101 ideas
19693 | There is practical wisdom (for action), and theoretical wisdom (for deep understanding) [Aristotle, by Whitcomb] |
1575 | For Aristotle logos is essentially the ability to talk rationally about questions of value [Roochnik on Aristotle] |
1589 | Aristotle is the supreme optimist about the ability of logos to explain nature [Roochnik on Aristotle] |
8200 | Aristotelian definitions aim to give the essential properties of the thing defined [Aristotle, by Quine] |
4385 | Aristotelian definition involves first stating the genus, then the differentia of the thing [Aristotle, by Urmson] |
9449 | The plausible Barcan formula implies modality in the actual world [Bird] |
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] |
10701 | Cantor showed that supposed contradictions in infinity were just a lack of clarity [Cantor, by Potter] |
10865 | The continuum is the powerset of the integers, which moves up a level [Cantor, by Clegg] |
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] |
13282 | Aristotle relativises the notion of wholeness to different measures [Aristotle, by Koslicki] |
4730 | For Aristotle, the subject-predicate structure of Greek reflected a substance-accident structure of reality [Aristotle, by O'Grady] |
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] |
8733 | The Continuum Hypothesis says there are no sets between the natural numbers and reals [Cantor, by Shapiro] |
17889 | CH: An infinite set of reals corresponds 1-1 either to the naturals or to the reals [Cantor, by Koellner] |
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] |
9501 | If all existents are causally active, that excludes abstracta and causally isolated objects [Bird] |
9500 | If naturalism refers to supervenience, that leaves necessary entities untouched [Bird] |
9502 | There might be just one fundamental natural property [Bird] |
9477 | Categorical properties are not modally fixed, but change across possible worlds [Bird] |
9490 | The categoricalist idea is that a property is only individuated by being itself [Bird] |
9495 | If we abstractly define a property, that doesn't mean some object could possess it [Bird] |
9492 | Categoricalists take properties to be quiddities, with no essential difference between them [Bird] |
9503 | To name an abundant property is either a Fregean concept, or a simple predicate [Bird] |
14540 | Only real powers are fundamental [Bird, by Mumford/Anjum] |
9450 | If all properties are potencies, and stimuli and manifestation characterise them, there is a regress [Bird] |
9498 | The essence of a potency involves relations, e.g. mass, to impressed force and acceleration [Bird] |
9474 | A disposition is finkish if a time delay might mean the manifestation fizzles out [Bird] |
9475 | A robust pot attached to a sensitive bomb is not fragile, but if struck it will easily break [Bird] |
9499 | Megarian actualists deny unmanifested dispositions [Bird] |
9486 | Why should a universal's existence depend on instantiation in an existing particular? [Bird] |
9472 | Resemblance itself needs explanation, presumably in terms of something held in common [Bird] |
13276 | The unmoved mover and the soul show Aristotelian form as the ultimate mereological atom [Aristotle, by Koslicki] |
13277 | The 'form' is the recipe for building wholes of a particular kind [Aristotle, by Koslicki] |
9482 | If the laws necessarily imply p, that doesn't give a new 'nomological' necessity [Bird] |
9481 | Logical necessitation is not a kind of necessity; George Orwell not being Eric Blair is not a real possibility [Bird] |
9505 | Empiricist saw imaginability and possibility as close, but now they seem remote [Bird] |
9491 | Haecceitism says identity is independent of qualities and without essence [Bird] |
5991 | For Aristotle, knowledge is of causes, and is theoretical, practical or productive [Aristotle, by Code] |
11239 | The notion of a priori truth is absent in Aristotle [Aristotle, by Politis] |
23312 | Aristotle is a rationalist, but reason is slowly acquired through perception and experience [Aristotle, by Frede,M] |
16111 | Aristotle wants to fit common intuitions, and therefore uses language as a guide [Aristotle, by Gill,ML] |
16971 | Plato says sciences are unified around Forms; Aristotle says they're unified around substance [Aristotle, by Moravcsik] |
11243 | Aristotelian explanations are facts, while modern explanations depend on human conceptions [Aristotle, by Politis] |
9487 | We can't reject all explanations because of a regress; inexplicable A can still explain B [Bird] |
3320 | Aristotle's standard analysis of species and genus involves specifying things in terms of something more general [Aristotle, by Benardete,JA] |
12000 | Aristotle regularly says that essential properties explain other significant properties [Aristotle, by Kung] |
23300 | Aristotle and the Stoics denied rationality to animals, while Platonists affirmed it [Aristotle, by Sorabji] |
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] |
11240 | The notion of analytic truth is absent in Aristotle [Aristotle, by Politis] |
6559 | Aristotle never actually says that man is a rational animal [Aristotle, by Fogelin] |
11150 | It is the mark of an educated mind to be able to entertain an idea without accepting it [Aristotle] |
3037 | Aristotle said the educated were superior to the uneducated as the living are to the dead [Aristotle, by Diog. Laertius] |
8660 | There are potential infinities (never running out), but actual infinity is incoherent [Aristotle, by Friend] |
12058 | Aristotle's matter can become any other kind of matter [Aristotle, by Wiggins] |
9493 | We should explain causation by powers, not powers by causation [Bird] |
9494 | Singularism about causes is wrong, as the universals involved imply laws [Bird] |
9507 | Laws are explanatory relationships of things, which supervene on their essences [Bird] |
9488 | Laws are either disposition regularities, or relations between properties [Bird] |
9496 | That other diamonds are hard does not explain why this one is [Bird] |
9479 | Dispositional essentialism says laws (and laws about laws) are guaranteed regularities [Bird] |
9473 | Laws cannot offer unified explanations if they don't involve universals [Bird] |
9484 | If the universals for laws must be instantiated, a vanishing particular could destroy a law [Bird] |
9506 | Salt necessarily dissolves in water, because of the law which makes the existence of salt possible [Bird] |
23713 | Most laws supervene on fundamental laws, which are explained by basic powers [Bird, by Friend/Kimpton-Nye] |
9489 | Essentialism can't use conditionals to explain regularities, because of possible interventions [Bird] |
10863 | Cantor proved that three dimensions have the same number of points as one dimension [Cantor, by Clegg] |
9504 | The relational view of space-time doesn't cover times and places where things could be [Bird] |
13465 | Only God is absolutely infinite [Cantor, by Hart,WD] |
22729 | The concepts of gods arose from observing the soul, and the cosmos [Aristotle, by Sext.Empiricus] |