70 ideas
| 6979 | Serious metaphysics cares about entailment between sentences [Jackson] |
| 6983 | Intuitions about possibilities are basic to conceptual analysis [Jackson] |
| 6980 | Conceptual analysis studies whether one story is made true by another story [Jackson] |
| 14707 | Conceptual analysis is needed to establish that metaphysical reductions respect original meanings [Jackson, by Schroeter] |
| 7005 | Something can only have a place in a preferred account of things if it is entailed by the account [Jackson] |
| 6994 | Truth supervenes on being [Jackson] |
| 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] |
| 6984 | Smooth reductions preserve high-level laws in the lower level [Jackson] |
| 6978 | Baldness is just hair distribution, but the former is indeterminate, unlike the latter [Jackson] |
| 6993 | Redness is a property, but only as a presentation to normal humans [Jackson] |
| 6987 | We should not multiply senses of necessity beyond necessity [Jackson] |
| 6988 | Mathematical sentences are a problem in a possible-worlds framework [Jackson] |
| 6975 | Possible worlds could be concrete, abstract, universals, sentences, or properties [Jackson] |
| 6982 | Long arithmetic calculations show the a priori can be fallible [Jackson] |
| 6991 | We examine objects to determine colour; we do not introspect [Jackson] |
| 16726 | Why can't we deduce secondary qualities from primary ones, if they cause them? [Buridan] |
| 6976 | In physicalism, the psychological depends on the physical, not the other way around [Jackson] |
| 6986 | Is the dependence of the psychological on the physical a priori or a posteriori? [Jackson] |
| 6992 | If different states can fulfil the same role, the converse must also be possible [Jackson] |
| 6996 | Folk psychology covers input, internal role, and output [Jackson] |
| 6977 | Egocentric or de se content seems to be irreducibly so [Jackson] |
| 6990 | Keep distinct the essential properties of water, and application conditions for the word 'water' [Jackson] |
| 8715 | Infinities expand the bounds of the conceivable; we explore concepts to explore conceivability [Cantor, by Friend] |
| 6985 | Analysis is finding necessary and sufficient conditions by studying possible cases [Jackson] |
| 13454 | Cantor says (vaguely) that we abstract numbers from equal sized sets [Hart,WD on Cantor] |
| 6995 | Successful predication supervenes on nature [Jackson] |
| 6989 | I can understand "He has a beard", without identifying 'he', and hence the truth conditions [Jackson] |
| 6998 | Folk morality does not clearly distinguish between doing and allowing [Jackson] |
| 6997 | Moral functionalism says moral terms get their meaning from their role in folk morality [Jackson] |
| 7000 | Which are prior - thin concepts like right, good, ought; or thick concepts like kindness, equity etc.? [Jackson] |
| 6999 | It is hard to justify the huge difference in our judgements of abortion and infanticide [Jackson] |
| 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] |