76 ideas
| 21761 | If we start with indeterminate being, we arrive at being and nothing as a united pair [Hegel, by Houlgate] |
| 21764 | Thought about being leads to a string of other concepts, like becoming, quantity, specificity, causality... [Hegel, by Houlgate] |
| 21769 | We must start with absolute abstraction, with no presuppositions, so we start with pure being [Hegel] |
| 22037 | Objectivity is not by correspondence, but by the historical determined necessity of Geist [Hegel, by Pinkard] |
| 21983 | Being and nothing are the same and not the same, which is the identity of identity and non-identity [Hegel] |
| 21985 | The so-called world is filled with contradiction [Hegel] |
| 21766 | Dialectic is the instability of thoughts generating their opposite, and then new more complex thoughts [Hegel, by Houlgate] |
| 21978 | Hegel's dialectic is not thesis-antithesis-synthesis, but usually negation of negation of the negation [Hegel, by Moore,AW] |
| 15842 | An ad hominem refutation is reasonable, if it uses the opponent's assumptions [Harte,V] |
| 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] |
| 15841 | Mereology began as a nominalist revolt against the commitments of set theory [Harte,V] |
| 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] |
| 21762 | To grasp an existence, we must consider its non-existence [Hegel, by Houlgate] |
| 21977 | Nothing exists, as thinkable and expressible [Hegel] |
| 21760 | Thinking of nothing is not the same as simply not thinking [Hegel, by Houlgate] |
| 15858 | Traditionally, the four elements are just what persists through change [Harte,V] |
| 21765 | The ground of a thing is not another thing, but the first thing's substance or rational concept [Hegel, by Houlgate] |
| 22059 | Kant's thing-in-itself is just an abstraction from our knowledge; things only exist for us [Hegel, by Bowie] |
| 22083 | Hegel believe that the genuine categories reveal things in themselves [Hegel, by Houlgate] |
| 22080 | The nature of each category relates itself to another [Hegel] |
| 15848 | Mereology treats constitution as a criterion of identity, as shown in the axiom of extensionality [Harte,V] |
| 15837 | What exactly is a 'sum', and what exactly is 'composition'? [Harte,V] |
| 15839 | If something is 'more than' the sum of its parts, is the extra thing another part, or not? [Harte,V] |
| 15838 | The problem with the term 'sum' is that it is singular [Harte,V] |
| 21772 | In absolute knowing, the gap between object and oneself closes, producing certainty [Hegel] |
| 20954 | The 'absolute idea' is when all the contradictions are exhausted [Hegel, by Bowie] |
| 21972 | Hegel, unlike Kant, said how things appear is the same as how things are [Hegel, by Moore,AW] |
| 22038 | Hegel's non-subjective idealism is the unity of subjective and objective viewpoints [Hegel, by Pinkard] |
| 22044 | Hegel claimed his system was about the world, but it only mapped conceptual interdependence [Pinkard on Hegel] |
| 22084 | Authentic thinking and reality have the same content [Hegel] |
| 21464 | The Absolute is the primitive system of concepts which are actualised [Hegel, by Gardner] |
| 21975 | The absolute idea is being, imperishable life, self-knowing truth, and all truth [Hegel] |
| 21976 | The absolute idea is the great unity of the infinite system of concepts [Hegel, by Moore,AW] |
| 22058 | Hegel's 'absolute idea' is the interdependence of all truths to justify any of them [Hegel, by Bowie] |
| 20953 | Every concept depends on the counter-concepts of what it is not [Hegel, by Bowie] |
| 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] |
| 21763 | When we explicate the category of being, we watch a new category emerge [Hegel, by Houlgate] |
| 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] |