24 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] |
| 7861 | Libet says the processes initiated in the cortex can still be consciously changed [Libet, by Papineau] |
| 6660 | Libet found conscious choice 0.2 secs before movement, well after unconscious 'readiness potential' [Libet, by Lowe] |
| 23865 | Morality would improve if people could pursue private interests [Weil] |
| 23866 | In oppressive societies the scope of actual control is extended by a religion of power [Weil] |
| 23871 | No central authority can initiate decentralisation [Weil] |
| 23867 | After a bloody revolution the group which already had the power comes to the fore [Weil] |
| 23870 | Decentralisation is only possible by co-operation between strong and weak - which is absurd [Weil] |
| 23863 | Only individual people of good will can achieve social progress [Weil] |
| 23869 | In the least evil societies people can think, control community life, and be autonomous [Weil] |
| 23861 | Marx showed that capitalist oppression, because of competition, is unstoppable [Weil] |
| 23868 | The pleasure of completing tasks motivates just as well as the whip of slavery [Weil] |
| 23864 | Inequality could easily be mitigated, if it were not for the struggle for power [Weil] |