82 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] |
| 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] |
| 15949 | The theory of infinity must rest on our inability to distinguish between very large sizes [Lavine] |
| 15947 | The infinite is extrapolation from the experience of indefinitely large size [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] |
| 2469 | The world is full of messy small things producing stable large-scale properties (e.g. mountains) [Fodor] |
| 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] |
| 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] |
| 2496 | Blindness doesn't destroy spatial concepts [Fodor] |
| 2497 | Something must take an overview of the modules [Fodor] |
| 2509 | Modules have in-built specialist information [Fodor] |
| 2491 | Modules have encapsulation, inaccessibility, private concepts, innateness [Fodor] |
| 2495 | Obvious modules are language and commonsense explanation [Fodor] |
| 2498 | Modules make the world manageable [Fodor] |
| 2500 | Babies talk in consistent patterns [Fodor] |
| 2507 | Rationality rises above modules [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] |
| 7357 | People who control others with fluent language often end up being hated [Kongzi (Confucius)] |
| 2484 | The theory of the content of thought as 'Mentalese' explains why the Private Language Argument doesn't work [Fodor] |
| 7358 | All men prefer outward appearance to true excellence [Kongzi (Confucius)] |
| 7362 | Humans are similar, but social conventions drive us apart (sages and idiots being the exceptions) [Kongzi (Confucius)] |
| 7360 | Do not do to others what you would not desire yourself [Kongzi (Confucius)] |
| 7359 | Excess and deficiency are equally at fault [Kongzi (Confucius)] |
| 7363 | The virtues of the best people are humility, maganimity, sincerity, diligence, and graciousness [Kongzi (Confucius)] |
| 7361 | Men of the highest calibre avoid political life completely [Kongzi (Confucius)] |
| 23393 | Confucianism assumes that all good developments have happened, and there is only one Way [Norden on Kongzi (Confucius)] |