Combining Texts

All the ideas for 'Clitophon', 'Letters to Thomas Burnett' and 'Principles of Arithmetic, by a new method'

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8 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 / B. Unity of Objects / 2. Substance / a. Substance
13197 The notion of substance is one of the keys to true philosophy [Leibniz]
22. Metaethics / B. Value / 2. Values / f. Altruism
1590 The just man does not harm his enemies, but benefits everyone [Plato]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / c. Essence and laws
13198 Gravity is within matter because of its structure, and it can be explained. [Leibniz]