12 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] |
17890 | There are at least eleven types of large cardinal, of increasing logical strength [Koellner] |
13949 | All models of Peano axioms are isomorphic, so the models all seem equally good for natural numbers [Cartwright,R on Peano] |
18113 | PA concerns any entities which satisfy the axioms [Peano, by Bostock] |
17634 | Peano axioms not only support arithmetic, but are also fairly obvious [Peano, by Russell] |
17887 | PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner] |
15653 | We can add Reflexion Principles to Peano Arithmetic, which assert its consistency or soundness [Halbach on Peano] |
17891 | Arithmetical undecidability is always settled at the next stage up [Koellner] |
17635 | Arithmetic can have even simpler logical premises than the Peano Axioms [Russell on Peano] |
1556 | By nature people are close to one another, but culture drives them apart [Hippias] |