Combining Texts

All the ideas for 'Phenomenalism', 'Infinity: Quest to Think the Unthinkable' and 'Natural Goodness'

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36 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 / 2. Mechanics of Set Theory / b. Terminology of ST
10859 A set is 'well-ordered' if every subset has a first element [Clegg]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets
10857 Set theory made a closer study of infinity possible [Clegg]
10864 Any set can always generate a larger set - its powerset, of subsets [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
10872 Extensionality: Two sets are equal if and only if they have the same elements [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / c. Axiom of Pairing II
10875 Pairing: For any two sets there exists a set to which they both belong [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / d. Axiom of Unions III
10876 Unions: There is a set of all the elements which belong to at least one set in a collection [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
10878 Infinity: There exists a set of the empty set and the successor of each element [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / g. Axiom of Powers VI
10877 Powers: All the subsets of a given set form their own new powerset [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
10879 Choice: For every set a mechanism will choose one member of any non-empty subset [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / k. Axiom of Existence
10871 Axiom of Existence: there exists at least one set [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / l. Axiom of Specification
10874 Specification: a condition applied to a set will always produce a new set [Clegg]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
10880 Mathematics can be 'pure' (unapplied), 'real' (physically grounded); or 'applied' (just applicable) [Clegg]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
10861 Beyond infinity cardinals and ordinals can come apart [Clegg]
10860 An ordinal number is defined by the set that comes before it [Clegg]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
10854 Transcendental numbers can't be fitted to finite equations [Clegg]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / k. Imaginary numbers
10858 By adding an axis of imaginary numbers, we get the useful 'number plane' instead of number line [Clegg]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / l. Zero
10853 Either lack of zero made early mathematics geometrical, or the geometrical approach made zero meaningless [Clegg]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
10866 Cantor's account of infinities has the shaky foundation of irrational numbers [Clegg]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
10869 The Continuum Hypothesis is independent of the axioms of set theory [Clegg]
10862 The 'continuum hypothesis' says aleph-one is the cardinality of the reals [Clegg]
11. Knowledge Aims / C. Knowing Reality / 2. Phenomenalism
2614 Modern phenomenalism holds that objects are logical constructions out of sense-data [Ayer]
12. Knowledge Sources / B. Perception / 4. Sense Data / a. Sense-data theory
2615 The concept of sense-data allows us to discuss appearances without worrying about reality [Ayer]
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]