29 ideas
| 17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
| 17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
| 17605 | Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy] |
| 17625 | If two mathematical themes coincide, that suggest a single deep truth [Maddy] |
| 1507 | We don't have time for infinite quantity, but we do for infinite divisibility, because time is also divisible [Aristotle on Zeno of Elea] |
| 5109 | The fast runner must always reach the point from which the slower runner started [Zeno of Elea, by Aristotle] |
| 1512 | Zeno is wrong that one grain of millet makes a sound; why should one grain achieve what the whole bushel does? [Aristotle on Zeno of Elea] |
| 1508 | Zeno's arrow paradox depends on the assumption that time is composed of nows [Aristotle on Zeno of Elea] |
| 17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
| 17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
| 17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
| 12157 | Kant gave form and status to aesthetics, and Hegel gave it content [Kant, by Scruton] |
| 20346 | The aesthetic attitude is a matter of disinterestedness [Kant, by Wollheim] |
| 18547 | Only rational beings can experience beauty [Kant, by Scruton] |
| 24172 | It is hard to see why we would have developed Kant's 'disinterested' aesthetic attitude [Cochrane on Kant] |
| 20408 | With respect to the senses, taste is an entirely personal matter [Kant] |
| 20409 | When we judge beauty, it isn't just personal; we judge on behalf of everybody [Kant] |
| 20411 | Saying everyone has their own taste destroys the very idea of taste [Kant] |
| 24170 | Kant thinks beauty ignores its objects, because it is only 'form' engaging with mind [Cochrane on Kant] |
| 22711 | The beautiful is not conceptualised as moral, but it symbolises or resembles goodness [Kant, by Murdoch] |
| 4025 | Kant saw beauty as a sort of disinterested pleasure, which has become separate from the good [Kant, by Taylor,C] |
| 20412 | Beauty is only judged in pure contemplation, and not with something else at stake [Kant] |
| 22046 | The mathematical sublime is immeasurable greatness; the dynamical sublime is overpowering [Kant, by Pinkard] |
| 21458 | The sublime is a moral experience [Kant, by Gardner] |
| 5643 | Aesthetic values are not objectively valid, but we must treat them as if they are [Kant, by Scruton] |
| 20410 | The judgement of beauty is not cognitive, but relates, via imagination, to pleasurable feelings [Kant] |
| 454 | If there are many things they must have a finite number, but there must be endless things between them [Zeno of Elea] |
| 455 | That which moves, moves neither in the place in which it is, nor in that in which it is not [Zeno of Elea] |
| 1511 | If everything is in a place, what is the place in? Place doesn't exist [Zeno of Elea, by Simplicius] |