92 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] |
21761 | If we start with indeterminate being, we arrive at being and nothing as a united pair [Hegel, by Houlgate] |
21764 | Thought about being leads to a string of other concepts, like becoming, quantity, specificity, causality... [Hegel, by Houlgate] |
21769 | We must start with absolute abstraction, with no presuppositions, so we start with pure being [Hegel] |
13515 | To study abstract problems, some knowledge of set theory is essential [Hart,WD] |
22037 | Objectivity is not by correspondence, but by the historical determined necessity of Geist [Hegel, by Pinkard] |
21983 | Being and nothing are the same and not the same, which is the identity of identity and non-identity [Hegel] |
21985 | The so-called world is filled with contradiction [Hegel] |
21978 | Hegel's dialectic is not thesis-antithesis-synthesis, but usually negation of negation of the negation [Hegel, by Moore,AW] |
21766 | Dialectic is the instability of thoughts generating their opposite, and then new more complex thoughts [Hegel, by Houlgate] |
18986 | Truth is just a name for verification-processes [James] |
13469 | Tarski showed how we could have a correspondence theory of truth, without using 'facts' [Hart,WD] |
18983 | In many cases there is no obvious way in which ideas can agree with their object [James] |
18972 | Ideas are true in so far as they co-ordinate our experiences [James] |
18973 | New opinions count as 'true' if they are assimilated to an individual's current beliefs [James] |
18984 | True ideas are those we can assimilate, validate, corroborate and verify (and false otherwise) [James] |
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] |
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] |
21762 | To grasp an existence, we must consider its non-existence [Hegel, by Houlgate] |
21977 | Nothing exists, as thinkable and expressible [Hegel] |
21760 | Thinking of nothing is not the same as simply not thinking [Hegel, by Houlgate] |
21765 | The ground of a thing is not another thing, but the first thing's substance or rational concept [Hegel, by Houlgate] |
13488 | Mass words do not have plurals, or numerical adjectives, or use 'fewer' [Hart,WD] |
22059 | Kant's thing-in-itself is just an abstraction from our knowledge; things only exist for us [Hegel, by Bowie] |
22083 | Hegel believe that the genuine categories reveal things in themselves [Hegel, by Houlgate] |
22080 | The nature of each category relates itself to another [Hegel] |
18987 | A 'thing' is simply carved out of reality for human purposes [James] |
18981 | 'Substance' is just a word for groupings and structures in experience [James] |
18974 | Truth is a species of good, being whatever proves itself good in the way of belief [James] |
21772 | In absolute knowing, the gap between object and oneself closes, producing certainty [Hegel] |
20954 | The 'absolute idea' is when all the contradictions are exhausted [Hegel, by Bowie] |
21972 | Hegel, unlike Kant, said how things appear is the same as how things are [Hegel, by Moore,AW] |
22038 | Hegel's non-subjective idealism is the unity of subjective and objective viewpoints [Hegel, by Pinkard] |
22044 | Hegel claimed his system was about the world, but it only mapped conceptual interdependence [Pinkard on Hegel] |
21464 | The Absolute is the primitive system of concepts which are actualised [Hegel, by Gardner] |
22084 | Authentic thinking and reality have the same content [Hegel] |
21975 | The absolute idea is being, imperishable life, self-knowing truth, and all truth [Hegel] |
21976 | The absolute idea is the great unity of the infinite system of concepts [Hegel, by Moore,AW] |
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] |
18989 | Pragmatism accepts any hypothesis which has useful consequences [James] |
22058 | Hegel's 'absolute idea' is the interdependence of all truths to justify any of them [Hegel, by Bowie] |
18971 | Theories are practical tools for progress, not answers to enigmas [James] |
18985 | True thoughts are just valuable instruments of action [James] |
18982 | Pragmatism says all theories are instrumental - that is, mental modes of adaptation to reality [James] |
20953 | Every concept depends on the counter-concepts of what it is not [Hegel, by Bowie] |
18975 | We return to experience with concepts, where they show us differences [James] |
13475 | The Fregean concept of GREEN is a function assigning true to green things, and false to the rest [Hart,WD] |
21763 | When we explicate the category of being, we watch a new category emerge [Hegel, by Houlgate] |
18980 | If there is a 'greatest knower', it doesn't follow that they know absolutely everything [James] |
18978 | It is hard to grasp a cosmic mind which produces such a mixture of goods and evils [James] |
18991 | If the God hypothesis works well, then it is true [James] |
18977 | The wonderful design of a woodpecker looks diabolical to its victims [James] |
18979 | Things with parts always have some structure, so they always appear to be designed [James] |
18976 | Private experience is the main evidence for God [James] |
18990 | Nirvana means safety from sense experience, and hindus and buddhists are just afraid of life [James] |