10 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] |
18189 | ZFC could contain a contradiction, and it can never prove its own consistency [MacLane] |
17894 | We have no argument to show a statement is absolutely undecidable [Koellner] |
16901 | The equivalent algebra model of geometry loses some essential spatial meaning [Burge] |
17890 | There are at least eleven types of large cardinal, of increasing logical strength [Koellner] |
16902 | Peano arithmetic requires grasping 0 as a primitive number [Burge] |
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] |
16892 | Is apriority predicated mainly of truths and proofs, or of human cognition? [Burge] |