71 ideas
| 6123 | Empirical investigation can't discover if holes exist, or if two things share a colour [Merricks] |
| 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] |
| 6143 | Prolonged events don't seem to endure or exist at any particular time [Merricks] |
| 6135 | A crumbling statue can't become vague, because vagueness is incoherent [Merricks] |
| 6145 | Intrinsic properties are those an object still has even if only that object exists [Merricks] |
| 6124 | I say that most of the objects of folk ontology do not exist [Merricks] |
| 6134 | Is swimming pool water an object, composed of its mass or parts? [Merricks] |
| 6125 | We can eliminate objects without a commitment to simples [Merricks] |
| 14229 | Merricks agrees that there are no composite objects, but offers a different semantics [Merricks, by Liggins] |
| 6142 | The 'folk' way of carving up the world is not intrinsically better than quite arbitrary ways [Merricks] |
| 14472 | If atoms 'arranged baseballwise' break a window, that analytically entails that a baseball did it [Merricks, by Thomasson] |
| 14469 | Overdetermination: the atoms do all the causing, so the baseball causes no breakage [Merricks] |
| 6137 | Clay does not 'constitute' a statue, as they have different persistence conditions (flaking, squashing) [Merricks] |
| 6141 | There is no visible difference between statues, and atoms arranged statuewise [Merricks] |
| 6127 | 'Unrestricted composition' says any two things can make up a third thing [Merricks] |
| 6131 | Composition as identity is false, as identity is never between a single thing and many things [Merricks] |
| 6132 | Composition as identity is false, as it implies that things never change their parts [Merricks] |
| 6130 | 'Composition' says things are their parts; 'constitution' says a whole substance is an object [Merricks] |
| 6138 | It seems wrong that constitution entails that two objects are wholly co-located [Merricks] |
| 6128 | Objects decompose (it seems) into non-overlapping parts that fill its whole region [Merricks] |
| 6136 | Eliminativism about objects gives the best understanding of the Sorites paradox [Merricks] |
| 3016 | Even the gods cannot strive against necessity [Pittacus, by Diog. Laertius] |
| 6133 | If my counterpart is happy, that is irrelevant to whether I 'could' have been happy [Merricks] |
| 6150 | The 'warrant' for a belief is what turns a true belief into knowledge [Merricks] |
| 6144 | You hold a child in your arms, so it is not mental substance, or mental state, or software [Merricks] |
| 6140 | Maybe the word 'I' can only refer to persons [Merricks] |
| 6149 | Free will and determinism are incompatible, since determinism destroys human choice [Merricks] |
| 6148 | Human organisms can exercise downward causation [Merricks] |
| 6147 | The hypothesis of solipsism doesn't seem to be made incoherent by the nature of mental properties [Merricks] |
| 6146 | Before Creation it is assumed that God still had many many mental properties [Merricks] |
| 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] |
| 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] |