137 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] |
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] |
19906 | All countries are in a mutual state of nature [Locke] |
19882 | We are not created for solitude, but are driven into society by our needs [Locke] |
19864 | In nature men can dispose of possessions and their persons in any way that is possible [Locke] |
19865 | There is no subjection in nature, and all creatures of the same species are equal [Locke] |
19866 | The rational law of nature says we are all equal and independent, and should show mutual respect [Locke] |
19872 | The animals and fruits of the earth belong to mankind [Locke] |
19907 | There is a natural right to inheritance within a family [Locke] |
19863 | Politics is the right to make enforceable laws to protect property and the state, for the common good [Locke] |
5654 | The Second Treatise explores the consequences of the contractual view of the state [Locke, by Scruton] |
19888 | A society only begins if there is consent of all the individuals to join it [Locke] |
6702 | If anyone enjoys the benefits of government (even using a road) they give tacit assent to its laws [Locke] |
19909 | A politic society is created from a state of nature by a unanimous agreement [Locke] |
19910 | A single will creates the legislature, which is duty-bound to preserve that will [Locke] |
19893 | Anyone who enjoys the benefits of a state has given tacit consent to be part of it [Locke] |
19894 | You can only become an actual member of a commonwealth by an express promise [Locke] |
19892 | Children are not born into citizenship of a state [Locke] |
19885 | Absolute monarchy is inconsistent with civil society [Locke] |
19886 | The idea that absolute power improves mankind is confuted by history [Locke] |
19903 | Despotism is arbitrary power to kill, based neither on natural equality, nor any social contract [Locke] |
19905 | People stripped of their property are legitimately subject to despotism [Locke] |
19904 | Legitimate prisoners of war are subject to despotism, because that continues the state of war [Locke] |
19895 | Even the legislature must be preceded by a law which gives it power to make laws [Locke] |
19900 | The executive must not be the legislature, or they may exempt themselves from laws [Locke] |
19902 | Any obstruction to the operation of the legislature can be removed forcibly by the people [Locke] |
19908 | Rebelling against an illegitimate power is no sin [Locke] |
19911 | If legislators confiscate property, or enslave people, they are no longer owed obedience [Locke] |
19901 | The people have supreme power, to depose a legislature which has breached their trust [Locke] |
19887 | Unanimous consent makes a united community, which is then ruled by the majority [Locke] |
19913 | A master forfeits ownership of slaves he abandons [Locke] |
19883 | Slaves captured in a just war have no right to property, so are not part of civil society [Locke] |
19870 | If you try to enslave me, you have declared war on me [Locke] |
19871 | Freedom is not absence of laws, but living under laws arrived at by consent [Locke] |
19880 | All value depends on the labour involved [Locke] |
19884 | There is only a civil society if the members give up all of their natural executive rights [Locke] |
19873 | We all own our bodies, and the work we do is our own [Locke] |
6580 | Locke (and Marx) held that ownership of objects is a natural relation, based on the labour put into it [Locke, by Fogelin] |
20520 | Locke says 'mixing of labour' entitles you to land, as well as nuts and berries [Wolff,J on Locke] |
19875 | A man's labour gives ownership rights - as long as there are fair shares for all [Locke] |
19874 | If a man mixes his labour with something in Nature, he thereby comes to own it [Locke] |
19877 | Fountain water is everyone's, but a drawn pitcher of water has an owner [Locke] |
19876 | Gathering natural fruits gives ownership; the consent of other people is irrelevant [Locke] |
19878 | Mixing labour with a thing bestows ownership - as long as the thing is not wasted [Locke] |
19879 | A man owns land if he cultivates it, to the limits of what he needs [Locke] |
19898 | Soldiers can be commanded to die, but not to hand over their money [Locke] |
19881 | The aim of law is not restraint, but to make freedom possible [Locke] |
19868 | It is only by a law of Nature that we can justify punishing foreigners [Locke] |
19867 | Reparation and restraint are the only justifications for punishment [Locke] |
19912 | Self-defence is natural, but not the punishment of superiors by inferiors [Locke] |
19869 | Punishment should make crime a bad bargain, leading to repentance and deterrence [Locke] |
19899 | The consent of the people is essential for any tax [Locke] |
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] |