82 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] |
| 22611 | Metaphysics can criticise interpretations of science theories, and give good feedback [Ingthorsson] |
| 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] |
| 22609 | Philosophers accepted first-order logic, because they took science to be descriptive, not explanatory [Ingthorsson] |
| 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] |
| 22629 | Basic processes are said to be either physical, or organic, or psychological [Ingthorsson] |
| 13488 | Mass words do not have plurals, or numerical adjectives, or use 'fewer' [Hart,WD] |
| 22633 | Indirect realists are cautious about the manifest image, and prefer the scientific image [Ingthorsson] |
| 22606 | Neo-Humeans say there are no substantial connections between anything [Ingthorsson] |
| 22631 | Properties are said to be categorical qualities or non-qualitative dispositions [Ingthorsson] |
| 22632 | Physics understands the charge of an electron as a power, not as a quality [Ingthorsson] |
| 22627 | Compound objects are processes, insofar as change is essential to them [Ingthorsson] |
| 22613 | Most materialist views postulate smallest indivisible components which are permanent [Ingthorsson] |
| 22612 | Endurance and perdurance just show the consequences of A or B series time [Ingthorsson] |
| 22625 | Science suggests causal aspects of the constitution and persistance of objects [Ingthorsson] |
| 22620 | If causation involves production, that needs persisting objects [Ingthorsson] |
| 22636 | Every philosophical theory must be true in some possible world, so the ontology is hopeless [Ingthorsson] |
| 22638 | Worlds may differ in various respects, but no overall similarity of worlds is implied [Ingthorsson] |
| 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] |
| 1457 | Morality requires a minimum commitment to the self [Rashdall] |
| 13475 | The Fregean concept of GREEN is a function assigning true to green things, and false to the rest [Hart,WD] |
| 6674 | All moral judgements ultimately concern the value of ends [Rashdall] |
| 6673 | Ideal Utilitarianism is teleological but non-hedonistic; the aim is an ideal end, which includes pleasure [Rashdall] |
| 22605 | Humeans describe the surface of causation, while powers accounts aim at deeper explanations [Ingthorsson] |
| 22607 | Time and space are not causal, but they determine natural phenomena [Ingthorsson] |
| 22608 | Casuation is the transmission of conserved quantities between causal processes [Ingthorsson] |
| 22614 | Interventionist causal theory says it gets a reliable result whenever you manipulate it [Ingthorsson] |
| 22621 | Causation as transfer only works for asymmetric interactions [Ingthorsson] |
| 22639 | Causal events are always reciprocal, and there is no distinction of action and reaction [Ingthorsson] |
| 22615 | One effect cannot act on a second effect in causation, because the second doesn't yet exist [Ingthorsson] |
| 22616 | Empiricists preferred events to objects as the relata, because they have observable motions [Ingthorsson] |
| 22617 | Science now says all actions are reciprocal, not unidirectional [Ingthorsson] |
| 22619 | Causes are not agents; the whole interaction is the cause, and the changed compound is the effect [Ingthorsson] |
| 22635 | People only accept the counterfactual when they know the underlying cause [Ingthorsson] |
| 22634 | Counterfactuals don't explain causation, but causation can explain counterfactuals [Ingthorsson] |
| 22637 | Counterfactual theories are false in possible worlds where causation is actual [Ingthorsson] |
| 22624 | A cause can fail to produce its normal effect, by prevention, pre-emption, finks or antidotes [Ingthorsson] |
| 22622 | Any process can go backwards or forwards in time without violating the basic laws of physics [Ingthorsson] |
| 22618 | In modern physics the first and second laws of motion (unlike the third) fail at extremes [Ingthorsson] |
| 22630 | If particles have decay rates, they can't really be elementary, in the sense of indivisible [Ingthorsson] |
| 22610 | It is difficult to handle presentism in first-order logic [Ingthorsson] |
| 1458 | Conduct is only reasonable or unreasonable if the world is governed by reason [Rashdall] |
| 1459 | Absolute moral ideals can't exist in human minds or material things, so their acceptance implies a greater Mind [Rashdall, by PG] |