30 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] |
| 17377 | All descriptive language is classificatory [Dupré] |
| 17376 | We should aim for a classification which tells us as much as possible about the object [Dupré] |
| 17390 | Natural kinds don't need essentialism to be explanatory [Dupré] |
| 17389 | A species might have its essential genetic mechanism replaced by a new one [Dupré] |
| 17388 | It seems that species lack essential properties, so they can't be natural kinds [Dupré] |
| 17374 | The possibility of prediction rests on determinism [Dupré] |
| 17378 | Presumably molecular structure seems important because we never have the Twin Earth experience [Dupré] |
| 17381 | Phylogenetics involves history, and cladism rests species on splits in lineage [Dupré] |
| 17385 | Kinds don't do anything (including evolve) because they are abstract [Dupré] |
| 17380 | Wales may count as fish [Dupré] |
| 17382 | Cooks, unlike scientists, distinguish garlic from onions [Dupré] |
| 17375 | Natural kinds are decided entirely by the intentions of our classification [Dupré] |
| 17379 | Borders between species are much less clear in vegetables than among animals [Dupré] |
| 17384 | Even atoms of an element differ, in the energy levels of their electrons [Dupré] |
| 17387 | Ecologists favour classifying by niche, even though that can clash with genealogy [Dupré] |
| 15877 | The aim of science is just to create a comprehensive, elegant language to describe brute facts [Poincaré, by Harré] |
| 17383 | Species are the lowest-level classification in biology [Dupré] |
| 17386 | The theory of evolution is mainly about species [Dupré] |