Combining Texts

All the ideas for 'A Short History of Ethics', 'A Mathematical Introduction to Logic (2nd)' and 'The Ages of the World'

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42 ideas

1. Philosophy / B. History of Ideas / 4. Early European Thought
8013 In the Reformation, morality became unconditional but irrational, individually autonomous, and secular [MacIntyre]
1. Philosophy / B. History of Ideas / 5. Later European Thought
8021 The Levellers and the Diggers mark a turning point in the history of morality [MacIntyre]
4. Formal Logic / B. Propositional Logic PL / 3. Truth Tables
9724 Until the 1960s the only semantics was truth-tables [Enderton]
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / a. Symbols of ST
9703 'dom R' indicates the 'domain' of objects having a relation [Enderton]
9705 'fld R' indicates the 'field' of all objects in the relation [Enderton]
9704 'ran R' indicates the 'range' of objects being related to [Enderton]
9710 We write F:A→B to indicate that A maps into B (the output of F on A is in B) [Enderton]
9707 'F(x)' is the unique value which F assumes for a value of x [Enderton]
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
9712 A relation is 'symmetric' on a set if every ordered pair has the relation in both directions [Enderton]
9713 A relation is 'transitive' if it can be carried over from two ordered pairs to a third [Enderton]
9699 The 'powerset' of a set is all the subsets of a given set [Enderton]
9700 Two sets are 'disjoint' iff their intersection is empty [Enderton]
9702 A 'domain' of a relation is the set of members of ordered pairs in the relation [Enderton]
9701 A 'relation' is a set of ordered pairs [Enderton]
9706 A 'function' is a relation in which each object is related to just one other object [Enderton]
9708 A function 'maps A into B' if the relating things are set A, and the things related to are all in B [Enderton]
9709 A function 'maps A onto B' if the relating things are set A, and the things related to are set B [Enderton]
9711 A relation is 'reflexive' on a set if every member bears the relation to itself [Enderton]
9714 A relation satisfies 'trichotomy' if all pairs are either relations, or contain identical objects [Enderton]
9717 A set is 'dominated' by another if a one-to-one function maps the first set into a subset of the second [Enderton]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / e. Equivalence classes
9715 An 'equivalence relation' is a reflexive, symmetric and transitive binary relation [Enderton]
9716 We 'partition' a set into distinct subsets, according to each relation on its objects [Enderton]
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
9722 Inference not from content, but from the fact that it was said, is 'conversational implicature' [Enderton]
5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence
9718 Validity is either semantic (what preserves truth), or proof-theoretic (following procedures) [Enderton]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
9721 A logical truth or tautology is a logical consequence of the empty set [Enderton]
5. Theory of Logic / I. Semantics of Logic / 4. Satisfaction
9994 A truth assignment to the components of a wff 'satisfy' it if the wff is then True [Enderton]
5. Theory of Logic / K. Features of Logics / 3. Soundness
9719 A proof theory is 'sound' if its valid inferences entail semantic validity [Enderton]
5. Theory of Logic / K. Features of Logics / 4. Completeness
9720 A proof theory is 'complete' if semantically valid inferences entail proof-theoretic validity [Enderton]
5. Theory of Logic / K. Features of Logics / 6. Compactness
9995 Proof in finite subsets is sufficient for proof in an infinite set [Enderton]
5. Theory of Logic / K. Features of Logics / 7. Decidability
9996 Expressions are 'decidable' if inclusion in them (or not) can be proved [Enderton]
5. Theory of Logic / K. Features of Logics / 8. Enumerability
9997 For a reasonable language, the set of valid wff's can always be enumerated [Enderton]
10. Modality / B. Possibility / 8. Conditionals / f. Pragmatics of conditionals
9723 Sentences with 'if' are only conditionals if they can read as A-implies-B [Enderton]
15. Nature of Minds / A. Nature of Mind / 2. Psuche
8006 When Aristotle speaks of soul he means something like personality [MacIntyre]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / j. Ethics by convention
8002 Sophists don't distinguish a person outside one social order from someone outside all order [MacIntyre]
22. Metaethics / B. Value / 1. Nature of Value / b. Fact and value
8012 The value/fact logical gulf is misleading, because social facts involve values [MacIntyre]
22. Metaethics / C. The Good / 2. Happiness / b. Eudaimonia
8005 'Happiness' is a bad translation of 'eudaimonia', which includes both behaving and faring well [MacIntyre]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / e. Character
20957 We don't choose our characters, yet we still claim credit for the actions our characters perform [Schelling]
23. Ethics / C. Virtue Theory / 3. Virtues / c. Justice
8001 'Dikaiosune' is justice, but also fairness and personal integrity [MacIntyre]
23. Ethics / D. Deontological Ethics / 2. Duty
8023 My duties depend on my identity, which depends on my social relations [MacIntyre]
24. Political Theory / A. Basis of a State / 3. Natural Values / a. Natural freedom
8022 I am naturally free if I am not tied to anyone by a contract [MacIntyre]
25. Social Practice / C. Rights / 1. Basis of Rights
8031 Fans of natural rights or laws can't agree on what the actual rights or laws are [MacIntyre]
29. Religion / B. Monotheistic Religion / 5. Bible
8008 The Bible is a story about God in which humans are incidental characters [MacIntyre]