15 ideas
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] |
13412 | Obtaining numbers by abstraction is impossible - there are too many; only a rule could give them, in order [Benacerraf] |
13413 | We must explain how we know so many numbers, and recognise ones we haven't met before [Benacerraf] |
13411 | If numbers are basically the cardinals (Frege-Russell view) you could know some numbers in isolation [Benacerraf] |
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] |
13415 | An adequate account of a number must relate it to its series [Benacerraf] |
23061 | Free atheism should start by questioning its faith in humanity [Gray] |
23057 | Gnosticism has a supreme creator God, giving way to a possibly hostile Demiurge [Gray] |
23056 | Judaism only became monotheistic around 550 BCE [Gray] |
23055 | Christians introduced the idea that a religion needs a creed [Gray] |
23058 | Buddhism has no divinity or souls, and the aim is to lose the illusion of a self [Gray] |