfactuals, both antecedent and consequent true is closest to actuality [Lewis] |
| 4255 | Externalist theories of knowledge are one species of foundationalism [Bonjour] |
| 4257 | The big problem for foundationalism is to explain how basic beliefs are possible [Bonjour] |
| 4256 | The main argument for foundationalism is that all other theories involve a regress leading to scepticism [Bonjour] |
| 4258 | Extreme externalism says no more justification is required than the truth of the belief [Bonjour] |
| 4259 | External reliability is not enough, if the internal state of the believer is known to be irrational [Bonjour] |
| 4260 | Even if there is no obvious irrationality, it may be irrational to base knowledge entirely on external criteria [Bonjour] |
| 8424 | Determinism says there can't be two identical worlds up to a time, with identical laws, which then differ [Lewis] |
| 8420 | A proposition is a set of possible worlds where it is true [Lewis] |
| 8405 | A theory of causation should explain why cause precedes effect, not take it for granted [Lewis, by Field,H] |
| 8427 | I reject making the direction of causation axiomatic, since that takes too much for granted [Lewis] |
| 10392 | It is just individious discrimination to pick out one cause and label it as 'the' cause [Lewis] |
| 8419 | The modern regularity view says a cause is a member of a minimal set of sufficient conditions [Lewis] |
| 8421 | Regularity analyses could make c an effect of e, or an epiphenomenon, or inefficacious, or pre-empted [Lewis] |
| 17525 | The counterfactual view says causes are necessary (rather than sufficient) for their effects [Lewis, by Bird] |
| 17524 | Lewis has basic causation, counterfactuals, and a general ancestral (thus handling pre-emption) [Lewis, by Bird] |
| 8397 | Counterfactual causation implies all laws are causal, which they aren't [Tooley on Lewis] |
| 8423 | My counterfactual analysis applies to particular cases, not generalisations [Lewis] |
| 8426 | One event causes another iff there is a causal chain from first to second [Lewis] |
| 4795 | Lewis's account of counterfactuals is fine if we know what a law of nature is, but it won't explain the latter [Cohen,LJ on Lewis] |