89 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] |
| 7426 | Critical philosophy is what questions domination at every level [Foucault] |
| 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] |
| 18194 | 'Forcing' can produce new models of ZFC from old models [Maddy] |
| 18195 | A Large Cardinal Axiom would assert ever-increasing stages in the hierarchy [Maddy] |
| 13011 | New axioms are being sought, to determine the size of the continuum [Maddy] |
| 13013 | The Axiom of Extensionality seems to be analytic [Maddy] |
| 13014 | Extensional sets are clearer, simpler, unique and expressive [Maddy] |
| 13021 | The Axiom of Infinity states Cantor's breakthrough that launched modern mathematics [Maddy] |
| 13022 | Infinite sets are essential for giving an account of the real numbers [Maddy] |
| 18191 | Axiom of Infinity: completed infinite collections can be treated mathematically [Maddy] |
| 13023 | The Power Set Axiom is needed for, and supported by, accounts of the continuum [Maddy] |
| 18193 | The Axiom of Foundation says every set exists at a level in the set hierarchy [Maddy] |
| 13024 | Efforts to prove the Axiom of Choice have failed [Maddy] |
| 13025 | Modern views say the Choice set exists, even if it can't be constructed [Maddy] |
| 13026 | A large array of theorems depend on the Axiom of Choice [Maddy] |
| 17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
| 18169 | Axiom of Reducibility: propositional functions are extensionally predicative [Maddy] |
| 13019 | The Iterative Conception says everything appears at a stage, derived from the preceding appearances [Maddy] |
| 13018 | Limitation of Size is a vague intuition that over-large sets may generate paradoxes [Maddy] |
| 17824 | The master science is physical objects divided into sets [Maddy] |
| 8755 | Maddy replaces pure sets with just objects and perceived sets of objects [Maddy, by Shapiro] |
| 10594 | Henkin semantics is more plausible for plural logic than for second-order logic [Maddy] |
| 17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
| 18168 | 'Propositional functions' are propositions with a variable as subject or predicate [Maddy] |
| 17605 | Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy] |
| 17625 | If two mathematical themes coincide, that suggest a single deep truth [Maddy] |
| 18190 | Completed infinities resulted from giving foundations to calculus [Maddy] |
| 18171 | Cantor and Dedekind brought completed infinities into mathematics [Maddy] |
| 17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
| 18172 | Infinity has degrees, and large cardinals are the heart of set theory [Maddy] |
| 18175 | For any cardinal there is always a larger one (so there is no set of all sets) [Maddy] |
| 18196 | An 'inaccessible' cardinal cannot be reached by union sets or power sets [Maddy] |
| 18187 | Theorems about limits could only be proved once the real numbers were understood [Maddy] |
| 18182 | The extension of concepts is not important to me [Maddy] |
| 18177 | In the ZFC hierarchy it is impossible to form Frege's set of all three-element sets [Maddy] |
| 18164 | Frege solves the Caesar problem by explicitly defining each number [Maddy] |
| 17825 | Set theory (unlike the Peano postulates) can explain why multiplication is commutative [Maddy] |
| 17826 | Standardly, numbers are said to be sets, which is neat ontology and epistemology [Maddy] |
| 17828 | Numbers are properties of sets, just as lengths are properties of physical objects [Maddy] |
| 10718 | A natural number is a property of sets [Maddy, by Oliver] |
| 18184 | Making set theory foundational to mathematics leads to very fruitful axioms [Maddy] |
| 18185 | Unified set theory gives a final court of appeal for mathematics [Maddy] |
| 18183 | Set theory brings mathematics into one arena, where interrelations become clearer [Maddy] |
| 18163 | Mathematics rests on the logic of proofs, and on the set theoretic axioms [Maddy] |
| 18186 | Identifying geometric points with real numbers revealed the power of set theory [Maddy] |
| 18188 | The line of rationals has gaps, but set theory provided an ordered continuum [Maddy] |
| 17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
| 17830 | Number theory doesn't 'reduce' to set theory, because sets have number properties [Maddy] |
| 17827 | Sets exist where their elements are, but numbers are more like universals [Maddy] |
| 17823 | If mathematical objects exist, how can we know them, and which objects are they? [Maddy] |
| 8756 | Intuition doesn't support much mathematics, and we should question its reliability [Maddy, by Shapiro] |
| 17733 | We know mind-independent mathematical truths through sets, which rest on experience [Maddy, by Jenkins] |
| 18204 | Scientists posit as few entities as possible, but set theorist posit as many as possible [Maddy] |
| 18207 | Maybe applications of continuum mathematics are all idealisations [Maddy] |
| 17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
| 17829 | Number words are unusual as adjectives; we don't say 'is five', and numbers always come first [Maddy] |
| 18167 | We can get arithmetic directly from HP; Law V was used to get HP from the definition of number [Maddy] |
| 18205 | The theoretical indispensability of atoms did not at first convince scientists that they were real [Maddy] |
| 15037 | Why does knowledge appear in sudden bursts, and not in a smooth continuous development? [Foucault] |
| 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] |
| 21941 | Unlike Marxists, Foucault explains thought internally, without deference to conscious ideas [Foucault, by Gutting] |
| 18206 | Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy] |
| 7422 | A subject is a form which can change, in (say) political or sexual situations [Foucault] |
| 22235 | Feelings are not unchanging, but have a history (especially if they are noble) [Foucault] |
| 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] |
| 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] |
| 6005 | Animals are dangerous and nourishing, and can't form contracts of justice [Hermarchus, by Sedley] |