Combining Texts

All the ideas for 'Natural Goodness', 'What is so bad about Contradictions?' and 'Introduction to the Theory of Logic'

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33 ideas

1. Philosophy / A. Wisdom / 1. Nature of Wisdom
22496 Wisdom only implies the knowledge achievable in any normal lifetime [Foot]
2. Reason / B. Laws of Thought / 3. Non-Contradiction
9123 Someone standing in a doorway seems to be both in and not-in the room [Priest,G, by Sorensen]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
10888 Sets can be defined by 'enumeration', or by 'abstraction' (based on a property) [Zalabardo]
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
10889 The 'Cartesian Product' of two sets relates them by pairing every element with every element [Zalabardo]
10890 A 'partial ordering' is reflexive, antisymmetric and transitive [Zalabardo]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
10886 Determinacy: an object is either in a set, or it isn't [Zalabardo]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / l. Axiom of Specification
10887 Specification: Determinate totals of objects always make a set [Zalabardo]
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
10897 A first-order 'sentence' is a formula with no free variables [Zalabardo]
5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
10893 Γ |= φ for sentences if φ is true when all of Γ is true [Zalabardo]
10899 Γ |= φ if φ is true when all of Γ is true, for all structures and interpretations [Zalabardo]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / b. Basic connectives
10896 Propositional logic just needs ¬, and one of ∧, ∨ and → [Zalabardo]
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
10898 The semantics shows how truth values depend on instantiations of properties and relations [Zalabardo]
10902 We can do semantics by looking at given propositions, or by building new ones [Zalabardo]
5. Theory of Logic / I. Semantics of Logic / 2. Formal Truth
10892 We make a truth assignment to T and F, which may be true and false, but merely differ from one another [Zalabardo]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
10895 'Logically true' (|= φ) is true for every truth-assignment [Zalabardo]
10900 Logically true sentences are true in all structures [Zalabardo]
5. Theory of Logic / I. Semantics of Logic / 4. Satisfaction
10901 Some formulas are 'satisfiable' if there is a structure and interpretation that makes them true [Zalabardo]
10894 A sentence-set is 'satisfiable' if at least one truth-assignment makes them all true [Zalabardo]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
10903 A structure models a sentence if it is true in the model, and a set of sentences if they are all true in the model [Zalabardo]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / f. Mathematical induction
10891 If a set is defined by induction, then proof by induction can be applied to it [Zalabardo]
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
22492 Virtues are as necessary to humans as stings are to bees [Foot]
22493 Sterility is a human defect, but the choice to be childless is not [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]