24 ideas
7910 | Pursue truth with the urgency of someone whose clothes are on fire [Ashvaghosha] |
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] |
10502 | We can rise by degrees through abstraction, with higher levels representing more things [Arnauld,A/Nicole,P] |
18258 | We can only know the exterior world via our ideas [Arnauld,A/Nicole,P] |
16784 | Forms make things distinct and explain the properties, by pure form, or arrangement of parts [Arnauld,A/Nicole,P] |
10499 | We know by abstraction because we only understand composite things a part at a time [Arnauld,A/Nicole,P] |
10501 | A triangle diagram is about all triangles, if some features are ignored [Arnauld,A/Nicole,P] |
10500 | No one denies that a line has width, but we can just attend to its length [Arnauld,A/Nicole,P] |
7906 | When the Buddha reached the highest level of insight, he could detect no self in the world [Ashvaghosha] |
7904 | The first stage of trance is calm amidst applied and discursive thinking [Ashvaghosha] |
7905 | The Buddha sought ultimate reality and the final goal of existence in his meditations [Ashvaghosha] |
7909 | The Eightfold Path concerns morality, wisdom, and tranquillity [Ashvaghosha] |
7908 | At the end of a saint, he is not located in space, but just ceases to be disturbed [Ashvaghosha] |