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Full Idea
Dedekind and Peano define the number series as the series of successors to the number zero, according to five postulates.
Gist of Idea
Numbers have been defined in terms of 'successors' to the concept of 'zero'
Source
report of Giuseppe Peano (works [1890]) by Simon Blackburn - Oxford Dictionary of Philosophy p.279
Book Ref
Benardete,José A.: 'Metaphysics: The Logical Approach' [OUP 1989], p.279
| 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] |
| 3338 | Numbers have been defined in terms of 'successors' to the concept of 'zero' [Peano, by Blackburn] |
| 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] |