106 ideas
| 3508 | Correspondence to the facts HAS to be the aim of enquiry [Searle] |
| 10073 | There cannot be a set theory which is complete [Smith,P] |
| 10616 | Second-order arithmetic can prove new sentences of first-order [Smith,P] |
| 10075 | A 'partial function' maps only some elements to another set [Smith,P] |
| 10074 | A 'total function' maps every element to one element in another set [Smith,P] |
| 10612 | An argument is a 'fixed point' for a function if it is mapped back to itself [Smith,P] |
| 10076 | The 'range' of a function is the set of elements in the output set created by the function [Smith,P] |
| 10605 | Two functions are the same if they have the same extension [Smith,P] |
| 10615 | The Comprehension Schema says there is a property only had by things satisfying a condition [Smith,P] |
| 10595 | A 'theorem' of a theory is a sentence derived from the axioms using the proof system [Smith,P] |
| 10602 | A 'natural deduction system' has no axioms but many rules [Smith,P] |
| 10613 | No nice theory can define truth for its own language [Smith,P] |
| 10078 | An 'injective' ('one-to-one') function creates a distinct output element from each original [Smith,P] |
| 10077 | A 'surjective' ('onto') function creates every element of the output set [Smith,P] |
| 10079 | A 'bijective' function has one-to-one correspondence in both directions [Smith,P] |
| 10070 | If everything that a theory proves is true, then it is 'sound' [Smith,P] |
| 10086 | Soundness is true axioms and a truth-preserving proof system [Smith,P] |
| 10596 | A theory is 'sound' iff every theorem is true (usually from true axioms and truth-preservation) [Smith,P] |
| 10598 | A theory is 'negation complete' if it proves all sentences or their negation [Smith,P] |
| 10597 | 'Complete' applies both to whole logics, and to theories within them [Smith,P] |
| 10069 | A theory is 'negation complete' if one of its sentences or its negation can always be proved [Smith,P] |
| 10609 | Two routes to Incompleteness: semantics of sound/expressible, or syntax of consistency/proof [Smith,P] |
| 10080 | 'Effective' means simple, unintuitive, independent, controlled, dumb, and terminating [Smith,P] |
| 10087 | A theory is 'decidable' if all of its sentences could be mechanically proved [Smith,P] |
| 10088 | Any consistent, axiomatized, negation-complete formal theory is decidable [Smith,P] |
| 10081 | A set is 'enumerable' is all of its elements can result from a natural number function [Smith,P] |
| 10083 | A set is 'effectively enumerable' if a computer could eventually list every member [Smith,P] |
| 10084 | A finite set of finitely specifiable objects is always effectively enumerable (e.g. primes) [Smith,P] |
| 10085 | The set of ordered pairs of natural numbers <i,j> is effectively enumerable [Smith,P] |
| 10601 | The thorems of a nice arithmetic can be enumerated, but not the truths (so they're diffferent) [Smith,P] |
| 10600 | Being 'expressible' depends on language; being 'capture/represented' depends on axioms and proof system [Smith,P] |
| 10599 | For primes we write (x not= 1 ∧ ∀u∀v(u x v = x → (u = 1 ∨ v = 1))) [Smith,P] |
| 10610 | The reals contain the naturals, but the theory of reals doesn't contain the theory of naturals [Smith,P] |
| 10619 | The truths of arithmetic are just true equations and their universally quantified versions [Smith,P] |
| 10618 | All numbers are related to zero by the ancestral of the successor relation [Smith,P] |
| 10608 | The number of Fs is the 'successor' of the Gs if there is a single F that isn't G [Smith,P] |
| 10849 | Baby arithmetic covers addition and multiplication, but no general facts about numbers [Smith,P] |
| 10850 | Baby Arithmetic is complete, but not very expressive [Smith,P] |
| 10852 | Robinson Arithmetic (Q) is not negation complete [Smith,P] |
| 10851 | Robinson Arithmetic 'Q' has basic axioms, quantifiers and first-order logic [Smith,P] |
| 10068 | Natural numbers have zero, unique successors, unending, no circling back, and no strays [Smith,P] |
| 10603 | The logic of arithmetic must quantify over properties of numbers to handle induction [Smith,P] |
| 10848 | Multiplication only generates incompleteness if combined with addition and successor [Smith,P] |
| 10604 | Incompleteness results in arithmetic from combining addition and successor with multiplication [Smith,P] |
| 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] |
| 10617 | The 'ancestral' of a relation is a new relation which creates a long chain of the original relation [Smith,P] |
| 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] |
| 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] |
| 3453 | Property dualism is the reappearance of Cartesianism [Searle] |
| 3455 | Property dualists tend to find the mind-body problem baffling [Searle] |
| 3475 | Property dualism denies reductionism [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] |
| 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] |
| 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] |
| 3031 | The greatest good is not the achievement of desire, but to desire what is proper [Menedemus, by Diog. Laertius] |
| 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] |