10 ideas
10528 | Definitions concern how we should speak, not how things are [Fine,K] |
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] |
17783 | A number is not a multitude, but a unified ratio between quantities [Newton] |
10529 | If Hume's Principle can define numbers, we needn't worry about its truth [Fine,K] |
10530 | Hume's Principle is either adequate for number but fails to define properly, or vice versa [Fine,K] |
17635 | Arithmetic can have even simpler logical premises than the Peano Axioms [Russell on Peano] |
10527 | An abstraction principle should not 'inflate', producing more abstractions than objects [Fine,K] |