Combining Texts

All the ideas for 'talk', 'Principles of Arithmetic, by a new method' and 'Essentialists and Essentialism'

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7 ideas

6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
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]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
15653 We can add Reflexion Principles to Peano Arithmetic, which assert its consistency or soundness [Halbach on Peano]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
17635 Arithmetic can have even simpler logical premises than the Peano Axioms [Russell on Peano]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / a. Essence as necessary properties
14380 The distinction between necessary and essential properties can be ignored [Rocca]
13. Knowledge Criteria / E. Relativism / 2. Knowledge as Convention
1556 By nature people are close to one another, but culture drives them apart [Hippias]