31 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] |
| 6007 | If you know your father, but don't recognise your father veiled, you know and don't know the same person [Eubulides, by Dancy,R] |
| 6006 | If you say truly that you are lying, you are lying [Eubulides, by Dancy,R] |
| 6008 | Removing one grain doesn't destroy a heap, so a heap can't be destroyed [Eubulides, by Dancy,R] |
| 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] |
| 1212 | Replacing timbers on Theseus' ship was the classic illustration of the problem of growth and change [Plutarch] |
| 5958 | The sun is always bright; it doesn't become bright when it emerges [Plutarch] |
| 5960 | When the soul is intelligent and harmonious, it is part of god and derives from god [Plutarch] |
| 5959 | Some philosophers say the soul is light [Plutarch] |
| 5952 | Rather than being the whole soul, maybe I am its chief part? [Plutarch] |
| 5951 | If atoms have no qualities, they cannot possibly produce a mind [Plutarch] |
| 5963 | Some say emotion is a sort of reason, and others say virtue concerns emotion [Plutarch] |
| 20796 | Action needs an affinity for a presentation, and an impulse toward the affinity [Plutarch] |
| 1477 | Being manly and brave is the result of convention, not of human nature [Plutarch] |
| 1478 | Animals don't value pleasure, as they cease sexual intercourse after impregnation [Plutarch] |
| 5948 | The good life involves social participation, loyalty, temperance and honesty [Plutarch] |
| 1479 | Animals have not been led into homosexuality, because they value pleasure very little [Plutarch] |
| 5950 | If only atoms exist, how do qualities arise when the atoms come together? [Plutarch] |
| 5974 | People report seeing through rocks, or over the horizon, or impossibly small works [Plutarch] |
| 5957 | Absurd superstitions make people atheist, not disharmony in nature [Plutarch] |
| 5955 | No one will ever find a city that lacks religious practices [Plutarch] |