71 ideas
| 7623 | For ancient Greeks being wise was an ethical value [Putnam] |
| 4714 | Putnam's epistemic notion of truth replaces the realism of correspondence with ontological relativism [Putnam, by O'Grady] |
| 7617 | Before Kant, all philosophers had a correspondence theory of truth [Putnam] |
| 4716 | The correspondence theory is wrong, because there is no one correspondence between reality and fact [Putnam, by O'Grady] |
| 7616 | Truth is an idealisation of rational acceptability [Putnam] |
| 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] |
| 10701 | Cantor showed that supposed contradictions in infinity were just a lack of clarity [Cantor, by Potter] |
| 10865 | The continuum is the powerset of the integers, which moves up a level [Cantor, by Clegg] |
| 13016 | The Axiom of Union dates from 1899, and seems fairly obvious [Cantor, by Maddy] |
| 17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
| 14199 | Cantor's sets were just collections, but Dedekind's were containers [Cantor, by Oliver/Smiley] |
| 17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
| 14203 | Intension is not meaning, as 'cube' and 'square-faced polyhedron' are intensionally the same [Putnam] |
| 14207 | If cats equal cherries, model theory allows reinterpretation of the whole language preserving truth [Putnam] |
| 17605 | Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy] |
| 17625 | If two mathematical themes coincide, that suggest a single deep truth [Maddy] |
| 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] |
| 8733 | The Continuum Hypothesis says there are no sets between the natural numbers and reals [Cantor, by Shapiro] |
| 17889 | CH: An infinite set of reals corresponds 1-1 either to the naturals or to the reals [Cantor, by Koellner] |
| 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] |
| 17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
| 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] |
| 17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
| 8631 | Cantor says that maths originates only by abstraction from objects [Cantor, by Frege] |
| 17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
| 14214 | If we try to cure the abundance of theories with causal links, this is 'just more theory' [Putnam, by Lewis] |
| 14205 | The sentence 'A cat is on a mat' remains always true when 'cat' means cherry and 'mat' means tree [Putnam] |
| 7610 | A fact is simply what it is rational to accept [Putnam] |
| 7618 | Very nominalistic philosophers deny properties, though scientists accept them [Putnam] |
| 4718 | If necessity is always relative to a description in a language, then there is only 'de dicto' necessity [Putnam, by O'Grady] |
| 7620 | Some kind of objective 'rightness' is a presupposition of thought itself [Putnam] |
| 14204 | Naïve operationalism would have meanings change every time the tests change [Putnam] |
| 7611 | Rationality is one part of our conception of human flourishing [Putnam] |
| 14200 | 'Water' on Twin Earth doesn't refer to water, but no mental difference can account for this [Putnam] |
| 7612 | Reference is social not individual, because we defer to experts when referring to elm trees [Putnam] |
| 8715 | Infinities expand the bounds of the conceivable; we explore concepts to explore conceivability [Cantor, by Friend] |
| 7613 | Concepts are (at least in part) abilities and not occurrences [Putnam] |
| 13454 | Cantor says (vaguely) that we abstract numbers from equal sized sets [Hart,WD on Cantor] |
| 14202 | Neither individual nor community mental states fix reference [Putnam] |
| 14201 | Maybe the total mental state of a language community fixes the reference of a term [Putnam] |
| 14206 | There are infinitely many interpretations of a sentence which can all seem to be 'correct' [Putnam] |
| 7624 | The word 'inconsiderate' nicely shows the blurring of facts and values [Putnam] |
| 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] |