84 ideas
7500 | Early Greeks cared about city and companions; later Greeks concentrated on the self [Foucault] |
19579 | The history of philosophy is just experiments in how to do philosophy [Novalis] |
15045 | The big issue since the eighteenth century has been: what is Reason? Its effect, limits and dangers? [Foucault] |
19583 | Philosophy only begins when it studies itself [Novalis] |
7426 | Critical philosophy is what questions domination at every level [Foucault] |
22026 | Philosophy is homesickness - the urge to be at home everywhere [Novalis] |
19588 | The highest aim of philosophy is to combine all philosophies into a unity [Novalis] |
19598 | Philosophy relies on our whole system of learning, and can thus never be complete [Novalis] |
19586 | Philosophers feed on problems, hoping they are digestible, and spiced with paradox [Novalis] |
19587 | Philosophy aims to produce a priori an absolute and artistic world system [Novalis] |
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] |
15924 | Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them? [Zermelo, by Lavine] |
19574 | If man sacrifices truth he sacrifices himself, by acting against his own convictions [Novalis] |
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] |
19571 | Delusion and truth differ in their life functions [Novalis] |
17608 | We take set theory as given, and retain everything valuable, while avoiding contradictions [Zermelo] |
17607 | Set theory investigates number, order and function, showing logical foundations for mathematics [Zermelo] |
10870 | ZFC: Existence, Extension, Specification, Pairing, Unions, Powers, Infinity, Choice [Zermelo, by Clegg] |
13012 | Zermelo published his axioms in 1908, to secure a controversial proof [Zermelo, by Maddy] |
17609 | Set theory can be reduced to a few definitions and seven independent axioms [Zermelo] |
9565 | Zermelo made 'set' and 'member' undefined axioms [Zermelo, by Chihara] |
3339 | For Zermelo's set theory the empty set is zero and the successor of each number is its unit set [Zermelo, by Blackburn] |
17832 | Zermelo showed that the ZF axioms in 1930 were non-categorical [Zermelo, by Hallett,M] |
13017 | Zermelo introduced Pairing in 1930, and it seems fairly obvious [Zermelo, by Maddy] |
13028 | Replacement was added when some advanced theorems seemed to need it [Zermelo, by Maddy] |
13015 | Zermelo used Foundation to block paradox, but then decided that only Separation was needed [Zermelo, by Maddy] |
13020 | The Axiom of Separation requires set generation up to one step back from contradiction [Zermelo, by Maddy] |
13486 | Not every predicate has an extension, but Separation picks the members that satisfy a predicate [Zermelo, by Hart,WD] |
19597 | Logic (the theory of relations) should be applied to mathematics [Novalis] |
19581 | A problem is a solid mass, which the mind must break up [Novalis] |
17626 | The antinomy of endless advance and of completion is resolved in well-ordered transfinite numbers [Zermelo] |
13487 | In ZF, the Burali-Forti Paradox proves that there is no set of all ordinals [Zermelo, by Hart,WD] |
19584 | Whoever first counted to two must have seen the possibility of infinite counting [Novalis] |
15897 | Zermelo realised that Choice would facilitate the sort of 'counting' Cantor needed [Zermelo, by Lavine] |
18178 | For Zermelo the successor of n is {n} (rather than n U {n}) [Zermelo, by Maddy] |
13027 | Zermelo believed, and Von Neumann seemed to confirm, that numbers are sets [Zermelo, by Maddy] |
9627 | Different versions of set theory result in different underlying structures for numbers [Zermelo, by Brown,JR] |
22025 | Novalis thought self-consciousness cannot disclose 'being', because we are temporal creatures [Novalis, by Pinkard] |
19575 | Refinement of senses increasingly distinguishes individuals [Novalis] |
15037 | Why does knowledge appear in sudden bursts, and not in a smooth continuous development? [Foucault] |
22067 | Poetry is true idealism, and the self-consciousness of the universe [Novalis] |
19572 | Experiences tests reason, and reason tests experience [Novalis] |
19590 | Empiricists are passive thinkers, given their philosophy by the external world and fate [Novalis] |
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] |
19594 | General statements about nature are not valid [Novalis] |
21941 | Unlike Marxists, Foucault explains thought internally, without deference to conscious ideas [Foucault, by Gutting] |
19591 | Desire for perfection is an illness, if it turns against what is imperfect [Novalis] |
7422 | A subject is a form which can change, in (say) political or sexual situations [Foucault] |
19596 | The whole body is involved in the formation of thoughts [Novalis] |
19573 | The seat of the soul is where our inner and outer worlds interpenetrate [Novalis] |
22235 | Feelings are not unchanging, but have a history (especially if they are noble) [Foucault] |
17613 | We should judge principles by the science, not science by some fixed principles [Zermelo] |
19577 | Everything is a chaotic unity, then we abstract, then we reunify the world into a free alliance [Novalis] |
19585 | Every person has his own language [Novalis] |
19578 | Only self-illuminated perfect individuals are beautiful [Novalis] |
21939 | The author function of any text is a plurality of selves [Foucault, by Gutting] |
7419 | Ethics is the conscious practice of freedom [Foucault] |
19582 | Morality and philosophy are mutually dependent [Novalis] |
7501 | Why couldn't a person's life become a work of art? [Foucault] |
7498 | Greeks and early Christians were much more concerned about food than about sex [Foucault] |
22027 | Life isn't given to us like a novel - we write the novel [Novalis] |
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] |
19589 | The whole point of a monarch is that we accept them as a higher-born, ideal person [Novalis] |
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] |
19580 | If the pupil really yearns for the truth, they only need a hint [Novalis] |
19593 | Persons are shaped by a life history; splendid persons are shaped by world history [Novalis] |
15039 | History lacks 'meaning', but it can be analysed in terms of its struggles [Foucault] |
19595 | Nature is a whole, and its individual parts cannot be wholly understood [Novalis] |
19592 | The basic relations of nature are musical [Novalis] |
19576 | Religion needs an intermediary, because none of us can connect directly to a godhead [Novalis] |