14 ideas
| 4037 | Ockham's Razor is the principle that we need reasons to believe in entities [Mellor/Oliver] |
| 10304 | Very few things in set theory remain valid in intuitionist mathematics [Bernays] |
| 3338 | Numbers have been defined in terms of 'successors' to the concept of 'zero' [Peano, by Blackburn] |
| 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] |
| 5897 | 0 is a non-successor number, all successors are numbers, successors can't duplicate, if P(n) and P(n+1) then P(all-n) [Peano, by Flew] |
| 15653 | We can add Reflexion Principles to Peano Arithmetic, which assert its consistency or soundness [Halbach on Peano] |
| 10303 | Restricted Platonism is just an ideal projection of a domain of thought [Bernays] |
| 17635 | Arithmetic can have even simpler logical premises than the Peano Axioms [Russell on Peano] |
| 10306 | Mathematical abstraction just goes in a different direction from logic [Bernays] |
| 4027 | Properties are respects in which particular objects may be alike or differ [Mellor/Oliver] |
| 4029 | Nominalists ask why we should postulate properties at all [Mellor/Oliver] |
| 4039 | Abstractions lack causes, effects and spatio-temporal locations [Mellor/Oliver] |