53 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] |
| 16519 | No one can conceive of a possible substance, apart from those which God has created [Arnauld] |
| 10859 | A set is 'well-ordered' if every subset has a first element [Clegg] |
| 10857 | Set theory made a closer study of infinity possible [Clegg] |
| 10864 | Any set can always generate a larger set - its powerset, of subsets [Clegg] |
| 10872 | Extensionality: Two sets are equal if and only if they have the same elements [Clegg] |
| 10875 | Pairing: For any two sets there exists a set to which they both belong [Clegg] |
| 10876 | Unions: There is a set of all the elements which belong to at least one set in a collection [Clegg] |
| 10878 | Infinity: There exists a set of the empty set and the successor of each element [Clegg] |
| 10877 | Powers: All the subsets of a given set form their own new powerset [Clegg] |
| 10879 | Choice: For every set a mechanism will choose one member of any non-empty subset [Clegg] |
| 10871 | Axiom of Existence: there exists at least one set [Clegg] |
| 10874 | Specification: a condition applied to a set will always produce a new set [Clegg] |
| 10880 | Mathematics can be 'pure' (unapplied), 'real' (physically grounded); or 'applied' (just applicable) [Clegg] |
| 10861 | Beyond infinity cardinals and ordinals can come apart [Clegg] |
| 10860 | An ordinal number is defined by the set that comes before it [Clegg] |
| 10854 | Transcendental numbers can't be fitted to finite equations [Clegg] |
| 10858 | By adding an axis of imaginary numbers, we get the useful 'number plane' instead of number line [Clegg] |
| 10853 | Either lack of zero made early mathematics geometrical, or the geometrical approach made zero meaningless [Clegg] |
| 7466 | Mesopotamian numbers applied to specific things, and then became abstract [Watson] |
| 10866 | Cantor's account of infinities has the shaky foundation of irrational numbers [Clegg] |
| 10869 | The Continuum Hypothesis is independent of the axioms of set theory [Clegg] |
| 10862 | The 'continuum hypothesis' says aleph-one is the cardinality of the reals [Clegg] |
| 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] |
| 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] |
| 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] |
| 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] |
| 7479 | Modern Judaism became stabilised in 200 CE [Watson] |
| 7481 | The Israelites may have asserted the uniqueness of Yahweh to justify land claims [Watson] |
| 7480 | Monotheism was a uniquely Israelite creation within the Middle East [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] |
| 7484 | Jesus never intended to start a new religion [Watson] |
| 7483 | Paul's early writings mention few striking episodes from Jesus' life [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] |