Combining Texts

All the ideas for 'fragments/reports', 'Set Theory and Its Philosophy' and 'Eight Theories of Ethics'

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29 ideas

4. Formal Logic / F. Set Theory ST / 1. Set Theory
10702 Set theory's three roles: taming the infinite, subject-matter of mathematics, and modes of reasoning [Potter]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
10713 Usually the only reason given for accepting the empty set is convenience [Potter]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
13044 Infinity: There is at least one limit level [Potter]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
10708 Nowadays we derive our conception of collections from the dependence between them [Potter]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
13546 The 'limitation of size' principles say whether properties collectivise depends on the number of objects [Potter]
4. Formal Logic / G. Formal Mereology / 1. Mereology
10707 Mereology elides the distinction between the cards in a pack and the suits [Potter]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
10704 We can formalize second-order formation rules, but not inference rules [Potter]
5. Theory of Logic / H. Proof Systems / 3. Proof from Assumptions
10703 Supposing axioms (rather than accepting them) give truths, but they are conditional [Potter]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
10712 If set theory didn't found mathematics, it is still needed to count infinite sets [Potter]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
17882 It is remarkable that all natural number arithmetic derives from just the Peano Axioms [Potter]
8. Modes of Existence / A. Relations / 4. Formal Relations / a. Types of relation
13043 A relation is a set consisting entirely of ordered pairs [Potter]
9. Objects / B. Unity of Objects / 2. Substance / b. Need for substance
13042 If dependence is well-founded, with no infinite backward chains, this implies substances [Potter]
9. Objects / C. Structure of Objects / 8. Parts of Objects / b. Sums of parts
13041 Collections have fixed members, but fusions can be carved in innumerable ways [Potter]
10. Modality / A. Necessity / 1. Types of Modality
10709 Priority is a modality, arising from collections and members [Potter]
13. Knowledge Criteria / E. Relativism / 3. Subjectivism
6685 'Subjectivism' is an extension of relativism from the social group to the individual [Graham]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
468 Musical performance can reveal a range of virtues [Damon of Ath.]
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]
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]