81 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] |
| 18390 | All metaphysical discussion should be guided by a quest for truthmakers [Armstrong] |
| 13515 | To study abstract problems, some knowledge of set theory is essential [Hart,WD] |
| 18467 | Truth-making can't be entailment, because truthmakers are portions of reality [Armstrong] |
| 18468 | Armstrong says truthmakers necessitate their truth, where 'necessitate' is a primitive relation [Armstrong, by MacBride] |
| 18377 | Negative truths have as truthmakers all states of affairs relevant to the truth [Armstrong] |
| 18382 | The nature of arctic animals is truthmaker for the absence of penguins there [Armstrong] |
| 18394 | In mathematics, truthmakers are possible instantiations of structures [Armstrong] |
| 18384 | One truthmaker will do for a contingent truth and for its contradictory [Armstrong] |
| 18387 | The truthmakers for possible unicorns are the elements in their combination [Armstrong] |
| 18386 | What is the truthmaker for 'it is possible that there could have been nothing'? [Armstrong] |
| 18381 | Necessitating general truthmakers must also specify their limits [Armstrong] |
| 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] |
| 18396 | The set theory brackets { } assert that the member is a unit [Armstrong] |
| 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] |
| 18393 | For 'there is a class with no members' we don't need the null set as truthmaker [Armstrong] |
| 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] |
| 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] |
| 18392 | Classes have cardinalities, so their members must all be treated as units [Armstrong] |
| 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] |
| 18385 | Logical atomism builds on the simple properties, but are they the only possible properties? [Armstrong] |
| 13488 | Mass words do not have plurals, or numerical adjectives, or use 'fewer' [Hart,WD] |
| 18391 | 'Naturalism' says only the world of space-time exists [Armstrong] |
| 18374 | Truthmaking needs states of affairs, to unite particulars with tropes or universals. [Armstrong] |
| 18372 | We need properties, as minimal truthmakers for the truths about objects [Armstrong] |
| 18379 | The determinates of a determinable must be incompatible with each other [Armstrong] |
| 18378 | Length is a 'determinable' property, and one mile is one its 'determinates' [Armstrong] |
| 18373 | If tropes are non-transferable, then they necessarily belong to their particular substance [Armstrong] |
| 18400 | Properties are not powers - they just have powers [Armstrong] |
| 18397 | Powers must result in some non-powers, or there would only be potential without result [Armstrong] |
| 18399 | How does the power of gravity know the distance it acts over? [Armstrong] |
| 18371 | The class of similar things is much too big a truthmaker for the feature of a particular [Armstrong] |
| 18389 | When entities contain entities, or overlap with them, there is 'partial' identity [Armstrong] |
| 18388 | Possible worlds don't fix necessities; intrinsic necessities imply the extension in worlds [Armstrong] |
| 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] |
| 18375 | General truths are a type of negative truth, saying there are no more ravens than black ones [Armstrong] |
| 13475 | The Fregean concept of GREEN is a function assigning true to green things, and false to the rest [Hart,WD] |
| 18368 | For all being, there is a potential proposition which expresses its existence and nature [Armstrong] |
| 18370 | A realm of abstract propositions is causally inert, so has no explanatory value [Armstrong] |
| 22808 | Liberalism is minimal government, or individual rights, or equality [Avineri/De-Shalit] |
| 22803 | Can individualist theories justify an obligation to fight in a war? [Avineri/De-Shalit] |
| 22804 | Autonomy is better achieved within a community [Avineri/De-Shalit] |
| 22806 | Communitarians avoid oppression for the common good, by means of small mediating communities [Avineri/De-Shalit] |
| 22807 | If our values are given to us by society then we have no grounds to criticise them [Avineri/De-Shalit] |
| 18380 | Negative causations supervene on positive causations plus their laws? [Armstrong] |
| 18401 | The pure present moment is too brief to be experienced [Armstrong] |