77 ideas
19023 | Slippery slope arguments are challenges to show where a non-arbitrary boundary lies [Vetter] |
19033 | Deontic modalities are 'ought-to-be', for sentences, and 'ought-to-do' for predicates [Vetter] |
19032 | S5 is undesirable, as it prevents necessities from having contingent grounds [Vetter] |
19036 | The Barcan formula endorses either merely possible things, or makes the unactualised impossible [Vetter] |
15901 | Trying to represent curves, we study arbitrary functions, leading to the ordinals, which produces set theory [Cantor, by Lavine] |
18098 | Cantor proved that all sets have more subsets than they have members [Cantor, by Bostock] |
13444 | Cantor's Theorem: for any set x, its power set P(x) has more members than x [Cantor, by Hart,WD] |
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] |
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] |
11015 | Cantor's diagonal argument proved you can't list all decimal numbers between 0 and 1 [Cantor, by Read] |
15906 | Cantor tried to prove points on a line matched naturals or reals - but nothing in between [Cantor, by Lavine] |
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] |
10883 | Cantor's Continuum Hypothesis says there is a gap between the natural and the real numbers [Cantor, by Horsten] |
8733 | The Continuum Hypothesis says there are no sets between the natural numbers and reals [Cantor, by Shapiro] |
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] |
13447 | Cantor: there is no size between naturals and reals, or between a set and its power set [Cantor, by Hart,WD] |
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] |
19034 | The world is either a whole made of its parts, or a container which contains its parts [Vetter] |
19015 | Grounding can be between objects ('relational'), or between sentences ('operational') [Vetter] |
19012 | The Humean supervenience base entirely excludes modality [Vetter] |
19024 | A determinate property must be a unique instance of the determinable class [Vetter] |
19021 | I have an 'iterated ability' to learn the violin - that is, the ability to acquire that ability [Vetter] |
19016 | We should think of dispositions as 'to do' something, not as 'to do something, if ....' [Vetter] |
19017 | Nomological dispositions (unlike ordinary ones) have to be continually realised [Vetter] |
19014 | How can spatiotemporal relations be understood in dispositional terms? [Vetter] |
19030 | Why does origin matter more than development; why are some features of origin more important? [Vetter] |
19040 | We take origin to be necessary because we see possibilities as branches from actuality [Vetter] |
19008 | The modern revival of necessity and possibility treated them as special cases of quantification [Vetter] |
19029 | It is necessary that p means that nothing has the potentiality for not-p [Vetter] |
19028 | Possibilities are potentialities of actual things, but abstracted from their location [Vetter] |
19010 | All possibility is anchored in the potentiality of individual objects [Vetter] |
19013 | Possibility is a generalised abstraction from the potentiality of its bearer [Vetter] |
23705 | A potentiality may not be a disposition, but dispositions are strong potentialities [Vetter, by Friend/Kimpton-Nye] |
19009 | Potentiality does the explaining in metaphysics; we don't explain it away or reduce it [Vetter] |
19027 | Potentiality logic is modal system T. Stronger systems collapse iterations, and necessitate potentials [Vetter] |
19022 | Water has a potentiality to acquire a potentiality to break (by freezing) [Vetter] |
19031 | There are potentialities 'to ...', but possibilities are 'that ....'. [Vetter] |
19025 | Potentialities may be too weak to count as 'dispositions' [Vetter] |
19019 | Potentiality is the common genus of dispositions, abilities, and similar properties [Vetter] |
19011 | If worlds are sets of propositions, how do we know which propositions are genuinely possible? [Vetter] |
19037 | Are there possible objects which nothing has ever had the potentiality to produce? [Vetter] |
18278 | Kant showed that our perceptions are partly constructed from our concepts [Reichenbach] |
19018 | Explanations by disposition are more stable and reliable than those be external circumstances [Vetter] |
19020 | Grounding is a kind of explanation, suited to metaphysics [Vetter] |
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] |
19039 | The view that laws are grounded in substance plus external necessity doesn't suit dispositionalism [Vetter] |
19038 | Dispositional essentialism allows laws to be different, but only if the supporting properties differ [Vetter] |
10863 | Cantor proved that three dimensions have the same number of points as one dimension [Cantor, by Clegg] |
19026 | If time is symmetrical between past and future, why do they look so different? [Vetter] |
19041 | Presentists explain cross-temporal relations using surrogate descriptions [Vetter] |
13465 | Only God is absolutely infinite [Cantor, by Hart,WD] |