92 ideas
22733 | Epicurus accepted God in his popular works, but not in his writings on nature [Epicurus, by Sext.Empiricus] |
13291 | Slavery to philosophy brings true freedom [Epicurus] |
22758 | Philosophy aims at a happy life, through argument and discussion [Epicurus] |
14523 | We should come to philosophy free from any taint of culture [Epicurus] |
22240 | The aim of medicine is removal of sickness, and philosophy similarly removes our affections [Epicurus] |
1484 | We should say nothing of the whole if our contact is with the parts [Epicurus, by Plutarch] |
2670 | Epicurus despises and laughs at the whole of dialectic [Epicurus, by Cicero] |
15901 | Trying to represent curves, we study arbitrary functions, leading to the ordinals, which produces set theory [Cantor, by Lavine] |
13444 | Cantor's Theorem: for any set x, its power set P(x) has more members than x [Cantor, by Hart,WD] |
18098 | Cantor proved that all sets have more subsets than they have members [Cantor, by Bostock] |
15505 | If a set is 'a many thought of as one', beginners should protest against singleton sets [Cantor, by Lewis] |
10701 | Cantor showed that supposed contradictions in infinity were just a lack of clarity [Cantor, by Potter] |
10865 | The continuum is the powerset of the integers, which moves up a level [Cantor, by Clegg] |
13016 | The Axiom of Union dates from 1899, and seems fairly obvious [Cantor, by Maddy] |
14199 | Cantor's sets were just collections, but Dedekind's were containers [Cantor, by Oliver/Smiley] |
21668 | Epicurus rejected excluded middle, because accepting it for events is fatalistic [Epicurus, by Cicero] |
21676 | Epicureans say disjunctions can be true whiile the disjuncts are not true [Epicurus, by Cicero] |
10082 | There are infinite sets that are not enumerable [Cantor, by Smith,P] |
13483 | Cantor's Paradox: the power set of the universe must be bigger than the universe, yet a subset of it [Cantor, by Hart,WD] |
8710 | The powerset of all the cardinal numbers is required to be greater than itself [Cantor, by Friend] |
15910 | Cantor named the third realm between the finite and the Absolute the 'transfinite' [Cantor, by Lavine] |
15905 | Cantor proved the points on a plane are in one-to-one correspondence to the points on a line [Cantor, by Lavine] |
9983 | Cantor took the ordinal numbers to be primary [Cantor, by Tait] |
17798 | Cantor presented the totality of natural numbers as finite, not infinite [Cantor, by Mayberry] |
9971 | Cantor introduced the distinction between cardinals and ordinals [Cantor, by Tait] |
9892 | Cantor showed that ordinals are more basic than cardinals [Cantor, by Dummett] |
14136 | A cardinal is an abstraction, from the nature of a set's elements, and from their order [Cantor] |
15906 | Cantor tried to prove points on a line matched naturals or reals - but nothing in between [Cantor, by Lavine] |
11015 | Cantor's diagonal argument proved you can't list all decimal numbers between 0 and 1 [Cantor, by Read] |
15903 | A real is associated with an infinite set of infinite Cauchy sequences of rationals [Cantor, by Lavine] |
18251 | Irrational numbers are the limits of Cauchy sequences of rational numbers [Cantor, by Lavine] |
15902 | Irrationals and the Dedekind Cut implied infinite classes, but they seemed to have logical difficulties [Cantor, by Lavine] |
15908 | It was Cantor's diagonal argument which revealed infinities greater than that of the real numbers [Cantor, by Lavine] |
13464 | Cantor proposes that there won't be a potential infinity if there is no actual infinity [Cantor, by Hart,WD] |
10112 | The naturals won't map onto the reals, so there are different sizes of infinity [Cantor, by George/Velleman] |
8733 | The Continuum Hypothesis says there are no sets between the natural numbers and reals [Cantor, by Shapiro] |
17889 | CH: An infinite set of reals corresponds 1-1 either to the naturals or to the reals [Cantor, by Koellner] |
13447 | Cantor: there is no size between naturals and reals, or between a set and its power set [Cantor, by Hart,WD] |
10883 | Cantor's Continuum Hypothesis says there is a gap between the natural and the real numbers [Cantor, by Horsten] |
13528 | Continuum Hypothesis: there are no sets between N and P(N) [Cantor, by Wolf,RS] |
9555 | Continuum Hypothesis: no cardinal greater than aleph-null but less than cardinality of the continuum [Cantor, by Chihara] |
18174 | Cantor extended ordinals into the transfinite, and they can thus measure infinite cardinalities [Cantor, by Maddy] |
15893 | Cantor's theory concerns collections which can be counted, using the ordinals [Cantor, by Lavine] |
18173 | Cardinality strictly concerns one-one correspondence, to test infinite sameness of size [Cantor, by Maddy] |
