Combining Texts

All the ideas for 'fragments/reports', 'The Philosophy of Mathematics' and 'Eight Theories of Ethics'

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22 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
9193 ZF set theory has variables which range over sets, 'equals' and 'member', and extensionality [Dummett]
9194 The main alternative to ZF is one which includes looser classes as well as sets [Dummett]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
9195 Intuitionists reject excluded middle, not for a third value, but for possibility of proof [Dummett]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
9186 First-order logic concerns objects; second-order adds properties, kinds, relations and functions [Dummett]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
9187 Logical truths and inference are characterized either syntactically or semantically [Dummett]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
9191 Ordinals seem more basic than cardinals, since we count objects in sequence [Dummett]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
9192 The number 4 has different positions in the naturals and the wholes, with the same structure [Dummett]
13. Knowledge Criteria / E. Relativism / 3. Subjectivism
6685 'Subjectivism' is an extension of relativism from the social group to the individual [Graham]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / g. Moral responsibility
6699 The chain of consequences may not be the same as the chain of responsibility [Graham]
22. Metaethics / C. The Good / 1. Goodness / g. Consequentialism
6698 Negative consequences are very hard (and possibly impossible) to assess [Graham]
22. Metaethics / C. The Good / 1. Goodness / i. Moral luck
6700 We can't criticise people because of unforeseeable consequences [Graham]
23. Ethics / A. Egoism / 1. Ethical Egoism
6704 Egoism submits to desires, but cannot help form them [Graham]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / h. Right feelings
6701 Rescue operations need spontaneous benevolence, not careful thought [Graham]
23. Ethics / D. Deontological Ethics / 4. Categorical Imperative
6693 'What if everybody did that?' rather misses the point as an objection to cheating [Graham]
23. Ethics / F. Existentialism / 1. Existentialism
6691 It is more plausible to say people can choose between values, than that they can create them [Graham]
23. Ethics / F. Existentialism / 2. Nihilism
6688 Life is only absurd if you expected an explanation and none turns up [Graham]
23. Ethics / F. Existentialism / 5. Existence-Essence
6705 Existentialism may transcend our nature, unlike eudaimonism [Graham]
23. Ethics / F. Existentialism / 6. Authentic Self
6690 A standard problem for existentialism is the 'sincere Nazi' [Graham]
23. Ethics / F. Existentialism / 7. Existential Action
6689 The key to existentialism: the way you make choices is more important than what you choose [Graham]
28. God / A. Divine Nature / 1. God
6011 There is a remote first god (the Good), and a second god who organises the material world [Numenius, by O'Meara]
29. Religion / D. Religious Issues / 1. Religious Commitment / a. Religious Belief
6706 The great religions are much more concerned with the religious life than with ethics [Graham]
29. Religion / D. Religious Issues / 2. Immortality / a. Immortality
6709 Western religion saves us from death; Eastern religion saves us from immortality [Graham]