21 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] |
10397 | Abelard's mereology involves privileged and natural divisions, and principal parts [Abelard, by King,P] |
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] |
10396 | If 'animal' is wholly present in Socrates and an ass, then 'animal' is rational and irrational [Abelard, by King,P] |
10395 | Abelard was an irrealist about virtually everything apart from concrete individuals [Abelard, by King,P] |
15384 | Only words can be 'predicated of many'; the universality is just in its mode of signifying [Abelard, by Panaccio] |
8481 | The de dicto-de re modality distinction dates back to Abelard [Abelard, by Orenstein] |
15385 | Abelard's problem is the purely singular aspects of things won't account for abstraction [Panaccio on Abelard] |
15383 | Nothing external can truly be predicated of an object [Abelard, by Panaccio] |
10398 | Natural kinds are not special; they are just well-defined resemblance collections [Abelard, by King,P] |
1515 | Pythagoreans believe it is absurd to seek for goodness anywhere except with the gods [Iamblichus] |