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] |
10468 | A metaphysics has an ontology (objects) and an ideology (expressed ideas about them) [Oliver] |
13515 | To study abstract problems, some knowledge of set theory is essential [Hart,WD] |
10471 | Ockham's Razor has more content if it says believe only in what is causal [Oliver] |
10749 | Necessary truths seem to all have the same truth-maker [Oliver] |
10750 | Slingshot Argument: seems to prove that all sentences have the same truth-maker [Oliver] |
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] |
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] |
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] |
10747 | Accepting properties by ontological commitment tells you very little about them [Oliver] |
10748 | Reference is not the only way for a predicate to have ontological commitment [Oliver] |
10719 | There are four conditions defining the relations between particulars and properties [Oliver] |
10721 | If properties are sui generis, are they abstract or concrete? [Oliver] |
10716 | There are just as many properties as the laws require [Oliver] |
10720 | We have four options, depending whether particulars and properties are sui generis or constructions [Oliver] |
10714 | The expressions with properties as their meanings are predicates and abstract singular terms [Oliver] |
10715 | There are five main semantic theories for properties [Oliver] |
10738 | Tropes are not properties, since they can't be instantiated twice [Oliver] |
10739 | The property of redness is the maximal set of the tropes of exactly similar redness [Oliver] |
10740 | The orthodox view does not allow for uninstantiated tropes [Oliver] |
10741 | Maybe concrete particulars are mereological wholes of abstract particulars [Oliver] |
10742 | Tropes can overlap, and shouldn't be splittable into parts [Oliver] |
10472 | 'Structural universals' methane and butane are made of the same universals, carbon and hydrogen [Oliver] |
10724 | Located universals are wholly present in many places, and two can be in the same place [Oliver] |
7963 | Aristotle's instantiated universals cannot account for properties of abstract objects [Oliver] |
10730 | If universals ground similarities, what about uniquely instantiated universals? [Oliver] |
10727 | Uninstantiated universals seem to exist if they themselves have properties [Oliver] |
7962 | Uninstantiated properties are useful in philosophy [Oliver] |
10722 | Instantiation is set-membership [Oliver] |
10744 | Nominalism can reject abstractions, or universals, or sets [Oliver] |
10726 | Things can't be fusions of universals, because two things could then be one thing [Oliver] |
10725 | Abstract sets of universals can't be bundled to make concrete things [Oliver] |
10745 | Science is modally committed, to disposition, causation and law [Oliver] |
2526 | Philosophers regularly confuse failures of imagination with insights into necessity [Dennett] |
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] |
2523 | That every mammal has a mother is a secure reality, but without foundations [Dennett] |
2528 | Does consciousness need the concept of consciousness? [Dennett] |
2525 | Maybe language is crucial to consciousness [Dennett] |
2527 | Unconscious intentionality is the foundation of the mind [Dennett] |
2530 | Could a robot be made conscious just by software? [Dennett] |
2524 | A language of thought doesn't explain content [Dennett] |
13475 | The Fregean concept of GREEN is a function assigning true to green things, and false to the rest [Hart,WD] |
10746 | Conceptual priority is barely intelligible [Oliver] |
2529 | Maybe there can be non-conscious concepts (e.g. in bees) [Dennett] |