Combining Texts

All the ideas for 'fragments/reports', 'Principles of Arithmetic, by a new method' and 'Equality and Partiality'

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14 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 / E. Objects over Time / 8. Continuity of Rivers
579 Cratylus said you couldn't even step into the same river once [Cratylus, by Aristotle]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
578 Cratylus decided speech was hopeless, and his only expression was the movement of a finger [Cratylus, by Aristotle]
20. Action / C. Motives for Action / 5. Action Dilemmas / c. Omissions
6479 Noninterference requires justification as much as interference does [Nagel]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / a. Preconditions for ethics
6450 Morality must be motivating, and not because of pre-moral motives [Nagel]
23. Ethics / B. Contract Ethics / 6. Game Theory
6447 Game theory misses out the motivation arising from the impersonal standpoint [Nagel]
23. Ethics / D. Deontological Ethics / 3. Universalisability
6446 In ethics we abstract from our identity, but not from our humanity [Nagel]
23. Ethics / D. Deontological Ethics / 4. Categorical Imperative
6477 I can only universalise a maxim if everyone else could also universalise it [Nagel]
24. Political Theory / D. Ideologies / 6. Liberalism / c. Liberal equality
6448 A legitimate system is one accepted as both impartial and reasonably partial [Nagel]
25. Social Practice / B. Equalities / 2. Political equality
6478 Democracy is opposed to equality, if the poor are not a majority [Nagel]