43 ideas
10702 | Set theory's three roles: taming the infinite, subject-matter of mathematics, and modes of reasoning [Potter] |
10713 | Usually the only reason given for accepting the empty set is convenience [Potter] |
13044 | Infinity: There is at least one limit level [Potter] |
10708 | Nowadays we derive our conception of collections from the dependence between them [Potter] |
13546 | The 'limitation of size' principles say whether properties collectivise depends on the number of objects [Potter] |
10707 | Mereology elides the distinction between the cards in a pack and the suits [Potter] |
10704 | We can formalize second-order formation rules, but not inference rules [Potter] |
10703 | Supposing axioms (rather than accepting them) give truths, but they are conditional [Potter] |
10712 | If set theory didn't found mathematics, it is still needed to count infinite sets [Potter] |
21382 | Things get smaller without end [Anaxagoras] |
17882 | It is remarkable that all natural number arithmetic derives from just the Peano Axioms [Potter] |
481 | Nothing is created or destroyed; there is only mixing and separation [Anaxagoras] |
21822 | Anaxagoras's concept of supreme Mind has a simple First and a multiple One [Anaxagoras, by Plotinus] |
17995 | Basic is the potentially perceptible, then comes the contrary qualities, and finally the 'elements' [Anaxagoras] |
13043 | A relation is a set consisting entirely of ordered pairs [Potter] |
13042 | If dependence is well-founded, with no infinite backward chains, this implies substances [Potter] |
13041 | Collections have fixed members, but fusions can be carved in innumerable ways [Potter] |
10709 | Priority is a modality, arising from collections and members [Potter] |
7301 | The phenomenalist says that to be is to be perceivable [Cardinal/Hayward/Jones] |
7302 | Linguistic phenomenalism says we can eliminate talk of physical objects [Cardinal/Hayward/Jones] |
7303 | If we lack enough sense-data, are we to say that parts of reality are 'indeterminate'? [Cardinal/Hayward/Jones] |
20802 | Snow is not white, and doesn't even appear white, because it is made of black water [Anaxagoras, by Cicero] |
7299 | Primary qualities can be described mathematically, unlike secondary qualities [Cardinal/Hayward/Jones] |
7300 | An object cannot remain an object without its primary qualities [Cardinal/Hayward/Jones] |
13257 | The senses are too feeble to determine the truth [Anaxagoras] |
7297 | My justifications might be very coherent, but totally unconnected to the world [Cardinal/Hayward/Jones] |
22761 | We reveal unreliability in the senses when we cannot discriminate a slow change of colour [Anaxagoras, by Sext.Empiricus] |
13256 | Nous is unlimited, self-ruling and pure; it is the finest thing, with great discernment and strength [Anaxagoras] |
13784 | Mind is self-ruling, pure, ordering and ubiquitous [Anaxagoras, by Plato] |
5118 | Anaxagoras says mind remains pure, and so is not affected by what it changes [Anaxagoras, by Aristotle] |
18231 | Anaxagoras said a person would choose to be born to contemplate the ordered heavens [Anaxagoras] |
631 | For Anaxagoras the Good Mind has no opposite, and causes all movement, for a higher reason [Anaxagoras, by Aristotle] |
22727 | Mind creates the world from a mixture of pure substances [Anaxagoras, by ] |
550 | Anaxagoras said that the number of principles was infinite [Anaxagoras, by Aristotle] |
21383 | The ultimate constituents of reality are the homoeomeries [Anaxagoras, by Vlastos] |
13208 | Anaxagoreans regard the homoeomeries as elements, which compose earth, air, fire and water [Anaxagoras, by Aristotle] |
367 | Anaxagoras says mind produces order and causes everything [Anaxagoras, by Plato] |
21381 | Germs contain microscopic organs, which become visible as they grow [Anaxagoras] |
22726 | When things were unified, Mind set them in order [Anaxagoras] |
2629 | Anaxagoras was the first to say that the universe is directed by an intelligence [Anaxagoras, by Cicero] |
480 | Past, present and future, and the movements of the heavens, were arranged by Mind [Anaxagoras] |
7488 | Anaxagoras was the first recorded atheist [Anaxagoras, by Watson] |
5956 | Anaxagoras was charged with impiety for calling the sun a lump of stone [Anaxagoras, by Plutarch] |