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] |
20100 | Classical liberalism seeks freedom of opinion, of private life, of expression, and of property [Micklethwait/Wooldridge] |
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] |
7544 | Many people imagine that to experience is to understand [Goethe] |
7541 | Man never understands how anthropomorphic he is [Goethe] |
7543 | We gain self-knowledge through action, not thought - especially when doing our duty [Goethe] |
7540 | Beauty is a manifestation of secret natural laws [Goethe] |
7538 | The happiest people link the beginning and end of life [Goethe] |
7542 | The best form of government teaches us to govern ourselves [Goethe] |
20097 | The welfare state aims at freedom from want, and equality of opportunity [Micklethwait/Wooldridge] |
20099 | For communists history is driven by the proletariat [Micklethwait/Wooldridge] |
20098 | Fans of economic freedom claim that capitalism is self-correcting [Micklethwait/Wooldridge] |
7539 | To get duties from people without rights, you must pay them well [Goethe] |
20096 | Roman law entrenched property rights [Micklethwait/Wooldridge] |