Combining Texts

All the ideas for 'The Problem of Empty Names', 'Set Theory and Its Philosophy' and 'Natural Goodness'

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

29 ideas

1. Philosophy / A. Wisdom / 1. Nature of Wisdom
22496 Wisdom only implies the knowledge achievable in any normal lifetime [Foot]
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 / F. Referring in Logic / 1. Naming / e. Empty names
18946 Unreflectively, we all assume there are nonexistents, and we can refer to them [Reimer]
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]
20. Action / C. Motives for Action / 3. Acting on Reason / a. Practical reason
23694 All criterions of practical rationality derive from goodness of will [Foot]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / b. Rational ethics
23686 Moral reason is not just neutral, because morality is part of the standard of rationality [Foot, by Hacker-Wright]
23693 Practical rationality must weigh both what is morally and what is non-morally required [Foot]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
23687 Moral virtues arise from human nature, as part of what makes us good human beings [Foot, by Hacker-Wright]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / k. Ethics from nature
22493 Sterility is a human defect, but the choice to be childless is not [Foot]
22492 Virtues are as necessary to humans as stings are to bees [Foot]
22. Metaethics / B. Value / 1. Nature of Value / b. Fact and value
22491 Moral evaluations are not separate from facts, but concern particular facts about functioning [Foot]
22. Metaethics / C. The Good / 2. Happiness / a. Nature of happiness
22497 Deep happiness usually comes from the basic things in life [Foot]
22498 Happiness is enjoying the pursuit and attainment of right ends [Foot]
23. Ethics / A. Egoism / 1. Ethical Egoism
23695 Good actions can never be justified by the good they brings to their agent [Foot]
23. Ethics / B. Contract Ethics / 5. Free Rider
22499 We all know that just pretending to be someone's friend is not the good life [Foot]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / e. Character
22495 Someone is a good person because of their rational will, not their body or memory [Foot]
23. Ethics / F. Existentialism / 7. Existential Action
22502 Refraining from murder is not made good by authenticity or self-fulfilment [Foot]