106 ideas
| 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] |
| 2505 | Turing invented the idea of mechanical rationality (just based on syntax) [Fodor] |
| 2470 | Transcendental arguments move from knowing Q to knowing P because it depends on Q [Fodor] |
| 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] |
| 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] |
| 10605 | Two functions are the same if they have the same extension [Smith,P] |
| 10075 | A 'partial function' maps only some elements to another set [Smith,P] |
| 10076 | The 'range' of a function is the set of elements in the output set created by the function [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] |
| 10079 | A 'bijective' function has one-to-one correspondence in both directions [Smith,P] |
| 10077 | A 'surjective' ('onto') function creates every element of the output set [Smith,P] |
| 10078 | An 'injective' ('one-to-one') function creates a distinct output element from each original [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] |
| 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] |
| 10080 | 'Effective' means simple, unintuitive, independent, controlled, dumb, and terminating [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] |
| 10851 | Robinson Arithmetic 'Q' has basic axioms, quantifiers and first-order logic [Smith,P] |
| 10852 | Robinson Arithmetic (Q) is not negation complete [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] |
| 10604 | Incompleteness results in arithmetic from combining addition and successor with multiplication [Smith,P] |
| 10848 | Multiplication only generates incompleteness if combined with addition and successor [Smith,P] |
| 10617 | The 'ancestral' of a relation is a new relation which creates a long chain of the original relation [Smith,P] |
| 2469 | The world is full of messy small things producing stable large-scale properties (e.g. mountains) [Fodor] |
| 4938 | Prior to language, concepts are universals created by self-mapping of brain activity [Edelman/Tononi] |
| 2475 | Don't define something by a good instance of it; a good example is a special case of the ordinary example [Fodor] |
| 2502 | How do you count beliefs? [Fodor] |
| 2501 | Berkeley seems to have mistakenly thought that chairs are the same as after-images [Fodor] |
| 2465 | Maybe explaining the mechanics of perception will explain the concepts involved [Fodor] |
| 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] |
| 4934 | Cultures have a common core of colour naming, based on three axes of colour pairs [Edelman/Tononi] |
| 2508 | The function of a mind is obvious [Fodor] |
| 2503 | Empirical approaches see mind connections as mirrors/maps of reality [Fodor] |
| 4924 | A conscious human being rapidly reunifies its mind after any damage to the brain [Edelman/Tononi] |
| 4932 | A conscious state endures for about 100 milliseconds, known as the 'specious present' [Edelman/Tononi] |
| 4931 | Consciousness is a process (of neural interactions), not a location, thing, property, connectivity, or activity [Edelman/Tononi] |
| 4923 | The three essentials of conscious experience are privateness, unity and informativeness [Edelman/Tononi] |
| 4941 | Consciousness can create new axioms, but computers can't do that [Edelman/Tononi] |
| 4930 | Consciousness arises from high speed interactions between clusters of neurons [Edelman/Tononi] |
| 4929 | Dreams and imagery show the brain can generate awareness and meaning without input [Edelman/Tononi] |
| 2485 | Do intentional states explain our behaviour? [Fodor] |
| 4940 | Physicists see information as a measure of order, but for biologists it is symbolic exchange between animals [Edelman/Tononi] |
| 4935 | The sensation of red is a point in neural space created by dimensions of neuronal activity [Edelman/Tononi] |
| 2506 | If I have a set of mental modules, someone had better be in charge of them! [Fodor] |
| 4936 | The self is founded on bodily awareness centred in the brain stem [Edelman/Tononi] |
| 4939 | A sense of self begins either internally, or externally through language and society [Edelman/Tononi] |
| 4925 | Brains can initiate free actions before the person is aware of their own decision [Edelman/Tononi] |
| 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] |
| 4933 | Consciousness is a process, not a thing, as it maintains unity as its composition changes [Edelman/Tononi] |
| 2476 | The goal of thought is to understand the world, not instantly sort it into conceptual categories [Fodor] |
| 2496 | Blindness doesn't destroy spatial concepts [Fodor] |
| 2509 | Modules have in-built specialist information [Fodor] |
| 2498 | Modules make the world manageable [Fodor] |
| 2499 | Modules analyse stimuli, they don't tell you what to do [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] |
| 4928 | Brain complexity balances segregation and integration, like a good team of specialists [Edelman/Tononi] |
| 2483 | Mentalese doesn't require a theory of meaning [Fodor] |
| 4927 | Information-processing views of the brain assume the existence of 'information', and dubious brain codes [Edelman/Tononi] |
| 2480 | Language is ambiguous, but thought isn't [Fodor] |
| 2487 | Mentalese may also incorporate some natural language [Fodor] |
| 4922 | Consciousness involves interaction with persons and the world, as well as brain functions [Edelman/Tononi] |
| 2486 | Content can't be causal role, because causal role is decided by content [Fodor] |
| 5793 | Concepts and generalisations result from brain 'global mapping' by 'reentry' [Edelman/Tononi, by Searle] |
| 4926 | Concepts arise when the brain maps its own activities [Edelman/Tononi] |
| 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] |
| 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] |
| 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] |
| 4937 | Systems that generate a sense of value are basic to the primitive brain [Edelman/Tononi] |