109 ideas
8797 | The negation of all my beliefs about my current headache would be fully coherent [Sosa] |
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] |
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] |
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] |
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] |
3491 | Beliefs are part of a network, and also exist against a background [Searle] |
3490 | Beliefs only make sense as part of a network of other beliefs [Searle] |
3482 | Perception is a function of expectation [Searle] |
8794 | There are very few really obvious truths, and not much can be proved from them [Sosa] |
3493 | Memory is mainly a guide for current performance [Searle] |
8796 | A single belief can trail two regresses, one terminating and one not [Sosa] |
8799 | If mental states are not propositional, they are logically dumb, and cannot be foundations [Sosa] |
8795 | Mental states cannot be foundational if they are not immune to error [Sosa] |
8798 | Vision causes and justifies beliefs; but to some extent the cause is the justification [Sosa] |
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] |
3455 | Property dualists tend to find the mind-body problem baffling [Searle] |
3475 | Property dualism denies reductionism [Searle] |
3453 | Property dualism is the reappearance of Cartesianism [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] |
3476 | Mind and brain are supervenient in respect of cause and effect [Searle] |
3478 | Upwards mental causation makes 'supervenience' irrelevant [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] |
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] |
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] |