95 ideas
| 3508 | Correspondence to the facts HAS to be the aim of enquiry [Searle] |
| 15945 | Second-order set theory just adds a version of Replacement that quantifies over functions [Lavine] |
| 15914 | An 'upper bound' is the greatest member of a subset; there may be several of these, so there is a 'least' one [Lavine] |
| 15921 | Collections of things can't be too big, but collections by a rule seem unlimited in size [Lavine] |
| 15937 | Those who reject infinite collections also want to reject the Axiom of Choice [Lavine] |
| 15936 | The Power Set is just the collection of functions from one collection to another [Lavine] |
| 15899 | Replacement was immediately accepted, despite having very few implications [Lavine] |
| 15930 | Foundation says descending chains are of finite length, blocking circularity, or ungrounded sets [Lavine] |
| 15920 | Pure collections of things obey Choice, but collections defined by a rule may not [Lavine] |
| 15898 | The controversy was not about the Axiom of Choice, but about functions as arbitrary, or given by rules [Lavine] |
| 15919 | The 'logical' notion of class has some kind of definition or rule to characterise the class [Lavine] |
| 15900 | The iterative conception of set wasn't suggested until 1947 [Lavine] |
| 15931 | The iterative conception needs the Axiom of Infinity, to show how far we can iterate [Lavine] |
| 15932 | The iterative conception doesn't unify the axioms, and has had little impact on mathematical proofs [Lavine] |
| 15933 | Limitation of Size: if it's the same size as a set, it's a set; it uses Replacement [Lavine] |
| 15913 | A collection is 'well-ordered' if there is a least element, and all of its successors can be identified [Lavine] |
| 15926 | Second-order logic presupposes a set of relations already fixed by the first-order domain [Lavine] |
| 15934 | Mathematical proof by contradiction needs the law of excluded middle [Lavine] |
| 15907 | Mathematics is nowadays (thanks to set theory) regarded as the study of structure, not of quantity [Lavine] |
| 15942 | Every rational number, unlike every natural number, is divisible by some other number [Lavine] |
| 15922 | For the real numbers to form a set, we need the Continuum Hypothesis to be true [Lavine] |
| 18250 | Cauchy gave a necessary condition for the convergence of a sequence [Lavine] |
| 15904 | The two sides of the Cut are, roughly, the bounding commensurable ratios [Lavine] |
| 15912 | Counting results in well-ordering, and well-ordering makes counting possible [Lavine] |
| 15947 | The infinite is extrapolation from the experience of indefinitely large size [Lavine] |
| 15949 | The theory of infinity must rest on our inability to distinguish between very large sizes [Lavine] |
| 15940 | The intuitionist endorses only the potential infinite [Lavine] |
| 15909 | 'Aleph-0' is cardinality of the naturals, 'aleph-1' the next cardinal, 'aleph-ω' the ω-th cardinal [Lavine] |
| 15915 | Ordinals are basic to Cantor's transfinite, to count the sets [Lavine] |
| 15917 | Paradox: the class of all ordinals is well-ordered, so must have an ordinal as type - giving a bigger ordinal [Lavine] |
| 15918 | Paradox: there is no largest cardinal, but the class of everything seems to be the largest [Lavine] |
| 15929 | Set theory will found all of mathematics - except for the notion of proof [Lavine] |
| 15935 | Modern mathematics works up to isomorphism, and doesn't care what things 'really are' [Lavine] |
| 15928 | Intuitionism rejects set-theory to found mathematics [Lavine] |
| 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] |
| 6019 | If someone squashed a horse to make a dog, something new would now exist [Mnesarchus] |
| 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] |
| 3485 | Wanting H2O only differs from wanting water in its mental component [Searle] |
| 3458 | Mental states only relate to behaviour contingently, not necessarily [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] |
| 3453 | Property dualism is the reappearance of Cartesianism [Searle] |
| 3455 | Property dualists tend to find the mind-body problem baffling [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] |
| 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] |
| 3502 | Mind involves fighting, fleeing, feeding and fornicating [Searle] |
| 3459 | You can only know the limits of knowledge if you know the other side of the limit [Searle] |