74 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] |
21697 | The Struthionic Fallacy is that of burying one's head in the sand [Quine] |
14415 | A ground must be about its truth, and not just necessitate it [Merricks] |
14408 | Truthmaker needs truths to be 'about' something, and that is often unclear [Merricks] |
14395 | If a ball changes from red to white, Truthmaker says some thing must make the change true [Merricks] |
14398 | Truthmaker says if an entity is removed, some nonexistence truthmaker must replace it [Merricks] |
14403 | If Truthmaker says each truth is made by the existence of something, the theory had de re modality at is core [Merricks] |
14397 | Truthmaker demands not just a predication, but an existing state of affairs with essential ingredients [Merricks] |
14396 | If 'truth supervenes on being', worlds with the same entities, properties and relations have the same truths [Merricks] |
14400 | If truth supervenes on being, that won't explain why truth depends on being [Merricks] |
14394 | It is implausible that claims about non-existence are about existing things [Merricks] |
14390 | Truthmaker isn't the correspondence theory, because it offers no analysis of truth [Merricks] |
14412 | Speculations about non-existent things are not about existent things, so Truthmaker is false [Merricks] |
14414 | I am a truthmaker for 'that a human exists', but is it about me? [Merricks] |
13469 | Tarski showed how we could have a correspondence theory of truth, without using 'facts' [Hart,WD] |
14418 | Being true is not a relation, it is a primitive monadic property [Merricks] |
14391 | If the correspondence theory is right, then necessary truths must correspond to something [Merricks] |
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] |
14419 | Deflationism just says there is no property of being truth [Merricks] |
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] |
21698 | All relations, apart from ancestrals, can be reduced to simpler logic [Quine] |
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] |
21696 | Nominalism rejects both attributes and classes (where extensionalism accepts the classes) [Quine] |
13471 | Mathematics makes existence claims, but philosophers usually say those are never analytic [Hart,WD] |
14393 | The totality state is the most plausible truthmaker for negative existential truths [Merricks] |
13488 | Mass words do not have plurals, or numerical adjectives, or use 'fewer' [Hart,WD] |
14413 | Some properties seem to be primitive, but others can be analysed [Merricks] |
14416 | An object can have a disposition when the revelant conditional is false [Merricks] |
14392 | Fregeans say 'hobbits do not exist' is just 'being a hobbit' is not exemplified [Merricks] |
14410 | You believe you existed last year, but your segment doesn't, so they have different beliefs [Merricks] |
14417 | Counterfactuals aren't about actuality, so they lack truthmakers or a supervenience base [Merricks] |
14402 | If 'Fido is possibly black' depends on Fido's counterparts, then it has no actual truthmaker [Merricks] |
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] |
13475 | The Fregean concept of GREEN is a function assigning true to green things, and false to the rest [Hart,WD] |
14407 | Presentist should deny there is a present time, and just say that things 'exist' [Merricks] |
14411 | Maybe only presentism allows change, by now having a property, and then lacking it [Merricks] |
14406 | Presentists say that things have existed and will exist, not that they are instantaneous [Merricks] |
14405 | How can a presentist explain an object's having existed? [Merricks] |