35 ideas
326 | For relaxation one can consider the world of change, instead of eternal things [Plato] |
315 | Philosophy is the supreme gift of the gods to mortals [Plato] |
306 | Nothing can come to be without a cause [Plato] |
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] |
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] |
324 | Before the existence of the world there must have been being, space and becoming [Plato] |
20364 | The apprehensions of reason remain unchanging, but reasonless sensation shows mere becoming [Plato] |
16660 | Are things distinct if they are both separate, or if only one of them can be separate? [Duns Scotus, by Pasnau] |
12042 | Plato's Forms were seen as part of physics, rather than of metaphysics [Plato, by Annas] |
307 | Something will always be well-made if the maker keeps in mind the eternal underlying pattern [Plato] |
318 | In addition to the underlying unchanging model and a changing copy of it, there must also be a foundation of all change [Plato] |
321 | For knowledge and true opinion to be different there must be Forms; otherwise we are just stuck with sensations [Plato] |
317 | The universe is basically an intelligible and unchanging model, and a visible and changing copy of it [Plato] |
16626 | Substance is only grasped under the general heading of 'being' [Duns Scotus] |
334 | Only bird-brained people think astronomy is entirely a matter of evidence [Plato] |
5962 | Plato says the soul is ordered by number [Plato, by Plutarch] |
330 | No one wants to be bad, but bad men result from physical and educational failures, which they do not want or choose [Plato] |
316 | Music has harmony like the soul, and serves to reorder disharmony within us [Plato] |
332 | One should exercise both the mind and the body, to avoid imbalance [Plato] |
328 | Everything that takes place naturally is pleasant [Plato] |
322 | Intelligence is the result of rational teaching; true opinion can result from irrational persuasion [Plato] |
331 | Bad governments prevent discussion, and discourage the study of virtue [Plato] |
310 | The creator of the cosmos had no envy, and so wanted things to be as like himself as possible [Plato] |
311 | The cosmos must be unique, because it resembles the creator, who is unique [Plato] |
325 | We must consider the four basic shapes as too small to see, only becoming visible in large numbers [Plato] |
327 | There are two types of cause, the necessary and the divine [Plato] |
314 | Heavenly movements gave us the idea of time, and caused us to inquire about the heavens [Plato] |
312 | Time came into existence with the heavens, so that there will be a time when they can be dissolved [Plato] |
309 | Clearly the world is good, so its maker must have been concerned with the eternal, not with change [Plato] |
308 | If the cosmos is an object of perception then it must be continually changing [Plato] |