19 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] |
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] |
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] |
10302 | Euclid says we can 'join' two points, but Hilbert says the straight line 'exists' [Euclid, by Bernays] |
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] |
19729 | 'Modal epistemology' demands a connection between the belief and facts in possible worlds [Black,T] |
19728 | Gettier and lottery cases seem to involve luck, meaning bad connection of beliefs to facts [Black,T] |
1457 | Morality requires a minimum commitment to the self [Rashdall] |
6674 | All moral judgements ultimately concern the value of ends [Rashdall] |
6673 | Ideal Utilitarianism is teleological but non-hedonistic; the aim is an ideal end, which includes pleasure [Rashdall] |
1458 | Conduct is only reasonable or unreasonable if the world is governed by reason [Rashdall] |
1459 | Absolute moral ideals can't exist in human minds or material things, so their acceptance implies a greater Mind [Rashdall, by PG] |