Combining Texts

All the ideas for 'Locke on Essences and Kinds', 'Philosophical Letters from England' and 'Principles of Arithmetic, by a new method'

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10 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 / 13. Nominal Essence
15642 If kinds depend only on what can be observed, many underlying essences might produce the same kind [Eagle]
15645 Nominal essence are the observable properties of things [Eagle]
15643 Nominal essence mistakenly gives equal weight to all underlying properties that produce appearances [Eagle]
23. Ethics / B. Contract Ethics / 2. Golden Rule
7844 The Golden Rule is accepted everywhere, and gives a fixed target for morality [Voltaire]
26. Natural Theory / B. Natural Kinds / 4. Source of Kinds
15641 Kinds are fixed by the essential properties of things - the properties that make it that kind of thing [Eagle]