96 ideas
| 16606 | Original philosophers invariably seek inspiration from past thinkers [Pasnau] |
| 16604 | Philosophy consists of choosing between Plato, Aristotle and Democritus [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] |
| 16607 | Renaissance Platonism is peripheral [Pasnau] |
| 16715 | Plato only made an impact locally in 15th century Italy [Pasnau] |
| 16605 | After c.1450 all of Plato was available. Before that, only the first half of 'Timaeus' was known [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] |
| 15901 | Trying to represent curves, we study arbitrary functions, leading to the ordinals, which produces set theory [Cantor, by Lavine] |
| 13444 | Cantor's Theorem: for any set x, its power set P(x) has more members than x [Cantor, by Hart,WD] |
| 18098 | Cantor proved that all sets have more subsets than they have members [Cantor, by Bostock] |
| 15505 | If a set is 'a many thought of as one', beginners should protest against singleton sets [Cantor, by Lewis] |
| 10865 | The continuum is the powerset of the integers, which moves up a level [Cantor, by Clegg] |
| 10701 | Cantor showed that supposed contradictions in infinity were just a lack of clarity [Cantor, by Potter] |
| 13016 | The Axiom of Union dates from 1899, and seems fairly obvious [Cantor, by Maddy] |
| 14199 | Cantor's sets were just collections, but Dedekind's were containers [Cantor, by Oliver/Smiley] |
| 10082 | There are infinite sets that are not enumerable [Cantor, by Smith,P] |
| 13483 | Cantor's Paradox: the power set of the universe must be bigger than the universe, yet a subset of it [Cantor, by Hart,WD] |
| 8710 | The powerset of all the cardinal numbers is required to be greater than itself [Cantor, by Friend] |
| 15910 | Cantor named the third realm between the finite and the Absolute the 'transfinite' [Cantor, by Lavine] |
| 15905 | Cantor proved the points on a plane are in one-to-one correspondence to the points on a line [Cantor, by Lavine] |
| 9983 | Cantor took the ordinal numbers to be primary [Cantor, by Tait] |
| 17798 | Cantor presented the totality of natural numbers as finite, not infinite [Cantor, by Mayberry] |
| 9971 | Cantor introduced the distinction between cardinals and ordinals [Cantor, by Tait] |
| 9892 | Cantor showed that ordinals are more basic than cardinals [Cantor, by Dummett] |
| 14136 | A cardinal is an abstraction, from the nature of a set's elements, and from their order [Cantor] |
| 15906 | Cantor tried to prove points on a line matched naturals or reals - but nothing in between [Cantor, by Lavine] |
| 11015 | Cantor's diagonal argument proved you can't list all decimal numbers between 0 and 1 [Cantor, by Read] |
| 15903 | A real is associated with an infinite set of infinite Cauchy sequences of rationals [Cantor, by Lavine] |
| 18251 | Irrational numbers are the limits of Cauchy sequences of rational numbers [Cantor, by Lavine] |
| 15902 | Irrationals and the Dedekind Cut implied infinite classes, but they seemed to have logical difficulties [Cantor, by Lavine] |
| 15908 | It was Cantor's diagonal argument which revealed infinities greater than that of the real numbers [Cantor, by Lavine] |
| 13464 | Cantor proposes that there won't be a potential infinity if there is no actual infinity [Cantor, by Hart,WD] |
| 10112 | The naturals won't map onto the reals, so there are different sizes of infinity [Cantor, by George/Velleman] |
| 17889 | CH: An infinite set of reals corresponds 1-1 either to the naturals or to the reals [Cantor, by Koellner] |
| 8733 | The Continuum Hypothesis says there are no sets between the natural numbers and reals [Cantor, by Shapiro] |
| 13447 | Cantor: there is no size between naturals and reals, or between a set and its power set [Cantor, by Hart,WD] |
| 10883 | Cantor's Continuum Hypothesis says there is a gap between the natural and the real numbers [Cantor, by Horsten] |
| 13528 | Continuum Hypothesis: there are no sets between N and P(N) [Cantor, by Wolf,RS] |
| 9555 | Continuum Hypothesis: no cardinal greater than aleph-null but less than cardinality of the continuum [Cantor, by Chihara] |
| 15893 | Cantor's theory concerns collections which can be counted, using the ordinals [Cantor, by Lavine] |
| 18174 | Cantor extended ordinals into the transfinite, and they can thus measure infinite cardinalities [Cantor, by Maddy] |
| 18173 | Cardinality strictly concerns one-one correspondence, to test infinite sameness of size [Cantor, by Maddy] |
| 10232 | Property extensions outstrip objects, so shortage of objects caused the Caesar problem [Cantor, by Shapiro] |
| 18176 | Pure mathematics is pure set theory [Cantor] |
| 8631 | Cantor says that maths originates only by abstraction from objects [Cantor, by Frege] |
| 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] |
| 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] |
| 16617 | Corpuscularian critics of scholasticism say only substances exist [Pasnau] |
| 16628 | Corpuscularianism promised a decent account of substance [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] |
| 16580 | A substrate may be 'prime matter', which endures through every change [Pasnau] |
| 16579 | There may be different types of substrate, or temporary substrates [Pasnau] |
| 16584 | If a substrate gives causal support for change, quite a lot of the ingredients must endure [Pasnau] |
| 16596 | A substratum can't be 'bare', because it has a job to do [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] |
| 8715 | Infinities expand the bounds of the conceivable; we explore concepts to explore conceivability [Cantor, by Friend] |
| 13454 | Cantor says (vaguely) that we abstract numbers from equal sized sets [Hart,WD on Cantor] |
| 4677 | If suicide is wrong because only God disposes of our lives, it must also be wrong to save lives [Hume] |
| 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] |
| 10863 | Cantor proved that three dimensions have the same number of points as one dimension [Cantor, by Clegg] |
| 16581 | Scholastic authors agree that matter was created by God, out of nothing [Pasnau] |
| 13465 | Only God is absolutely infinite [Cantor, by Hart,WD] |
| 16642 | Transubstantion says accidents of bread and wine don't inhere in the substance [Pasnau] |