92 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] |
| 13462 | With the Axiom of Choice every set can be well-ordered [Hart,WD] |
| 13461 | We can choose from finite and evident sets, but not from infinite opaque ones [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] |
| 13460 | 'Well-ordering' must have a least member, so it does the natural numbers but not the integers [Hart,WD] |
| 13458 | A partial ordering becomes 'total' if any two members of its field are comparable [Hart,WD] |
| 13457 | A 'partial ordering' is irreflexive and transitive; the sets are ordered, but not the subsets [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] |
| 17505 | Using proper names properly doesn't involve necessary and sufficient conditions [Putnam] |
| 13506 | The universal quantifier can't really mean 'all', because there is no universal set [Hart,WD] |
| 13513 | Models are ways the world might be from a first-order point of view [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] |
| 13512 | Modern model theory begins with the proof of Los's Conjecture in 1962 [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] |
| 13463 | There are at least as many infinite cardinals as transfinite ordinals (because they will map) [Hart,WD] |
| 13491 | The axiom of infinity with separation gives a least limit ordinal ω [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] |
| 14334 | Modest realism says there is a reality; the presumptuous view says we can accurately describe it [Mumford] |
| 14306 | Anti-realists deny truth-values to all statements, and say evidence and ontology are inseparable [Mumford] |
| 14333 | Dispositions and categorical properties are two modes of presentation of the same thing [Mumford] |
| 14315 | Categorical properties and dispositions appear to explain one another [Mumford] |
| 14332 | There are four reasons for seeing categorical properties as the most fundamental [Mumford] |
| 14336 | Categorical predicates are those unconnected to functions [Mumford] |
| 14302 | A lead molecule is not leaden, and macroscopic properties need not be microscopically present [Mumford] |
| 14294 | Dispositions are attacked as mere regularities of events, or place-holders for unknown properties [Mumford] |
| 14316 | If dispositions have several categorical realisations, that makes the two separate [Mumford] |
| 14317 | I say the categorical base causes the disposition manifestation [Mumford] |
| 14310 | Dispositions are classifications of properties by functional role [Mumford] |
| 14313 | All properties must be causal powers (since they wouldn't exist otherwise) [Mumford] |
| 14318 | Intrinsic properties are just causal powers, and identifying a property as causal is then analytic [Mumford] |
| 14293 | Dispositions are ascribed to at least objects, substances and persons [Mumford] |
| 14298 | Dispositions can be contrasted either with occurrences, or with categorical properties [Mumford] |
| 14326 | Unlike categorical bases, dispositions necessarily occupy a particular causal role [Mumford] |
| 14314 | If dispositions are powers, background conditions makes it hard to say what they do [Mumford] |
| 14325 | Maybe dispositions can replace powers in metaphysics, as what induces property change [Mumford] |
| 14312 | Orthodoxy says dispositions entail conditionals (rather than being equivalent to them) [Mumford] |
| 14291 | Dispositions are not just possibilities - they are features of actual things [Mumford] |
| 14299 | There could be dispositions that are never manifested [Mumford] |
| 14323 | If every event has a cause, it is easy to invent a power to explain each case [Mumford] |
| 14328 | Traditional powers initiate change, but are mysterious between those changes [Mumford] |
| 14331 | Categorical eliminativists say there are no dispositions, just categorical states or mechanisms [Mumford] |
| 11908 | Putnam bases essences on 'same kind', but same kinds may not share properties [Mackie,P on Putnam] |
| 14295 | Many artefacts have dispositional essences, which make them what they are [Mumford] |
| 14309 | Truth-functional conditionals can't distinguish whether they are causal or accidental [Mumford] |
| 14311 | Dispositions are not equivalent to stronger-than-material conditionals [Mumford] |
| 13480 | Fregean self-evidence is an intrinsic property of basic truths, rules and definitions [Hart,WD] |
| 13476 | The failure of key assumptions in geometry, mereology and set theory throw doubt on the a priori [Hart,WD] |
| 17508 | Science aims at truth, not at 'simplicity' [Putnam] |
| 14319 | Nomothetic explanations cite laws, and structural explanations cite mechanisms [Mumford] |
| 14342 | General laws depend upon the capacities of particulars, not the other way around [Mumford] |
| 14322 | If fragile just means 'breaks when dropped', it won't explain a breakage [Mumford] |
| 14320 | Subatomic particles may terminate explanation, if they lack structure [Mumford] |
| 14337 | Maybe dispositions can replace the 'laws of nature' as the basis of explanation [Mumford] |
| 14343 | To avoid a regress in explanations, ungrounded dispositions will always have to be posited [Mumford] |
| 14324 | Ontology is unrelated to explanation, which concerns modes of presentation and states of knowledge [Mumford] |
| 13475 | The Fregean concept of GREEN is a function assigning true to green things, and false to the rest [Hart,WD] |
| 17506 | I now think reference by the tests of experts is a special case of being causally connected [Putnam] |
| 14344 | Natural kinds, such as electrons, all behave the same way because we divide them by dispositions [Mumford] |
| 11904 | Express natural kinds as a posteriori predicate connections, not as singular terms [Putnam, by Mackie,P] |
| 17507 | Natural kind stereotypes are 'strong' (obvious, like tiger) or 'weak' (obscure, like molybdenum) [Putnam] |
| 14338 | In the 'laws' view events are basic, and properties are categorical, only existing when manifested [Mumford] |
| 14339 | Without laws, how can a dispositionalist explain general behaviour within kinds? [Mumford] |
| 14340 | It is a regularity that whenever a person sneezes, someone (somewhere) promptly coughs [Mumford] |
| 14341 | Dretske and Armstrong base laws on regularities between individual properties, not between events [Mumford] |
| 14345 | The necessity of an electron being an electron is conceptual, and won't ground necessary laws [Mumford] |
| 14307 | Some dispositions are so far unknown, until we learn how to manifest them [Mumford] |