107 ideas
16604 | Philosophy consists of choosing between Plato, Aristotle and Democritus [Pasnau] |
16606 | Original philosophers invariably seek inspiration from past thinkers [Pasnau] |
16586 | The commentaries of Averroes were the leading guide to Aristotle [Pasnau] |
16568 | Modernity begins in the late 12th century, with Averroes's commentaries on Aristotle [Pasnau] |
16653 | Once accidents were seen as real, 'Categories' became the major text for ontology [Pasnau] |
16704 | In 1347, the Church effectively stopped philosophy for the next 300 years [Pasnau] |
16605 | After c.1450 all of Plato was available. Before that, only the first half of 'Timaeus' was known [Pasnau] |
16607 | Renaissance Platonism is peripheral [Pasnau] |
16715 | Plato only made an impact locally in 15th century Italy [Pasnau] |
16610 | Philosophy could easily have died in 17th century, if it weren't for Descartes [Pasnau] |
16781 | The 17th century is a metaphysical train wreck [Pasnau] |
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] |
16677 | Anti-Razor: if you can't account for a truth, keep positing things until you can [Pasnau] |
5784 | In its primary and formal sense, 'true' applies to propositions, not beliefs [Russell] |
5777 | The truth or falsehood of a belief depends upon a fact to which the belief 'refers' [Russell] |
5783 | Propositions of existence, generalities, disjunctions and hypotheticals make correspondence tricky [Russell] |
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] |
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] |
16598 | Priority was a major topic of dispute for scholastics [Pasnau] |
13488 | Mass words do not have plurals, or numerical adjectives, or use 'fewer' [Hart,WD] |
16727 | In mixtures, the four elements ceased to exist, replaced by a mixed body with a form [Pasnau] |
16732 | 17th C qualities are either microphysical, or phenomenal, or powers [Pasnau] |
16733 | 17th century authors only recognised categorical properties, never dispositions [Pasnau] |
16662 | The biggest question for scholastics is whether properties are real, or modes of substances [Pasnau] |
16767 | There is no centralised power, but we still need essence for a metaphysical understanding [Pasnau] |
16788 | Instead of adding Aristotelian forms to physical stuff, one could add dispositions [Pasnau] |
16738 | Scholastics reject dispositions, because they are not actual, as forms require [Pasnau] |
16649 | Scholastics say there is a genuine thing if it is 'separable' [Pasnau] |
16785 | If you reject essences, questions of individuation become extremely difficult [Pasnau] |
16680 | Scholastics thought Quantity could be the principle of individuation [Pasnau] |
16628 | Corpuscularianism promised a decent account of substance [Pasnau] |
16617 | Corpuscularian critics of scholasticism say only substances exist [Pasnau] |
16741 | Scholastics wanted to treat Aristotelianism as physics, rather than as metaphysics [Pasnau] |
16777 | If crowds are things at all, they seem to be Substances, since they bear properties [Pasnau] |
16615 | Scholastics use 'substantia' for thick concrete entities, and for thin metaphysical ones [Pasnau] |
16775 | For corpuscularians, a substance is just its integral parts [Pasnau] |
16769 | If clay survives destruction of the statue, the statue wasn't a substance, but a mere accident [Pasnau] |
16602 | Corpuscularianism rejected not only form, but also the dependence of matter on form [Pasnau] |
16612 | Hylomorphism may not be a rival to science, but an abstract account of unity and endurance [Pasnau] |
16613 | Hylomorphism declined because scholastics made it into a testable physical theory [Pasnau] |
16747 | Scholastics made forms substantial, in a way unintended by Aristotle [Pasnau] |
16759 | Scholastics began to see substantial form more as Aristotle's 'efficient' cause [Pasnau] |
16748 | Aquinas says a substance has one form; Scotists say it has many forms [Pasnau] |
16671 | Scholastic Quantity either gives a body parts, or spreads them out in a unified way [Pasnau] |
16579 | There may be different types of substrate, or temporary substrates [Pasnau] |
16596 | A substratum can't be 'bare', because it has a job to do [Pasnau] |
16584 | If a substrate gives causal support for change, quite a lot of the ingredients must endure [Pasnau] |
16580 | A substrate may be 'prime matter', which endures through every change [Pasnau] |
16749 | Aristotelians deny that all necessary properties are essential [Pasnau] |
16694 | Typical successive things are time and motion [Pasnau] |
16583 | Weak ex nihilo says it all comes from something; strong version says the old must partly endure [Pasnau] |
5780 | The three questions about belief are its contents, its success, and its character [Russell] |
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] |
16783 | Essences must explain, so we can infer them causally from the accidents [Pasnau] |
5778 | If we object to all data which is 'introspective' we will cease to believe in toothaches [Russell] |
5779 | There are distinct sets of psychological and physical causal laws [Russell] |
13475 | The Fregean concept of GREEN is a function assigning true to green things, and false to the rest [Hart,WD] |
5781 | Our important beliefs all, if put into words, take the form of propositions [Russell] |
5782 | A proposition expressed in words is a 'word-proposition', and one of images an 'image-proposition' [Russell] |
5776 | A proposition is what we believe when we believe truly or falsely [Russell] |
16609 | Atomists say causation is mechanical collisions, and all true qualities are microscopic [Pasnau] |
16603 | In the 17th C matter became body, and was then studied by science [Pasnau] |
16592 | Atomism is the commonest version of corpuscularianism, but isn't required by it [Pasnau] |
16750 | If there are just arrangements of corpuscles, where are the boundaries between substances? [Pasnau] |
16722 | Scholastic causation is by changes in the primary qualities of hot, cold, wet, dry [Pasnau] |
16760 | Substantial forms were a step towards scientific essentialism [Pasnau] |
16581 | Scholastic authors agree that matter was created by God, out of nothing [Pasnau] |
16642 | Transubstantion says accidents of bread and wine don't inhere in the substance [Pasnau] |