93 ideas
23948 | Wisdom needs both thought and passion, with each reflecting on the other [Solomon] |
23942 | Philosophy is creating an intellectual conceptual structure for life [Solomon] |
23945 | Reason is actually passions, guided by perspicacious reflection [Solomon] |
15901 | Trying to represent curves, we study arbitrary functions, leading to the ordinals, which produces set theory [Cantor, by Lavine] |
15946 | Cantor developed sets from a progression into infinity by addition, multiplication and exponentiation [Cantor, by Lavine] |
9616 | A set is a collection into a whole of distinct objects of our intuition or thought [Cantor] |
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] |
17831 | Cantor gives informal versions of ZF axioms as ways of getting from one set to another [Cantor, by Lake] |
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] |
15911 | Ordinals are generated by endless succession, followed by a limit ordinal [Cantor, by Lavine] |
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] |
15896 | Cantor needed Power Set for the reals, but then couldn't count the new collections [Cantor, by Lavine] |
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] |
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] |
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] |
9992 | The 'extension of a concept' in general may be quantitatively completely indeterminate [Cantor] |
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] |
23957 | We often trust our intuitions as rational, despite their lack of reflection [Solomon] |
23943 | Distinguishing reason from passion is based on an archaic 'faculty' theory [Solomon] |
23952 | I say bodily chemistry and its sensations have nothing to do with emotions [Solomon] |
23954 | Emotions are judgements about ourselves, and our place in the world [Solomon] |
23960 | Emotions are defined by their objects [Solomon] |
23961 | The heart of an emotion is its judgement of values and morality [Solomon] |
23965 | Emotions can be analysed under fifteen headings [Solomon] |
23959 | Some emotions are externally directed, others internally [Solomon] |
23936 | It is only our passions which give our lives meaning [Solomon] |
23963 | Which emotions we feel depends on our sense of our own powers [Solomon] |
23946 | The passions are subjective, concerning what is important to me, rather than facts [Solomon] |
23940 | Emotions are strategies for maximising our sense of dignity and self-esteem [Solomon] |
23949 | Passions exist as emotions, moods and desires, which all generate meaning [Solomon] |
23956 | The Myth of the Passions says they are irrational, uncontrolled and damaging [Solomon] |
23953 | Feeling is a superficial aspect of emotion, and may be indeterminate, or even absent [Solomon] |
23964 | There are no 'basic' emotions, only socially prevalent ones [Solomon] |
23937 | It is reason which needs the anchorage of passions, rather than vice versa [Solomon] |
23947 | Dividing ourselves into confrontational reason and passion destroys our harmonious whole [Solomon] |
23958 | The supposed irrationality of our emotions is often tactless or faulty expression of them [Solomon] |
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] |
9145 | We form the image of a cardinal number by a double abstraction, from the elements and from their order [Cantor] |
23944 | Emotions are our life force, and the source of most of our values [Solomon] |
23962 | Lovers adopt the interests of their beloved, rather than just valuing them [Solomon] |
23941 | 'Absurdity' is just the result of our wrong choices in life [Solomon] |
23955 | Ideologies are mythologies which guide our actions [Solomon] |
20624 | Work degrades into heat, but not vice versa [Close] |
20623 | First Law: energy can change form, but is conserved overall [Close] |
20625 | Third Law: total order and minimum entropy only occurs at absolute zero [Close] |
20622 | All motions are relative and ambiguous, but acceleration is the same in all inertial frames [Close] |
20628 | The electric and magnetic are tightly linked, and viewed according to your own motion [Close] |
20635 | The general relativity equations relate curvature in space-time to density of energy-momentum [Close] |
20642 | Photon exchange drives the electro-magnetic force [Close] |
20627 | Electric fields have four basic laws (two by Gauss, one by Ampère, one by Faraday) [Close] |
20630 | Light isn't just emitted in quanta called photons - light is photons [Close] |
20637 | In general relativity the energy and momentum of photons subjects them to gravity [Close] |
20629 | Electro-magnetic waves travel at light speed - so light is electromagnetism! [Close] |
20632 | In QED, electro-magnetism exists in quantum states, emitting and absorbing electrons [Close] |
20639 | Quantum fields contain continual rapid creation and disappearance [Close] |
20641 | Electrons get their mass by interaction with the Higgs field [Close] |
20631 | Dirac showed how electrons conform to special relativity [Close] |
20626 | Modern theories of matter are grounded in heat, work and energy [Close] |
20633 | The Higgs field is an electroweak plasma - but we don't know what stuff it consists of [Close] |
10863 | Cantor proved that three dimensions have the same number of points as one dimension [Cantor, by Clegg] |
20640 | Space-time is indeterminate foam over short distances [Close] |
13465 | Only God is absolutely infinite [Cantor, by Hart,WD] |