84 ideas
| 7490 | Because of Darwin, wisdom as a definite attainable state has faded [Watson] |
| 7461 | The three key ideas are the soul, Europe, and the experiment [Watson] |
| 7464 | The big idea: imitation, the soul, experiments, God, heliocentric universe, evolution? [Watson] |
| 7465 | Babylonian thinking used analogy, rather than deduction or induction [Watson] |
| 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] |
| 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] |
| 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] |
| 6007 | If you know your father, but don't recognise your father veiled, you know and don't know the same person [Eubulides, by Dancy,R] |
| 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] |
| 6006 | If you say truly that you are lying, you are lying [Eubulides, by Dancy,R] |
| 6008 | Removing one grain doesn't destroy a heap, so a heap can't be destroyed [Eubulides, by Dancy,R] |
| 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] |
| 7466 | Mesopotamian numbers applied to specific things, and then became abstract [Watson] |
| 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] |
| 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] |
| 18174 | Cantor extended ordinals into the transfinite, and they can thus measure infinite cardinalities [Cantor, by Maddy] |
| 15893 | Cantor's theory concerns collections which can be counted, using the ordinals [Cantor, by Lavine] |
| 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] |
| 20657 | There are 23 core brain functions, with known circuit, transmitters, genes and behaviour [Watson] |
| 20656 | Traditional ideas of the mind were weakened in the 1950s by mind-influencing drugs [Watson] |
| 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] |
| 20655 | Humans have been hunter-gatherers for 99.5% of their existence [Watson] |
| 7477 | Modern democracy is actually elective oligarchy [Watson] |
| 7478 | Greek philosophers invented the concept of 'nature' as their special subject [Watson] |
| 20650 | The Uncertainty Principle implies that cause and effect can't be measured [Watson] |
| 20649 | The interference of light through two slits confirmed that it is waves [Watson] |
| 20661 | Electrons rotate in hyrogen atoms 10^13 times per second [Watson] |
| 20647 | Quantum theory explains why nature is made up of units, such as elements [Watson] |
| 20654 | Only four particles are needed for matter: up and down quark, electron, electron-neutrino [Watson] |
| 10863 | Cantor proved that three dimensions have the same number of points as one dimension [Cantor, by Clegg] |
| 20651 | The shape of molecules is important, as well as the atoms and their bonds [Watson] |
| 20652 | In 1828 the animal substance urea was manufactured from inorganic ingredients [Watson] |
| 20658 | Information is physical, and living can be seen as replicating and preserving information [Watson] |
| 7462 | DNA mutation suggests humans and chimpanzees diverged 6.6 million years ago [Watson] |
| 13465 | Only God is absolutely infinite [Cantor, by Hart,WD] |
| 7470 | During the rise of civilizations, the main gods changed from female to male [Watson] |
| 7474 | Hinduism has no founder, or prophet, or creed, or ecclesiastical structure [Watson] |
| 7480 | Monotheism was a uniquely Israelite creation within the Middle East [Watson] |
| 7479 | Modern Judaism became stabilised in 200 CE [Watson] |
| 7481 | The Israelites may have asserted the uniqueness of Yahweh to justify land claims [Watson] |
| 7471 | The Gathas (hymns) of Zoroastrianism date from about 1000 BCE [Watson] |
| 7473 | Zoroaster conceived the afterlife, judgement, heaven and hell, and the devil [Watson] |
| 7483 | Paul's early writings mention few striking episodes from Jesus' life [Watson] |
| 7484 | Jesus never intended to start a new religion [Watson] |
| 7475 | Confucius revered the spiritual world, but not the supernatural, or a personal god, or the afterlife [Watson] |
| 7476 | Taoism aims at freedom from the world, the body, the mind, and nature [Watson] |
| 7463 | The three basic ingredients of religion are: the soul, seers or priests, and ritual [Watson] |
| 7468 | In ancient Athens the souls of the dead are received by the 'upper air' [Watson] |