Combining Texts

All the ideas for 'fragments/reports', 'The Methods of Ethics (7th edn)' and 'Continuity and Irrational Numbers'

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9 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
We want the essence of continuity, by showing its origin in arithmetic [Dedekind]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / i. Reals from cuts
A cut between rational numbers creates and defines an irrational number [Dedekind]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic
Arithmetic is just the consequence of counting, which is the successor operation [Dedekind]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / l. Limits
If x changes by less and less, it must approach a limit [Dedekind]
16. Persons / F. Free Will / 2. Sources of Free Will
If we say that freedom depends on rationality, the irrational actions are not free [Sidgwick]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
Musical performance can reveal a range of virtues [Damon of Ath.]
23. Ethics / A. Egoism / 1. Ethical Egoism
Self-interest is not rational, if the self is just a succession of memories and behaviour [Sidgwick, by Gray]
23. Ethics / E. Utilitarianism / 1. Utilitarianism
It is self-evident (from the point of view of the Universe) that no individual has more importance than another [Sidgwick]
24. Political Theory / D. Ideologies / 4. Social Utilitarianism
Sidwick argues for utilitarian institutions, rather than actions [Sidgwick, by Tuckness/Wolf]