Combining Texts

All the ideas for 'Clitophon', 'Introductions to Utilitarianism and its Critics' and 'Believing the Axioms I'

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18 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
13011 New axioms are being sought, to determine the size of the continuum [Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
13013 The Axiom of Extensionality seems to be analytic [Maddy]
13014 Extensional sets are clearer, simpler, unique and expressive [Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
13021 The Axiom of Infinity states Cantor's breakthrough that launched modern mathematics [Maddy]
13022 Infinite sets are essential for giving an account of the real numbers [Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / g. Axiom of Powers VI
13023 The Power Set Axiom is needed for, and supported by, accounts of the continuum [Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
13024 Efforts to prove the Axiom of Choice have failed [Maddy]
13025 Modern views say the Choice set exists, even if it can't be constructed [Maddy]
13026 A large array of theorems depend on the Axiom of Choice [Maddy]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
13019 The Iterative Conception says everything appears at a stage, derived from the preceding appearances [Maddy]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
13018 Limitation of Size is a vague intuition that over-large sets may generate paradoxes [Maddy]
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 / g. Consequentialism
3785 You can't separate acts from the people performing them [Glover]
22. Metaethics / C. The Good / 1. Goodness / h. Good as benefit
3786 Aggression in defence may be beneficial but morally corrupting [Glover]
23. Ethics / D. Deontological Ethics / 1. Deontology
3784 Duty prohibits some acts, whatever their consequences [Glover]
23. Ethics / E. Utilitarianism / 1. Utilitarianism
3782 Satisfaction of desires is not at all the same as achieving happiness [Glover, by PG]
23. Ethics / E. Utilitarianism / 5. Rule Utilitarianism
3787 Rule-utilitarianism is either act-utilitarianism, or not really utilitarian [Glover]
24. Political Theory / A. Basis of a State / 2. Population / a. Human population
3783 How can utilitarianism decide the ideal population size? [Glover]