10 ideas
10882 | Predicative definitions only refer to entities outside the defined collection [Horsten] |
10884 | A theory is 'categorical' if it has just one model up to isomorphism [Horsten] |
10885 | Computer proofs don't provide explanations [Horsten] |
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] |
15653 | We can add Reflexion Principles to Peano Arithmetic, which assert its consistency or soundness [Halbach on Peano] |
10881 | The concept of 'ordinal number' is set-theoretic, not arithmetical [Horsten] |
17635 | Arithmetic can have even simpler logical premises than the Peano Axioms [Russell on Peano] |
15710 | Bohr explained the periodic table and chemical properties of elements, using the quantum atom [Kumar] |