10232 | Property extensions outstrip objects, so shortage of objects caused the Caesar problem [Cantor, by Shapiro] |
18176 | Pure mathematics is pure set theory [Cantor] |
8631 | Cantor says that maths originates only by abstraction from objects [Cantor, by Frege] |
10467 | Individuals consist of 'compresent' tropes [Bacon,John] |
10464 | A trope is a bit of a property or relation (not an exemplification or a quality) [Bacon,John] |
10465 | Trope theory is ontologically parsimonious, with possibly only one-category [Bacon,John] |
10466 | Maybe possible worlds are just sets of possible tropes [Bacon,John] |
1823 | We can't seek for things if we have no idea of them [Epicurus, by Diog. Laertius] |
1824 | To name something, you must already have an idea of what it is [Epicurus, by Diog. Laertius] |
5949 | Epicurus says colours are relative to the eye, not intrinsic to bodies [Epicurus, by Plutarch] |
1821 | Sensations cannot be judged, because similar sensations have equal value, and different ones have nothing in common [Epicurus, by Diog. Laertius] |
1820 | The criteria of truth are senses, preconceptions and passions [Epicurus, by Diog. Laertius] |
1822 | Reason can't judge senses, as it is based on them [Epicurus, by Diog. Laertius] |
4549 | Epicurus denied knowledge in order to retain morality or hedonism as the highest values [Nietzsche on Epicurus] |
2668 | Epicurus says if one of a man's senses ever lies, none of his senses should ever be believed [Epicurus, by Cicero] |
1482 | If two people disagree over taste, who is right? [Epicurus, by Plutarch] |
1483 | Bath water is too hot for some, too cold for others [Epicurus, by Plutarch] |
1487 | When entering a dark room it is colourless, but colour gradually appears [Epicurus] |
14526 | The rational soul is in the chest, and the non-rational soul is spread through the body [Epicurus] |
6035 | Soul is made of four stuffs, giving warmth, rest, motion and perception [Epicurus, by Aetius] |
6018 | Epicurus was the first to see the free will problem, and he was a libertarian [Epicurus, by Long/Sedley] |
20922 | Epicurus showed that the swerve can give free motion in the atoms [Epicurus, by Diogenes of Oen.] |
14516 | There is no necessity to live with necessity [Epicurus] |
1909 | How can pleasure or judgement occur in a heap of atoms? [Sext.Empiricus on Epicurus] |
8715 | Infinities expand the bounds of the conceivable; we explore concepts to explore conceivability [Cantor, by Friend] |
13454 | Cantor says (vaguely) that we abstract numbers from equal sized sets [Hart,WD on Cantor] |
7814 | It was Epicurus who made the question of the will's freedom central to ethics [Epicurus, by Grayling] |
3562 | Fine things are worthless if they give no pleasure [Epicurus] |
1840 | Pleasure is the chief good because it is the most natural, especially for animals [Epicurus, by Diog. Laertius] |
1839 | Pains of the soul are worse than pains of the body, because it feels the past and future [Epicurus, by Diog. Laertius] |
1842 | Pleasures only differ in their duration and the part of the body affected [Epicurus] |
3557 | The end for Epicurus is static pleasure [Epicurus, by Annas] |
1845 | Justice has no independent existence, but arises entirely from keeping contracts [Epicurus] |
1841 | We choose virtue because of pleasure, not for its own sake [Epicurus, by Diog. Laertius] |
1829 | A wise man would be happy even under torture [Epicurus, by Diog. Laertius] |
1843 | Friendship is by far the most important ingredient of a complete and happy life [Epicurus] |
1831 | Wise men should partake of life even if they go blind [Epicurus, by Diog. Laertius] |
12044 | Only Epicurus denied purpose in nature, for the whole world, or for its parts [Epicurus, by Annas] |
20907 | Democritus says atoms have size and shape, and Epicurus added weight [Epicurus, by Ps-Plutarch] |
21669 | Atoms don't swerve by being struck, because they move in parallel, so the swerve is uncaused [Cicero on Epicurus] |
21680 | What causes atomic swerves? Do they draw lots? What decides the size or number of swerves? [Cicero on Epicurus] |
10863 | Cantor proved that three dimensions have the same number of points as one dimension [Cantor, by Clegg] |
14525 | Stoics say time is incorporeal and self-sufficient; Epicurus says it is a property of properties of things [Epicurus] |
13465 | Only God is absolutely infinite [Cantor, by Hart,WD] |
2637 | For Epicureans gods are made of atoms, and are not eternal [Epicurus, by Cicero] |
2633 | Epicurus saw that gods must exist, because nature has imprinted them on human minds [Epicurus, by Cicero] |
2639 | Some say Epicurus only pretended to believe in the gods, so as not to offend Athenians [Epicurus, by Cicero] |
14527 | If god answered prayers we would be destroyed, because we pray for others to suffer [Epicurus] |