Combining Texts

All the ideas for 'Clitophon', 'Aristotle and Kant on the Source of Value' and 'Principles of Arithmetic, by a new method'

expand these ideas     |    start again     |     specify just one area for these texts

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]
22. Metaethics / B. Value / 1. Nature of Value / f. Ultimate value
18228 An end can't be an ultimate value just because it is useless! [Korsgaard]
18225 If we can't reason about value, we can reason about the unconditional source of value [Korsgaard]
22. Metaethics / B. Value / 2. Values / f. Altruism
1590 The just man does not harm his enemies, but benefits everyone [Plato]
22. Metaethics / C. The Good / 1. Goodness / b. Types of good
18224 Goodness is given either by a psychological state, or the attribution of a property [Korsgaard]
23. Ethics / C. Virtue Theory / 3. Virtues / g. Contemplation
18233 Contemplation is final because it is an activity which is not a process [Korsgaard]
18226 For Aristotle, contemplation consists purely of understanding [Korsgaard]