23 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] |
1590 | The just man does not harm his enemies, but benefits everyone [Plato] |
23529 | Conduct is not isolated from its effect on the moral code [Hart,HLA] |
23530 | The great danger of democracy is that the oppression of the minority becomes unobjectionable [Hart,HLA] |
23522 | In an organised society all actions have some effect on other people [Hart,HLA] |
23528 | The value of liberty allows freedom of action, even if that distresses other people [Hart,HLA] |
23523 | The principle of legality requires crimes to be precisely defined in advance of any action [Hart,HLA] |
23524 | Some private moral issues are no concern of the law [Hart,HLA] |
23521 | Do morals influence law? Is morality an aspect of law? Can law be morally criticised? [Hart,HLA] |
23525 | Is the enforcement of morality morally justifiable? [Hart,HLA] |
23526 | Modern law still suppresses practices seen as immoral, and yet harmless [Hart,HLA] |
23527 | Moral wickedness of an offence is always relevant to the degree of punishment [Hart,HLA] |