108 ideas
| 19693 | There is practical wisdom (for action), and theoretical wisdom (for deep understanding) [Aristotle, by Whitcomb] |
| 2474 | It seems likely that analysis of concepts is impossible, but justification can survive without it [Fodor] |
| 2481 | Despite all the efforts of philosophers, nothing can ever be reduced to anything [Fodor] |
| 1575 | For Aristotle logos is essentially the ability to talk rationally about questions of value [Roochnik on Aristotle] |
| 1589 | Aristotle is the supreme optimist about the ability of logos to explain nature [Roochnik on Aristotle] |
| 2505 | Turing invented the idea of mechanical rationality (just based on syntax) [Fodor] |
| 8200 | Aristotelian definitions aim to give the essential properties of the thing defined [Aristotle, by Quine] |
| 4385 | Aristotelian definition involves first stating the genus, then the differentia of the thing [Aristotle, by Urmson] |
| 2470 | Transcendental arguments move from knowing Q to knowing P because it depends on Q [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] |
| 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] |
| 13282 | Aristotle relativises the notion of wholeness to different measures [Aristotle, by Koslicki] |
| 4730 | For Aristotle, the subject-predicate structure of Greek reflected a substance-accident structure of reality [Aristotle, by O'Grady] |
| 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] |
| 2469 | The world is full of messy small things producing stable large-scale properties (e.g. mountains) [Fodor] |
| 2475 | Don't define something by a good instance of it; a good example is a special case of the ordinary example [Fodor] |
| 13276 | The unmoved mover and the soul show Aristotelian form as the ultimate mereological atom [Aristotle, by Koslicki] |
| 13277 | The 'form' is the recipe for building wholes of a particular kind [Aristotle, by Koslicki] |
| 5991 | For Aristotle, knowledge is of causes, and is theoretical, practical or productive [Aristotle, by Code] |
| 2502 | How do you count beliefs? [Fodor] |
| 2501 | Berkeley seems to have mistakenly thought that chairs are the same as after-images [Fodor] |
| 11239 | The notion of a priori truth is absent in Aristotle [Aristotle, by Politis] |
| 2465 | Maybe explaining the mechanics of perception will explain the concepts involved [Fodor] |
| 23312 | Aristotle is a rationalist, but reason is slowly acquired through perception and experience [Aristotle, by Frede,M] |
| 2504 | Rationalism can be based on an evolved computational brain with innate structure [Fodor] |
| 2493 | According to empiricists abstraction is the fundamental mental process [Fodor] |
| 2494 | Rationalists say there is more to a concept than the experience that prompts it [Fodor] |
| 16111 | Aristotle wants to fit common intuitions, and therefore uses language as a guide [Aristotle, by Gill,ML] |
| 16971 | Plato says sciences are unified around Forms; Aristotle says they're unified around substance [Aristotle, by Moravcsik] |
| 11243 | Aristotelian explanations are facts, while modern explanations depend on human conceptions [Aristotle, by Politis] |
| 3320 | Aristotle's standard analysis of species and genus involves specifying things in terms of something more general [Aristotle, by Benardete,JA] |
| 12000 | Aristotle regularly says that essential properties explain other significant properties [Aristotle, by Kung] |
| 2508 | The function of a mind is obvious [Fodor] |
| 2503 | Empirical approaches see mind connections as mirrors/maps of reality [Fodor] |
| 2485 | Do intentional states explain our behaviour? [Fodor] |
| 2506 | If I have a set of mental modules, someone had better be in charge of them! [Fodor] |
| 2467 | Functionalists see pains as properties involving relations and causation [Fodor] |
| 2489 | Why bother with neurons? You don't explain bird flight by examining feathers [Fodor] |
| 2468 | Type physicalism is a stronger claim than token physicalism [Fodor] |
| 2490 | Modern connectionism is just Hume's theory of the 'association' of 'ideas' [Fodor] |
| 2476 | The goal of thought is to understand the world, not instantly sort it into conceptual categories [Fodor] |
| 23300 | Aristotle and the Stoics denied rationality to animals, while Platonists affirmed it [Aristotle, by Sorabji] |
| 2499 | Modules analyse stimuli, they don't tell you what to do [Fodor] |
| 2496 | Blindness doesn't destroy spatial concepts [Fodor] |
| 2509 | Modules have in-built specialist information [Fodor] |
| 2498 | Modules make the world manageable [Fodor] |
| 2500 | Babies talk in consistent patterns [Fodor] |
| 2507 | Rationality rises above modules [Fodor] |
| 2491 | Modules have encapsulation, inaccessibility, private concepts, innateness [Fodor] |
| 2497 | Something must take an overview of the modules [Fodor] |
| 2495 | Obvious modules are language and commonsense explanation [Fodor] |
| 2483 | Mentalese doesn't require a theory of meaning [Fodor] |
| 2480 | Language is ambiguous, but thought isn't [Fodor] |
| 2487 | Mentalese may also incorporate some natural language [Fodor] |
| 2486 | Content can't be causal role, because causal role is decided by content [Fodor] |
| 8715 | Infinities expand the bounds of the conceivable; we explore concepts to explore conceivability [Cantor, by Friend] |
| 2492 | Experience can't explain itself; the concepts needed must originate outside experience [Fodor] |
| 2471 | Are concepts best seen as capacities? [Fodor] |
| 2472 | For Pragmatists having a concept means being able to do something [Fodor] |
| 13454 | Cantor says (vaguely) that we abstract numbers from equal sized sets [Hart,WD on Cantor] |
| 2482 | It seems unlikely that meaning can be reduced to communicative intentions, or any mental states [Fodor] |
| 2477 | If to understand "fish" you must know facts about them, where does that end? [Fodor] |
| 11240 | The notion of analytic truth is absent in Aristotle [Aristotle, by Politis] |
| 2473 | Analysis is impossible without the analytic/synthetic distinction [Fodor] |
| 2484 | The theory of the content of thought as 'Mentalese' explains why the Private Language Argument doesn't work [Fodor] |
| 6559 | Aristotle never actually says that man is a rational animal [Aristotle, by Fogelin] |
| 11150 | It is the mark of an educated mind to be able to entertain an idea without accepting it [Aristotle] |
| 3037 | Aristotle said the educated were superior to the uneducated as the living are to the dead [Aristotle, by Diog. Laertius] |
| 8660 | There are potential infinities (never running out), but actual infinity is incoherent [Aristotle, by Friend] |
| 12058 | Aristotle's matter can become any other kind of matter [Aristotle, by Wiggins] |
| 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] |
| 22729 | The concepts of gods arose from observing the soul, and the cosmos [Aristotle, by Sext.Empiricus] |