99 ideas
7500 | Early Greeks cared about city and companions; later Greeks concentrated on the self [Foucault] |
15045 | The big issue since the eighteenth century has been: what is Reason? Its effect, limits and dangers? [Foucault] |
13466 | We are all post-Kantians, because he set the current agenda for philosophy [Hart,WD] |
7426 | Critical philosophy is what questions domination at every level [Foucault] |
13477 | The problems are the monuments of philosophy [Hart,WD] |
13515 | To study abstract problems, some knowledge of set theory is essential [Hart,WD] |
7423 | Philosophy and politics are fundamentally linked [Foucault] |
15038 | Structuralism systematically abstracted the event from sciences, and even from history [Foucault] |
7420 | When logos controls our desires, we have actually become the logos [Foucault] |
21945 | Foucault originally felt that liberating reason had become an instrument of domination [Foucault, by Gutting] |
15044 | 'Truth' is the procedures for controlling which statements are acceptable [Foucault] |
15042 | Truth doesn't arise from solitary freedom, but from societies with constraints [Foucault] |
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] |
9117 | The smallest heap has four objects: three on the bottom, one on the top [Hart,WD, by Sorensen] |
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] |
458 | Nothing could come out of nothing, and existence could never completely cease [Empedocles] |
5112 | Empedocles says things are at rest, unless love unites them, or hatred splits them [Empedocles, by Aristotle] |
13488 | Mass words do not have plurals, or numerical adjectives, or use 'fewer' [Hart,WD] |
13209 | There is no coming-to-be of anything, but only mixing and separating [Empedocles, by Aristotle] |
457 | Substance is not created or destroyed in mortals, but there is only mixing and exchange [Empedocles] |
15037 | Why does knowledge appear in sudden bursts, and not in a smooth continuous development? [Foucault] |
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] |
21942 | Foucault challenges knowledge in psychology and sociology, not in the basic sciences [Foucault, by Gutting] |
7424 | Saying games of truth were merely power relations would be a horrible exaggeration [Foucault] |
462 | One vision is produced by both eyes [Empedocles] |
21941 | Unlike Marxists, Foucault explains thought internally, without deference to conscious ideas [Foucault, by Gutting] |
7422 | A subject is a form which can change, in (say) political or sexual situations [Foucault] |
22765 | Wisdom and thought are shared by all things [Empedocles] |
1524 | For Empedocles thinking is almost identical to perception [Empedocles, by Theophrastus] |
22235 | Feelings are not unchanging, but have a history (especially if they are noble) [Foucault] |
13475 | The Fregean concept of GREEN is a function assigning true to green things, and false to the rest [Hart,WD] |
21939 | The author function of any text is a plurality of selves [Foucault, by Gutting] |
7419 | Ethics is the conscious practice of freedom [Foucault] |
7501 | Why couldn't a person's life become a work of art? [Foucault] |
552 | Empedocles said good and evil were the basic principles [Empedocles, by Aristotle] |
7498 | Greeks and early Christians were much more concerned about food than about sex [Foucault] |
21940 | Nature is not the basis of rights, but the willingness to risk death in asserting them [Foucault] |
15043 | Every society has a politics of truth, concerning its values, functions, prestige and mechanisms [Foucault] |
15040 | Marxists denounced power as class domination, but never analysed its mechanics [Foucault] |
15041 | Power doesn't just repress, but entices us with pleasure, artefacts, knowledge and discourse [Foucault] |
8991 | Foucault can't accept that power is sometimes decent and benign [Foucault, by Scruton] |
7425 | The aim is not to eliminate power relations, but to reduce domination [Foucault] |
22236 | The big question of the Renaissance was how to govern everything, from the state to children [Foucault] |
21947 | Power is localised, so we either have totalitarian centralisation, or local politics [Foucault, by Gutting] |
21946 | Prisons gradually became our models for schools, hospitals and factories [Foucault, by Gutting] |
7418 | The idea of liberation suggests there is a human nature which has been repressed [Foucault] |
21116 | Power is used to create identities and ways of life for other people [Foucault, by Shorten] |
15039 | History lacks 'meaning', but it can be analysed in terms of its struggles [Foucault] |
589 | 'Nature' is just a word invented by people [Empedocles] |
21823 | The principle of 'Friendship' in Empedocles is the One, and is bodiless [Empedocles, by Plotinus] |
2680 | Empedocles said that there are four material elements, and two further creative elements [Empedocles, by Aristotle] |
6002 | Empedocles says bone is water, fire and earth in ratio 2:4:2 [Empedocles, by Inwood] |
13207 | Fire, Water, Air and Earth are elements, being simple as well as homoeomerous [Empedocles, by Aristotle] |
459 | All change is unity through love or division through hate [Empedocles] |
13218 | The elements combine in coming-to-be, but how do the elements themselves come-to-be? [Aristotle on Empedocles] |
13225 | Love and Strife only explain movement if their effects are distinctive [Aristotle on Empedocles] |
460 | If the one Being ever diminishes it would no longer exist, and what could ever increase it? [Empedocles] |
5090 | Maybe bodies are designed by accident, and the creatures that don't work are destroyed [Empedocles, by Aristotle] |
466 | God is pure mind permeating the universe [Empedocles] |
461 | God is a pure, solitary, and eternal sphere [Empedocles] |
1719 | In Empedocles' theory God is ignorant because, unlike humans, he doesn't know one of the elements (strife) [Aristotle on Empedocles] |
1522 | It is wretched not to want to think clearly about the gods [Empedocles] |