more on this theme | more from this thinker
Full Idea
Peano's premises are not the ultimate logical premises of arithmetic. Simpler premises and simpler primitive ideas are to be had by carrying our analysis on into symbolic logic.
Gist of Idea
Arithmetic can have even simpler logical premises than the Peano Axioms
Source
comment on Giuseppe Peano (Principles of Arithmetic, by a new method [1889], p.276) by Bertrand Russell - Regressive Method for Premises in Mathematics p.276
Book Ref
Russell,Bertrand: 'Essays in Analysis', ed/tr. Lackey,Douglas [George Braziller 1973], p.276
Related Idea
Idea 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] |
| 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] |
| 17635 | Arithmetic can have even simpler logical premises than the Peano Axioms [Russell on Peano] |