13 ideas
12452 | Our dislike of contradiction in logic is a matter of psychology, not mathematics [Brouwer] |
17884 | Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner] |
17893 | 'Reflection principles' say the whole truth about sets can't be captured [Koellner] |
17894 | We have no argument to show a statement is absolutely undecidable [Koellner] |
12451 | Scientific laws largely rest on the results of counting and measuring [Brouwer] |
17890 | There are at least eleven types of large cardinal, of increasing logical strength [Koellner] |
17887 | PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner] |
17891 | Arithmetical undecidability is always settled at the next stage up [Koellner] |
12454 | Intuitionists only accept denumerable sets [Brouwer] |
12453 | Neo-intuitionism abstracts from the reuniting of moments, to intuit bare two-oneness [Brouwer] |
3291 | Emergent properties appear at high levels of complexity, but aren't explainable by the lower levels [Nagel] |
10117 | Intuitonists in mathematics worried about unjustified assertion, as well as contradiction [Brouwer, by George/Velleman] |
3290 | Given the nature of heat and of water, it is literally impossible for water not to boil at the right heat [Nagel] |