78 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] |
| 16241 | The metaphysics of nature should focus on physics [Maudlin] |
| 16257 | Kant survives in seeing metaphysics as analysing our conceptual system, which is a priori [Maudlin] |
| 16276 | Wide metaphysical possibility may reduce metaphysics to analysis of fantasies [Maudlin] |
| 13515 | To study abstract problems, some knowledge of set theory is essential [Hart,WD] |
| 16244 | If the universe is profligate, the Razor leads us astray [Maudlin] |
| 16255 | The Razor rightly prefers one cause of multiple events to coincidences of causes [Maudlin] |
| 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] |
| 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] |
| 16243 | The Humean view is wrong; laws and direction of time are primitive, and atoms are decided by physics [Maudlin] |
| 16271 | Lewis says it supervenes on the Mosaic, but actually thinks the Mosaic is all there is [Maudlin] |
| 16273 | If the Humean Mosaic is ontological bedrock, there can be no explanation of its structure [Maudlin] |
| 16275 | The 'spinning disc' is just impossible, because there cannot be 'homogeneous matter' [Maudlin] |
| 13488 | Mass words do not have plurals, or numerical adjectives, or use 'fewer' [Hart,WD] |
| 16258 | To get an ontology from ontological commitment, just add that some theory is actually true [Maudlin] |
| 16259 | Naïve translation from natural to formal language can hide or multiply the ontology [Maudlin] |
| 16253 | A property is fundamental if two objects can differ in only that respect [Maudlin] |
| 16263 | Fundamental physics seems to suggest there are no such things as properties [Maudlin] |
| 16260 | Existence of universals may just be decided by acceptance, or not, of second-order logic [Maudlin] |
| 16277 | Logically impossible is metaphysically impossible, but logically possible is not metaphysically possible [Maudlin] |
| 16249 | A counterfactual antecedent commands the redescription of a selected moment [Maudlin] |
| 16285 | A possible world can be seen as a complete and consistent novel [Jeffrey] |
| 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] |
| 16254 | Induction leaps into the unknown, but usually lands safely [Maudlin] |
| 19155 | Instead of gambling, Jeffrey made the objects of Bayesian preference to be propositions [Jeffrey, by Davidson] |
| 16245 | Laws should help explain the things they govern, or that manifest them [Maudlin] |
| 13475 | The Fregean concept of GREEN is a function assigning true to green things, and false to the rest [Hart,WD] |
| 16248 | Evaluating counterfactuals involves context and interests [Maudlin] |
| 16250 | We don't pick a similar world from many - we construct one possibility from the description [Maudlin] |
| 16267 | If we know the cause of an event, we seem to assent to the counterfactual [Maudlin] |
| 16268 | The counterfactual is ruined if some other cause steps in when the antecedent fails [Maudlin] |
| 16269 | If the effect hadn't occurred the cause wouldn't have happened, so counterfactuals are two-way [Maudlin] |
| 16242 | Laws of nature are ontological bedrock, and beyond analysis [Maudlin] |
| 16247 | Laws are primitive, so two indiscernible worlds could have the same laws [Maudlin] |
| 16272 | Fundamental laws say how nature will, or might, evolve from some initial state [Maudlin] |
| 16251 | 'Humans with prime house numbers are mortal' is not a law, because not a natural kind [Maudlin] |
| 16270 | If laws are just regularities, then there have to be laws [Maudlin] |
| 16264 | I believe the passing of time is a fundamental fact about the world [Maudlin] |
| 16265 | If time passes, presumably it passes at one second per second [Maudlin] |
| 16266 | There is one ordered B series, but an infinitude of A series, depending on when the present is [Maudlin] |