92 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] |
18137 | Impredicative definitions are wrong, because they change the set that is being defined? [Bostock] |
2470 | Transcendental arguments move from knowing Q to knowing P because it depends on Q [Fodor] |
18122 | Classical interdefinitions of logical constants and quantifiers is impossible in intuitionism [Bostock] |
18114 | There is no single agreed structure for set theory [Bostock] |
18107 | A 'proper class' cannot be a member of anything [Bostock] |
18115 | We could add axioms to make sets either as small or as large as possible [Bostock] |
18139 | The Axiom of Choice relies on reference to sets that we are unable to describe [Bostock] |
18105 | Replacement enforces a 'limitation of size' test for the existence of sets [Bostock] |
18109 | The completeness of first-order logic implies its compactness [Bostock] |
18108 | First-order logic is not decidable: there is no test of whether any formula is valid [Bostock] |
18123 | Substitutional quantification is just standard if all objects in the domain have a name [Bostock] |
18120 | The Deduction Theorem is what licenses a system of natural deduction [Bostock] |
18125 | Berry's Paradox considers the meaning of 'The least number not named by this name' [Bostock] |
18100 | ω + 1 is a new ordinal, but its cardinality is unchanged [Bostock] |
18101 | Each addition changes the ordinality but not the cardinality, prior to aleph-1 [Bostock] |
18102 | A cardinal is the earliest ordinal that has that number of predecessors [Bostock] |
18106 | Aleph-1 is the first ordinal that exceeds aleph-0 [Bostock] |
18095 | Instead of by cuts or series convergence, real numbers could be defined by axioms [Bostock] |
18099 | The number of reals is the number of subsets of the natural numbers [Bostock] |
18093 | For Eudoxus cuts in rationals are unique, but not every cut makes a real number [Bostock] |
18110 | Infinitesimals are not actually contradictory, because they can be non-standard real numbers [Bostock] |
18156 | Modern axioms of geometry do not need the real numbers [Bostock] |
18097 | The Peano Axioms describe a unique structure [Bostock] |
18149 | There are many criteria for the identity of numbers [Bostock] |
18148 | Hume's Principle is a definition with existential claims, and won't explain numbers [Bostock] |
18145 | Many things will satisfy Hume's Principle, so there are many interpretations of it [Bostock] |
18143 | Frege makes numbers sets to solve the Caesar problem, but maybe Caesar is a set! [Bostock] |
18116 | Numbers can't be positions, if nothing decides what position a given number has [Bostock] |
18117 | Structuralism falsely assumes relations to other numbers are numbers' only properties [Bostock] |
18141 | Nominalism about mathematics is either reductionist, or fictionalist [Bostock] |
18157 | Nominalism as based on application of numbers is no good, because there are too many applications [Bostock] |
18150 | Actual measurement could never require the precision of the real numbers [Bostock] |
18158 | Ordinals are mainly used adjectively, as in 'the first', 'the second'... [Bostock] |
18127 | Simple type theory has 'levels', but ramified type theory has 'orders' [Bostock] |
18144 | Neo-logicists agree that HP introduces number, but also claim that it suffices for the job [Bostock] |
18147 | Neo-logicists meet the Caesar problem by saying Hume's Principle is unique to number [Bostock] |
18111 | Treating numbers as objects doesn't seem like logic, since arithmetic fixes their totality [Bostock] |
18129 | Many crucial logicist definitions are in fact impredicative [Bostock] |
18146 | If Hume's Principle is the whole story, that implies structuralism [Bostock] |
18159 | Higher cardinalities in sets are just fairy stories [Bostock] |
18155 | A fairy tale may give predictions, but only a true theory can give explanations [Bostock] |
18140 | The best version of conceptualism is predicativism [Bostock] |
18138 | Conceptualism fails to grasp mathematical properties, infinity, and objective truth values [Bostock] |
18133 | The usual definitions of identity and of natural numbers are impredicative [Bostock] |
18131 | If abstracta only exist if they are expressible, there can only be denumerably many of them [Bostock] |
18134 | Predicativism makes theories of huge cardinals impossible [Bostock] |
18135 | If mathematics rests on science, predicativism may be the best approach [Bostock] |
18136 | If we can only think of what we can describe, predicativism may be implied [Bostock] |
18132 | The predicativity restriction makes a difference with the real numbers [Bostock] |
2469 | The world is full of messy small things producing stable large-scale properties (e.g. mountains) [Fodor] |
16643 | Accidents always remain suited to a subject [Bonaventura] |
2475 | Don't define something by a good instance of it; a good example is a special case of the ordinary example [Fodor] |
16696 | Successive things reduce to permanent things [Bonaventura] |
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] |
2503 | Empirical approaches see mind connections as mirrors/maps of reality [Fodor] |
2508 | The function of a mind is obvious [Fodor] |
2485 | Do intentional states explain our behaviour? [Fodor] |
2506 | If I have a set of mental modules, someone had better be in charge of them! [Fodor] |
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] |
2476 | The goal of thought is to understand the world, not instantly sort it into conceptual categories [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] |
2498 | Modules make the world manageable [Fodor] |
2496 | Blindness doesn't destroy spatial concepts [Fodor] |
2509 | Modules have in-built specialist information [Fodor] |
2483 | Mentalese doesn't require a theory of meaning [Fodor] |
2480 | Language is ambiguous, but thought isn't [Fodor] |
2487 | Mentalese may also incorporate some natural language [Fodor] |
2486 | Content can't be causal role, because causal role is decided by content [Fodor] |
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] |
18121 | In logic a proposition means the same when it is and when it is not asserted [Bostock] |
2484 | The theory of the content of thought as 'Mentalese' explains why the Private Language Argument doesn't work [Fodor] |