85 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] |
16677 | Anti-Razor: if you can't account for a truth, keep positing things until you can [Pasnau] |
10482 | The logic of ZF is classical first-order predicate logic with identity [Boolos] |
10492 | A few axioms of set theory 'force themselves on us', but most of them don't [Boolos] |
18192 | Do the Replacement Axioms exceed the iterative conception of sets? [Boolos, by Maddy] |
7785 | The use of plurals doesn't commit us to sets; there do not exist individuals and collections [Boolos] |
10485 | Naïve sets are inconsistent: there is no set for things that do not belong to themselves [Boolos] |
10484 | The iterative conception says sets are formed at stages; some are 'earlier', and must be formed first [Boolos] |
13547 | Limitation of Size is weak (Fs only collect is something the same size does) or strong (fewer Fs than objects) [Boolos, by Potter] |
10699 | Does a bowl of Cheerios contain all its sets and subsets? [Boolos] |
14249 | Boolos reinterprets second-order logic as plural logic [Boolos, by Oliver/Smiley] |
10225 | Monadic second-order logic might be understood in terms of plural quantifiers [Boolos, by Shapiro] |
10830 | Second-order logic metatheory is set-theoretic, and second-order validity has set-theoretic problems [Boolos] |
10736 | Boolos showed how plural quantifiers can interpret monadic second-order logic [Boolos, by Linnebo] |
10780 | Any sentence of monadic second-order logic can be translated into plural first-order logic [Boolos, by Linnebo] |
10829 | A sentence can't be a truth of logic if it asserts the existence of certain sets [Boolos] |
10697 | Identity is clearly a logical concept, and greatly enhances predicate calculus [Boolos] |
10832 | '∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed [Boolos] |
13671 | Second-order quantifiers are just like plural quantifiers in ordinary language, with no extra ontology [Boolos, by Shapiro] |
10267 | We should understand second-order existential quantifiers as plural quantifiers [Boolos, by Shapiro] |
10698 | Plural forms have no more ontological commitment than to first-order objects [Boolos] |
7806 | Boolos invented plural quantification [Boolos, by Benardete,JA] |
10834 | Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences [Boolos] |
13841 | Why should compactness be definitive of logic? [Boolos, by Hacking] |
10491 | Infinite natural numbers is as obvious as infinite sentences in English [Boolos] |
10483 | Mathematics and science do not require very high orders of infinity [Boolos] |
10833 | Many concepts can only be expressed by second-order logic [Boolos] |
10490 | Mathematics isn't surprising, given that we experience many objects as abstract [Boolos] |
16598 | Priority was a major topic of dispute for scholastics [Pasnau] |
16727 | In mixtures, the four elements ceased to exist, replaced by a mixed body with a form [Pasnau] |
10700 | First- and second-order quantifiers are two ways of referring to the same things [Boolos] |
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] |
10488 | It is lunacy to think we only see ink-marks, and not word-types [Boolos] |
10487 | I am a fan of abstract objects, and confident of their existence [Boolos] |
10489 | We deal with abstract objects all the time: software, poems, mistakes, triangles.. [Boolos] |
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] |
16783 | Essences must explain, so we can infer them causally from the accidents [Pasnau] |
8693 | An 'abstraction principle' says two things are identical if they are 'equivalent' in some respect [Boolos] |
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] |
1513 | The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus] |