80 ideas
| 16010 | While faith is a passion (as Kierkegaard says), wisdom is passionless [Wittgenstein] |
| 22223 | Being-in-the-world is projection to possibilities, thrownness among them, and fallenness within them [Heidegger, by Caputo] |
| 22158 | Pheomenology seeks things themselves, without empty theories, problems and concepts [Heidegger] |
| 15574 | 'Logos' really means 'making something manifest' [Heidegger, by Polt] |
| 15569 | Heidegger says truth is historical, and never absolute [Heidegger, by Polt] |
| 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] |
| 21897 | Reducing being to the study of beings too readily accepts the modern scientific view [Heidegger, by May] |
| 15573 | For us, Being is constituted by awareness of other sorts of Being [Heidegger] |
| 9273 | Heidegger turns to 'Being' to affirm the uniqueness of humans in the world [Heidegger, by Gray] |
| 22157 | Dasein is a mode of Being distinguished by concern for its own Being [Heidegger] |
| 8137 | Dasein is ahead of itself in the world, and alongside encountered entities [Heidegger] |
| 21951 | In company with others one's Dasein dissolves, and even the others themselves dissolve [Heidegger] |
| 20745 | 'Dasein' expresses not 'what' the entity is, but its being [Heidegger] |
| 8134 | The word 'dasein' is used to mean 'the manner of Being which man possesses', and also the human creature [Heidegger, by Cooper,DE] |
| 8135 | 'Dasein' is Being which is laid claim to, and which matters to its owner [Heidegger, by Cooper,DE] |
| 21948 | Dasein is being which can understand itself, and possess itself in a way allowing authenticity [Heidegger] |
| 7680 | Ontology is possible only as phenomenology [Heidegger] |
| 22161 | Readiness-to-hand defines things in themselves ontologically [Heidegger] |
| 15576 | Heidegger seeks a non-traditional concept of essence as 'essential unfolding' [Heidegger, by Polt] |
| 15578 | Propositions don't provide understanding, because the understanding must come first [Heidegger, by Polt] |
| 22159 | If we posit 'I' as the starting point, we miss the mind's phenomenal content [Heidegger] |
| 22160 | Our relationship to a hammer strengthens when we use [Heidegger] |
| 15580 | There are no raw sense-data - our experiences are of the sound or colour of something [Heidegger] |
| 20749 | Perceived objects always appear in a context [Heidegger] |
| 22163 | The scandal of philosophy is expecting to prove reality when the prover's Being is vague [Heidegger] |
| 21949 | Having thoughts and feelings need engagement in the world [Heidegger, by Wrathall] |
| 22222 | Dasein finds itself already amongst others [Heidegger, by Caputo] |
| 8136 | If we work and play with other people, they are bound to be 'Dasein', intelligent agents [Heidegger, by Cooper,DE] |
| 22164 | When Dasein grasps something it exists externally alongside the thing [Heidegger] |
| 22162 | There is an everyday self, and an authentic self, when it is grasped in its own way [Heidegger] |
| 20114 | Everyone is other, and no one is himself [Heidegger] |
| 15577 | Moods are more fundamentally revealing than theories - as when fear reveals a threat [Heidegger, by Polt] |
| 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] |
| 20748 | We do not add value to naked things; its involvement is disclosed in understanding it [Heidegger] |
| 22166 | Dasein has the potential to be itself, but must be shown this in the midst of ordinariness [Heidegger] |
| 22165 | Anxiety reveals the possibility and individuality of Dasein [Heidegger] |
| 21952 | Anxiety about death frees me to live my own life [Heidegger, by Wrathall] |
| 22224 | Anxiety is the uncanniness felt when constantly fleeing from asserting one's own freedom [Heidegger, by Caputo] |
| 15572 | Being what it is (essentia) must be conceived in terms of Being (existence) [Heidegger] |
| 20453 | Heidegger says we must either choose an inauthentic hero, or choose yourself as hero [Heidegger, by Critchley] |
| 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] |