100 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] |
7001 | If you begin philosophy with language, you find yourself trapped in it [Heil] |
13515 | To study abstract problems, some knowledge of set theory is essential [Hart,WD] |
7037 | Parsimony does not imply the world is simple, but that our theories should try to be [Heil] |
7038 | A theory with few fundamental principles might still posit a lot of entities [Heil] |
7004 | The view that truth making is entailment is misguided and misleading [Heil] |
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] |
13490 | Von Neumann defines α<β as α∈β [Hart,WD] |
13460 | 'Well-ordering' must have a least member, so it does the natural numbers but not the integers [Hart,WD] |
13481 | Maybe sets should be rethought in terms of the even more basic categories [Hart,WD] |
7035 | God does not create the world, and then add the classes [Heil] |
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] |
7017 | The reductionist programme dispenses with levels of reality [Heil] |
7003 | There are levels of organisation, complexity, description and explanation, but not of reality [Heil] |
13488 | Mass words do not have plurals, or numerical adjectives, or use 'fewer' [Hart,WD] |
7045 | Realism says some of our concepts 'cut nature at the joints' [Heil] |
7065 | Anti-realists who reduce reality to language must explain the existence of language [Heil] |
7020 | Concepts don't carve up the world, which has endless overlooked or ignored divisions [Heil] |
7007 | I think of properties as simultaneously dispositional and qualitative [Heil] |
7015 | A predicate applies truly if it picks out a real property of objects [Heil] |
7042 | A theory of universals says similarity is identity of parts; for modes, similarity is primitive [Heil] |
14296 | Dispositions are physical states of mechanism; when known, these replace the old disposition term [Quine] |
7023 | Powers or dispositions are usually seen as caused by lower-level qualities [Heil] |
7025 | Are a property's dispositions built in, or contingently added? [Heil] |
7034 | Universals explain one-over-many relations, and similar qualities, and similar behaviour [Heil] |
7039 | How could you tell if the universals were missing from a world of instances? [Heil] |
7009 | Similarity among modes will explain everthing universals were for [Heil] |
7041 | Similar objects have similar properties; properties are directly similar [Heil] |
7032 | Objects join sets because of properties; the property is not bestowed by set membership [Heil] |
7008 | Trope theorists usually see objects as 'bundles' of tropes [Heil] |
7018 | Objects are substances, which are objects considered as the bearer of properties [Heil] |
7019 | Maybe there is only one substance, space-time or a quantum field [Heil] |
7046 | Rather than 'substance' I use 'objects', which have properties [Heil] |
7047 | Statues and bronze lumps have discernible differences, so can't be identical [Heil] |
7048 | Do we reduce statues to bronze, or eliminate statues, or allow statues and bronze? [Heil] |
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] |
7028 | If properties were qualities without dispositions, they would be undetectable [Heil] |
7029 | Can we distinguish the way a property is from the property? [Heil] |
7030 | Properties don't possess ways they are, because that just is the property [Heil] |
7051 | Objects only have secondary qualities because they have primary qualities [Heil] |
7044 | Secondary qualities are just primary qualities considered in the light of their effect on us [Heil] |
7052 | Colours aren't surface properties, because of radiant sources and the colour of the sky [Heil] |
7053 | Treating colour as light radiation has the implausible result that tomatoes are not red [Heil] |
7066 | If the world is just texts or social constructs, what are texts and social constructs? [Heil] |
7021 | If the world is theory-dependent, the theories themselves can't be theory-dependent [Heil] |
7026 | Science is sometimes said to classify powers, neglecting qualities [Heil] |
7060 | One form of explanation is by decomposition [Heil] |
7010 | Dispositionality provides the grounding for intentionality [Heil] |
7054 | Intentionality now has internalist (intrinsic to thinkers) and externalist (environment or community) views [Heil] |
7011 | Qualia are not extra appendages, but intrinsic ingredients of material states and processes [Heil] |
7061 | Philosophers' zombies aim to show consciousness is over and above the physical world [Heil] |
7063 | Zombies are based on the idea that consciousness relates contingently to the physical [Heil] |
7064 | Functionalists deny zombies, since identity of functional state means identity of mental state [Heil] |
7027 | Functionalists say objects can be the same in disposition but differ in quality [Heil] |
7062 | Functionalism cannot explain consciousness just by functional organisation [Heil] |
7059 | The 'explanatory gap' is used to say consciousness is inexplicable, at least with current concepts [Heil] |
7012 | If a car is a higher-level entity, distinct from its parts, how could it ever do anything? [Heil] |
7043 | Multiple realisability is actually one predicate applying to a diverse range of properties [Heil] |
7058 | Externalism is causal-historical, or social, or biological [Heil] |
7057 | Intentionality is based in dispositions, which are intrinsic to agents, suggesting internalism [Heil] |
13475 | The Fregean concept of GREEN is a function assigning true to green things, and false to the rest [Hart,WD] |
7013 | The Picture Theory claims we can read reality from our ways of speaking about it [Heil] |
7002 | If propositions are states of affairs or sets of possible worlds, these lack truth values [Heil] |
7016 | The standard view is that causal sequences are backed by laws, and between particular events [Heil] |
7036 | The real natural properties are sparse, but there are many complex properties [Heil] |