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] |
10302 | Euclid says we can 'join' two points, but Hilbert says the straight line 'exists' [Euclid, by Bernays] |
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] |
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] |
12699 | A body would be endless disunited parts, if it did not have a unifying form or soul [Leibniz] |
12700 | Form or soul gives unity and duration; matter gives multiplicity and change [Leibniz] |
12736 | If we understand God and his choices, we have a priori knowledge of contingent truths [Leibniz, by Garber] |
12698 | Every body contains a kind of sense and appetite, or a soul [Leibniz] |
21991 | The middle class gain freedom through property, but workers can only free all of humanity [Marx, by Singer] |
21990 | Theory is as much a part of a revolution as material force is [Marx] |
7128 | Religion is the opium of the people, and real happiness requires its abolition [Marx] |