35 ideas
22338 | An unexamined life can be virtuous [Murdoch] |
22337 | Philosophy must keep returning to the beginning [Murdoch] |
23563 | Philosophy moves continually between elaborate theories and the obvious facts [Murdoch] |
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] |
22591 | We know perfection when we see what is imperfect [Murdoch] |
22709 | We should first decide what are the great works of art, with aesthetic theory following from that [Murdoch] |
22341 | Literature is the most important aspect of culture, because it teaches understanding of living [Murdoch] |
22715 | Great art proves the absurdity of art for art's sake [Murdoch] |
22714 | Because art is love, it improves us morally [Murdoch] |
22347 | Appreciating beauty in art or nature opens up the good life, by restricting selfishness [Murdoch] |
22712 | Art and morals are essentially the same, and are both identical with love [Murdoch] |
22339 | Love is a central concept in morals [Murdoch] |
22348 | Ordinary human love is good evidence of transcendent goodness [Murdoch] |
22713 | Love is realising something other than oneself is real [Murdoch] |
22343 | If I attend properly I will have no choices [Murdoch] |
22349 | Art trains us in the love of virtue [Murdoch] |
22340 | It is hard to learn goodness from others, because their virtues are part of their personal history [Murdoch] |
22350 | Only trivial virtues can be possessed on their own [Murdoch] |
22346 | Moral reflection and experience gradually reveals unity in the moral world [Murdoch] |
20765 | Man is a brave naked will, separate from a background of values and realities [Murdoch] |
22342 | Kantian existentialists care greatly for reasons for action, whereas Surrealists care nothing [Murdoch] |
22351 | Only a philosopher might think choices create values [Murdoch] |
22345 | Moral philosophy needs a central concept with all the traditional attributes of God [Murdoch] |
1513 | The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus] |