Combining Texts

All the ideas for 'The Courtier and the Heretic', 'Principles of Arithmetic, by a new method' and 'Concepts without Boundaries'

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11 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]
7. Existence / D. Theories of Reality / 10. Vagueness / b. Vagueness of reality
8983 If 'red' is vague, then membership of the set of red things is vague, so there is no set of red things [Sainsbury]
7. Existence / E. Categories / 2. Categorisation
8986 We should abandon classifying by pigeon-holes, and classify around paradigms [Sainsbury]
9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects
8982 Vague concepts are concepts without boundaries [Sainsbury]
8984 If concepts are vague, people avoid boundaries, can't spot them, and don't want them [Sainsbury]
8985 Boundaryless concepts tend to come in pairs, such as child/adult, hot/cold [Sainsbury]
24. Political Theory / D. Ideologies / 10. Theocracy
7825 The politics of Leibniz was the reunification of Christianity [Stewart,M]