109 ideas
| 3508 | Correspondence to the facts HAS to be the aim of enquiry [Searle] |
| 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] |
| 3473 | Reduction can be of things, properties, ideas or causes [Searle] |
| 3532 | Solidity in a piston is integral to its structure, not supervenient [Maslin on Searle] |
| 3533 | Is supervenience just causality? [Searle, by Maslin] |
| 3454 | Reality is entirely particles in force fields [Searle] |
| 3471 | Some properties depend on components, others on their relations [Searle] |
| 3472 | Fully 'emergent' properties contradict our whole theory of causation [Searle] |
| 12149 | Indexicals are a problem for beliefs being just subject-proposition relations [Perry] |
| 3490 | Beliefs only make sense as part of a network of other beliefs [Searle] |
| 3491 | Beliefs are part of a network, and also exist against a background [Searle] |
| 3482 | Perception is a function of expectation [Searle] |
| 3493 | Memory is mainly a guide for current performance [Searle] |
| 3463 | We don't have a "theory" that other people have minds [Searle] |
| 3457 | Other minds are not inferred by analogy, but are our best explanation [Searle] |
| 3480 | We experience unity at an instant and across time [Searle] |
| 3479 | The mind experiences space, but it is not experienced as spatial [Searle] |
| 3470 | Conscious creatures seem able to discriminate better [Searle] |
| 3486 | Unconscious thoughts are those capable of causing conscious ones [Searle] |
| 3503 | Consciousness results directly from brain processes, not from some intermediary like information [Searle] |
| 3465 | Either there is intrinsic intentionality, or everything has it [Searle] |
| 3484 | Water flowing downhill can be described as if it had intentionality [Searle] |
| 3489 | Intentional phenomena only make sense within a background [Searle] |
| 3494 | Intentionality is defined in terms of representation [Searle] |
| 3481 | Consciousness is essential and basic to intentionality [Searle] |
| 4088 | Pain is not intentional, because it does not represent anything beyond itself [Searle] |
| 3467 | Neither introspection nor privileged access makes sense [Searle] |
| 3483 | Introspection is just thinking about mental states, not a special sort of vision [Searle] |
| 3468 | I cannot observe my own subjectivity [Searle] |
| 3469 | Mind and brain don't interact if they are the same [Searle] |
| 3487 | Without internal content, a zombie's full behaviour couldn't be explained [Searle] |
| 3458 | Mental states only relate to behaviour contingently, not necessarily [Searle] |
| 3485 | Wanting H2O only differs from wanting water in its mental component [Searle] |
| 3461 | Functionalists like the externalist causal theory of reference [Searle] |
| 3496 | A program for Chinese translation doesn't need to understand Chinese [Searle] |
| 3499 | Computation presupposes consciousness [Searle] |
| 3501 | If we are computers, who is the user? [Searle] |
| 3456 | Consciousness is a brain property as liquidity is a water property [Searle] |
| 3475 | Property dualism denies reductionism [Searle] |
| 3455 | Property dualists tend to find the mind-body problem baffling [Searle] |
| 3453 | Property dualism is the reappearance of Cartesianism [Searle] |
| 3478 | Upwards mental causation makes 'supervenience' irrelevant [Searle] |
| 3476 | Mind and brain are supervenient in respect of cause and effect [Searle] |
| 3477 | If mind-brain supervenience isn't causal, this implies epiphenomenalism [Searle] |
| 3531 | Mental events can cause even though supervenient, like the solidity of a piston [Searle] |
| 3466 | Consciousness seems indefinable by conditions or categories [Searle] |
| 3500 | Can the homunculus fallacy be beaten by recursive decomposition? [Searle] |
| 9317 | Searle argues that biology explains consciousness, but physics won't explain biology [Searle, by Kriegel/Williford] |
| 3474 | If mind is caused by brain, does this mean mind IS brain? [Searle] |
| 3497 | If mind is multiply realisable, it is possible that anything could realise it [Searle] |
| 3462 | We don't postulate folk psychology, we experience it [Searle] |
| 3498 | Computation isn't a natural phenomenon, it is a way of seeing phenomena [Searle] |
| 3492 | Content is much more than just sentence meaning [Searle] |
| 3464 | There is no such thing as 'wide content' [Searle] |
| 3506 | We explain behaviour in terms of actual internal representations in the agent [Searle] |
| 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] |
| 3451 | Meaning is derived intentionality [Searle] |
| 3450 | Philosophy of language is a branch of philosophy of mind [Searle] |
| 3507 | Universal grammar doesn't help us explain anything [Searle] |
| 12151 | If we replace 'I' in sentences about me, they are different beliefs and explanations of behaviour [Perry] |
| 18412 | Indexicals individuate certain belief states, helping in explanation and prediction [Perry] |
| 12150 | Indexicals reveal big problems with the traditional idea of a proposition [Perry] |
| 3495 | Shared Background makes translation possible, though variation makes it hard [Searle] |
| 3505 | The function of a heart depends on what we want it to do [Searle] |
| 3504 | Chemistry entirely explains plant behaviour [Searle] |
| 10863 | Cantor proved that three dimensions have the same number of points as one dimension [Cantor, by Clegg] |
| 15203 | Tense is essential for thought and action [Perry, by Le Poidevin] |
| 15204 | Actual tensed sentences cannot be tenseless, because they can cite their own context [Perry, by Le Poidevin] |
| 3502 | Mind involves fighting, fleeing, feeding and fornicating [Searle] |
| 13465 | Only God is absolutely infinite [Cantor, by Hart,WD] |
| 3459 | You can only know the limits of knowledge if you know the other side of the limit [Searle] |