71 ideas
| 22216 | Phenomenology studies different types of correlation between consciousness and its objects [Husserl, by Bernet] |
| 22217 | Phenomenology aims to validate objects, on the basis of intentional intuitive experience [Husserl, by Bernet] |
| 21217 | Phenomenology needs absolute reflection, without presuppositions [Husserl] |
| 22218 | There can only be a science of fluctuating consciousness if it focuses on stable essences [Husserl, by Bernet] |
| 22219 | Husserl saw transcendental phenomenology as idealist, in its construction of objects [Husserl, by Bernet] |
| 22204 | Start philosophising with no preconceptions, from the intuitively non-theoretical self-given [Husserl] |
| 22207 | Epoché or 'bracketing' is refraining from judgement, even when some truths are certain [Husserl] |
| 22208 | 'Bracketing' means no judgements at all about spatio-temporal existence [Husserl] |
| 22210 | After everything is bracketed, consciousness still has a unique being of its own [Husserl] |
| 22215 | Phenomenology describes consciousness, in the light of pure experiences [Husserl] |
| 22201 | The use of mathematical-style definitions in philosophy is fruitless and harmful [Husserl] |
| 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] |
| 10865 | The continuum is the powerset of the integers, which moves up a level [Cantor, by Clegg] |
| 10701 | Cantor showed that supposed contradictions in infinity were just a lack of clarity [Cantor, by Potter] |
| 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] |
| 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] |
| 17889 | CH: An infinite set of reals corresponds 1-1 either to the naturals or to the reals [Cantor, by Koellner] |
| 8733 | The Continuum Hypothesis says there are no sets between the natural numbers and reals [Cantor, by Shapiro] |
| 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] |
| 15893 | Cantor's theory concerns collections which can be counted, using the ordinals [Cantor, by Lavine] |
| 18174 | Cantor extended ordinals into the transfinite, and they can thus measure infinite cardinalities [Cantor, by Maddy] |
| 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] |
| 22209 | Our goal is to reveal a new hidden region of Being [Husserl] |
| 22211 | As a thing and its perception are separated, two modes of Being emerge [Husserl] |
| 22202 | The World is all experiencable objects [Husserl] |
| 22213 | Absolute reality is an absurdity [Husserl] |
| 21218 | The sense of anything contingent has a purely apprehensible essence or Eidos [Husserl] |
| 19263 | Imagine an object's properties varying; the ones that won't vary are the essential ones [Husserl, by Vaidya] |
| 21220 | The physical given, unlike the mental given, could be non-existing [Husserl] |
| 22205 | Feelings of self-evidence (and necessity) are just the inventions of theory [Husserl] |
| 21221 | Direct 'seeing' by consciousness is the ultimate rational legitimation [Husserl] |
| 22220 | The phenomena of memory are given in the present, but as being past [Husserl, by Bernet] |
| 22206 | Natural science has become great by just ignoring ancient scepticism [Husserl] |
| 22221 | We know another's mind via bodily expression, while also knowing it is inaccessible [Husserl, by Bernet] |
| 22212 | Pure consciousness is a sealed off system of actual Being [Husserl] |
| 22214 | We never meet the Ego, as part of experience, or as left over from experience [Husserl] |
| 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] |
| 8063 | Baumgarten founded aesthetics in 1750 [Baumgarten, by Tolstoy] |
| 8118 | Beauty is an order between parts, and in relation to the whole [Baumgarten, by Tolstoy] |
| 22203 | Only facts follow from facts [Husserl] |
| 8117 | Perfection comes through the senses (Beauty), through reason (Truth), and through moral will (Good) [Baumgarten, by Tolstoy] |
| 10863 | Cantor proved that three dimensions have the same number of points as one dimension [Cantor, by Clegg] |
| 13465 | Only God is absolutely infinite [Cantor, by Hart,WD] |