73 ideas
| 13466 | We are all post-Kantians, because he set the current agenda for philosophy [Hart,WD] |
| 13477 | The problems are the monuments of philosophy [Hart,WD] |
| 13515 | To study abstract problems, some knowledge of set theory is essential [Hart,WD] |
| 13469 | Tarski showed how we could have a correspondence theory of truth, without using 'facts' [Hart,WD] |
| 13504 | Truth for sentences is satisfaction of formulae; for sentences, either all sequences satisfy it (true) or none do [Hart,WD] |
| 13503 | A first-order language has an infinity of T-sentences, which cannot add up to a definition of truth [Hart,WD] |
| 13500 | Conditional Proof: infer a conditional, if the consequent can be deduced from the antecedent [Hart,WD] |
| 13502 | ∃y... is read as 'There exists an individual, call it y, such that...', and not 'There exists a y such that...' [Hart,WD] |
| 13456 | Set theory articulates the concept of order (through relations) [Hart,WD] |
| 13497 | Nowadays ZFC and NBG are the set theories; types are dead, and NF is only useful for the whole universe [Hart,WD] |
| 13443 | ∈ relates across layers, while ⊆ relates within layers [Hart,WD] |
| 13442 | Without the empty set we could not form a∩b without checking that a and b meet [Hart,WD] |
| 13493 | In the modern view, foundation is the heart of the way to do set theory [Hart,WD] |
| 13495 | Foundation Axiom: an nonempty set has a member disjoint from it [Hart,WD] |
| 13461 | We can choose from finite and evident sets, but not from infinite opaque ones [Hart,WD] |
| 13462 | With the Axiom of Choice every set can be well-ordered [Hart,WD] |
| 13516 | If we accept that V=L, it seems to settle all the open questions of set theory [Hart,WD] |
| 13441 | Naïve set theory has trouble with comprehension, the claim that every predicate has an extension [Hart,WD] |
| 13494 | The iterative conception may not be necessary, and may have fixed points or infinitely descending chains [Hart,WD] |
| 13457 | A 'partial ordering' is irreflexive and transitive; the sets are ordered, but not the subsets [Hart,WD] |
| 13458 | A partial ordering becomes 'total' if any two members of its field are comparable [Hart,WD] |
| 13460 | 'Well-ordering' must have a least member, so it does the natural numbers but not the integers [Hart,WD] |
| 13490 | Von Neumann defines α<β as α∈β [Hart,WD] |
| 13481 | Maybe sets should be rethought in terms of the even more basic categories [Hart,WD] |
| 3005 | 'Jocasta' needs to be distinguished from 'Oedipus's mother' because they are connected by different properties [Fodor] |
| 13506 | The universal quantifier can't really mean 'all', because there is no universal set [Hart,WD] |
| 13512 | Modern model theory begins with the proof of Los's Conjecture in 1962 [Hart,WD] |
| 13505 | Model theory studies how set theory can model sets of sentences [Hart,WD] |
| 13511 | Model theory is mostly confined to first-order theories [Hart,WD] |
| 13513 | Models are ways the world might be from a first-order point of view [Hart,WD] |
| 13496 | First-order logic is 'compact': consequences of a set are consequences of a finite subset [Hart,WD] |
| 13484 | Berry's Paradox: we succeed in referring to a number, with a term which says we can't do that [Hart,WD] |
| 13482 | The Burali-Forti paradox is a crisis for Cantor's ordinals [Hart,WD] |
| 13507 | The machinery used to solve the Liar can be rejigged to produce a new Liar [Hart,WD] |
| 13459 | The less-than relation < well-orders, and partially orders, and totally orders the ordinal numbers [Hart,WD] |
| 13491 | The axiom of infinity with separation gives a least limit ordinal ω [Hart,WD] |
| 13463 | There are at least as many infinite cardinals as transfinite ordinals (because they will map) [Hart,WD] |
| 13492 | Von Neumann's ordinals generalise into the transfinite better, because Zermelo's ω is a singleton [Hart,WD] |
| 13446 | 19th century arithmetization of analysis isolated the real numbers from geometry [Hart,WD] |
| 13509 | We can establish truths about infinite numbers by means of induction [Hart,WD] |
| 13474 | Euclid has a unique parallel, spherical geometry has none, and saddle geometry has several [Hart,WD] |
| 13471 | Mathematics makes existence claims, but philosophers usually say those are never analytic [Hart,WD] |
| 13488 | Mass words do not have plurals, or numerical adjectives, or use 'fewer' [Hart,WD] |
| 7014 | A particle and a coin heads-or-tails pick out to perfectly well-defined predicates and properties [Fodor] |
| 13480 | Fregean self-evidence is an intrinsic property of basic truths, rules and definitions [Hart,WD] |
| 3008 | Evolution suggests that innate knowledge of human psychology would be beneficial [Fodor] |
| 2990 | Contrary to commonsense, most of what is in the mind seems to be unlearned [Fodor] |
| 3009 | Sticklebacks have an innate idea that red things are rivals [Fodor] |
| 13476 | The failure of key assumptions in geometry, mereology and set theory throw doubt on the a priori [Hart,WD] |
| 2994 | In CRTT thought may be represented, content must be [Fodor] |
| 15494 | We can't use propositions to explain intentional attitudes, because they would need explaining [Fodor] |
| 7326 | Intentionality doesn't go deep enough to appear on the physicists' ultimate list of things [Fodor] |
| 3001 | Behaviourism has no theory of mental causation [Fodor] |
| 2993 | Any piece of software can always be hard-wired [Fodor] |
| 3011 | Causal powers must be a crucial feature of mental states [Fodor] |
| 5498 | Mind is a set of hierarchical 'homunculi', which are made up in turn from subcomponents [Fodor, by Lycan] |
| 2995 | Supervenience gives good support for mental causation [Fodor] |
| 2991 | Hume's associationism offers no explanation at all of rational thought [Fodor] |
| 3002 | If mind is just physical, how can it follow the rules required for intelligent thought? [Fodor] |
| 2992 | We may be able to explain rationality mechanically [Fodor] |
| 2988 | Folk psychology is the only explanation of behaviour we have [Fodor] |
| 3010 | Belief and desire are structured states, which need mentalese [Fodor] |
| 2999 | Obsession with narrow content leads to various sorts of hopeless anti-realism [Fodor] |
| 3012 | Do identical thoughts have identical causal roles? [Fodor] |
| 13475 | The Fregean concept of GREEN is a function assigning true to green things, and false to the rest [Hart,WD] |
| 2998 | Grice thinks meaning is inherited from the propositional attitudes which sentences express [Fodor] |
| 3006 | Whatever in the mind delivers falsehood is parasitic on what delivers truth [Fodor] |
| 3007 | Many different verification procedures can reach 'star', but it only has one semantic value [Fodor] |
| 3004 | The meaning of a sentence derives from its use in expressing an attitude [Fodor] |
| 3000 | Meaning holism is a crazy doctrine [Fodor] |
| 3003 | Very different mental states can share their contents, so content doesn't seem to be constructed from functional role [Fodor] |
| 2996 | Mental states may have the same content but different extensions [Fodor] |
| 16591 | Prime matter is nothing but its parts [Vanini] |