84 ideas
| 12644 | Who cares what 'philosophy' is? Most pre-1950 thought doesn't now count as philosophy [Fodor] |
| 12633 | Definitions often give necessary but not sufficient conditions for an extension [Fodor] |
| 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] |
| 14199 | Cantor's sets were just collections, but Dedekind's were containers [Cantor, by Oliver/Smiley] |
| 12664 | A truth-table, not inferential role, defines 'and' [Fodor] |
| 12648 | Names in thought afford a primitive way to bring John before the mind [Fodor] |
| 12650 | 'Paderewski' has two names in mentalese, for his pianist file and his politician file [Fodor] |
| 12656 | P-and-Q gets its truth from the truth of P and truth of Q, but consistency isn't like that [Fodor] |
| 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] |
| 18174 | Cantor extended ordinals into the transfinite, and they can thus measure infinite cardinalities [Cantor, by Maddy] |
| 15893 | Cantor's theory concerns collections which can be counted, using the ordinals [Cantor, by Lavine] |
| 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] |
| 12653 | There's statistical, logical, nomological, conceptual and metaphysical possibility [Fodor] |
| 12651 | Some beliefs are only inferred when needed, like 'Shakespeare had not telephone' [Fodor] |
| 12628 | Knowing that must come before knowing how [Fodor] |
| 12625 | Pragmatism is the worst idea ever [Fodor] |
| 22668 | Apprehension is a complex intellect grasping the essence of a complex object [Holt,L] |
| 12636 | Mental states have causal powers [Fodor] |
| 12661 | The different types of resemblance don't resemble one another [Fodor] |
| 12632 | In the Representational view, concepts play the key linking role [Fodor] |
| 12624 | Only the labels of nodes have semantic content in connectionism, and they play no role [Fodor] |
| 12640 | Associative thinking avoids syntax, but can't preserve sense, reference or truth [Fodor] |
| 12641 | Connectionism gives no account of how constituents make complex concepts [Fodor] |
| 12643 | Ambiguities in English are the classic reason for claiming that we don't think in English [Fodor] |
| 12647 | Mental representations name things in the world, but also files in our memory [Fodor] |
| 12649 | We think in file names [Fodor] |
| 12655 | Frame Problem: how to eliminate most beliefs as irrelevant, without searching them? [Fodor] |
| 12630 | If concept content is reference, then my Twin and I are referring to the same stuff [Fodor] |
| 8715 | Infinities expand the bounds of the conceivable; we explore concepts to explore conceivability [Cantor, by Friend] |
| 12658 | Nobody knows how concepts are acquired [Fodor] |
| 12662 | We have an innate capacity to form a concept, once we have grasped the stereotype [Fodor] |
| 12635 | Having a concept isn't a pragmatic matter, but being able to think about the concept [Fodor] |
| 12652 | Concepts have two sides; they are files that face thought, and also face subject-matter [Fodor] |
| 12626 | Cartesians put concept individuation before concept possession [Fodor] |
| 12637 | Frege's puzzles suggest to many that concepts have sense as well as reference [Fodor] |
| 12638 | If concepts have sense, we can't see the connection to their causal powers [Fodor] |
| 12639 | Belief in 'senses' may explain intentionality, but not mental processes [Fodor] |
| 12654 | You can't think 'brown dog' without thinking 'brown' and 'dog' [Fodor] |
| 12659 | Maybe stereotypes are a stage in concept acquisition (rather than a by-product) [Fodor] |
| 12660 | One stereotype might be a paradigm for two difference concepts [Fodor] |
| 12629 | For the referential view of thought, the content of a concept is just its reference [Fodor] |
| 12631 | Compositionality requires that concepts be atomic [Fodor] |
| 12657 | Abstractionism claims that instances provide criteria for what is shared [Fodor] |
| 13454 | Cantor says (vaguely) that we abstract numbers from equal sized sets [Hart,WD on Cantor] |
| 12634 | 'Inferential-role semantics' says meaning is determined by role in inference [Fodor] |
| 12642 | Co-referring terms differ if they have different causal powers [Fodor] |
| 12663 | We refer to individuals and to properties, and we use singular terms and predicates [Fodor] |
| 12645 | Semantics (esp. referential semantics) allows inferences from utterances to the world [Fodor] |
| 12646 | Semantics relates to the world, so it is never just psychological [Fodor] |
| 12627 | Before you can plan action, you must decide on the truth of your estimate of success [Fodor] |
| 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] |