89 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] |
16676 | Why use more things when fewer will do? [William of Ockham] |
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] |
4098 | The theory of descriptions supports internalism, since they are thinkable when the object is non-existent [Crane] |
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] |
4077 | Aesthetic properties of thing supervene on their physical properties [Crane] |
4078 | Constitution (as in a statue constituted by its marble) is supervenience without identity [Crane] |
13488 | Mass words do not have plurals, or numerical adjectives, or use 'fewer' [Hart,WD] |
4082 | The distinction between 'resultant' properties (weight) and 'emergent' properties is a bit vague [Crane] |
4083 | If mental properties are emergent they add a new type of causation, and physics is not complete [Crane] |
4079 | Properties are causes [Crane] |
4068 | Traditional substance is separate from properties and capable of independent existence [Crane] |
4097 | Maybe there are two kinds of belief - 'de re' beliefs and 'de dicto' beliefs [Crane] |
4096 | Maybe beliefs don't need to be conscious, if you are not conscious of the beliefs guiding your actions [Crane] |
4093 | Many cases of knowing how can be expressed in propositional terms (like how to get somewhere) [Crane] |
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] |
4108 | Phenol-thio-urea tastes bitter to three-quarters of people, but to the rest it is tasteless, so which is it? [Crane] |
4105 | The traditional supports for the sense datum theory were seeing double and specks before one's eyes [Crane] |
4104 | One can taste that the wine is sour, and one can also taste the sourness of the wine [Crane] |
4101 | If we smell something we are aware of the smell separately, but we don't perceive a 'look' when we see [Crane] |
4102 | The problems of perception disappear if it is a relation to an intentional state, not to an object or sense datum [Crane] |
4109 | If perception is much richer than our powers of description, this suggests that it is non-conceptual [Crane] |
4103 | The adverbial theory of perceptions says it is the experiences which have properties, not the objects [Crane] |
4065 | Is knowledge just a state of mind, or does it also involve the existence of external things? [Crane] |
4092 | The core of the consciousness problem is the case of Mary, zombies, and the Hard Question [Crane] |
4087 | Intentionalism does not require that all mental states be propositional attitudes [Crane] |
4095 | Object-directed attitudes like love are just as significant as propositional attitudes [Crane] |
4106 | If someone removes their glasses the content of experience remains, but the quality changes [Crane] |
4089 | Pains have a region of the body as their intentional content, not some pain object [Crane] |
4090 | Weak intentionalism says qualia are extra properties; strong intentionalism says they are intentional [Crane] |
4107 | With inverted qualia a person's experiences would change, but their beliefs remain the same [Crane] |
4069 | Descartes did not think of minds as made of a substance, because they are not divisible [Crane] |
4074 | Functionalism defines mental states by their causal properties, which rules out epiphenomenalism [Crane] |
4091 | The problems of misrepresentation and error have dogged physicalist reductions of intentionality [Crane] |
4070 | Properties dualism says mental properties are distinct from physical, despite a single underlying substance [Crane] |
4084 | Non-reductive physicalism seeks an explanation of supervenience, but emergentists accept it as basic [Crane] |
4080 | If mental supervenes on the physical, then every physical cause will be accompanied by a mental one [Crane] |
4075 | Identity theory is either of particular events, or of properties, depending on your theory of causation [Crane] |
4085 | Physicalism may be the source of the mind-body problem, rather than its solution [Crane] |
4073 | Overdetermination occurs if two events cause an effect, when each would have caused it alone [Crane] |
4072 | The completeness of physics must be an essential component of any physicalist view of mind [Crane] |
4094 | Experience teaches us propositions, because we can reason about our phenomenal experience [Crane] |
4100 | The Twin Earth argument depends on reference being determined by content, which may be false. [Crane] |
4067 | Broad content entails the existence of the object of the thought [Crane] |
4063 | In intensional contexts, truth depends on how extensions are conceived. [Crane] |
13475 | The Fregean concept of GREEN is a function assigning true to green things, and false to the rest [Hart,WD] |
16675 | Every extended material substance is composed of parts distant from one another [William of Ockham] |
4071 | Causation can be seen in counterfactual terms, or as increased probability, or as energy flow [Crane] |
4076 | Causes are properties, not events, because properties are what make a difference in a situation [Crane] |
4066 | It seems that 'exists' could sometimes be a predicate [Crane] |