27 ideas
| 8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
| 8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
| 18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
| 10855 | Actual infinities are not allowed in mathematics - only limits which may increase without bound [Gauss] |
| 8764 | Categories are the best foundation for mathematics [Shapiro] |
| 8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
| 8760 | Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro] |
| 8761 | A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro] |
| 8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
| 8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
| 8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
| 8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
| 8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
| 8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |
| 8730 | 'Impredicative' definitions refer to the thing being described [Shapiro] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 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] |
| 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] |