Combining Texts

All the ideas for 'Introduction to the Theory of Logic', 'Nietzsche and Philosophy' and 'Virtues and Vices'

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27 ideas

1. Philosophy / A. Wisdom / 1. Nature of Wisdom
22396 We take courage, temperance, wisdom and justice as moral, but Aristotle takes wisdom as intellectual [Foot]
1. Philosophy / A. Wisdom / 2. Wise People
22397 Wisdom is open to all, and not just to the clever or well trained [Foot]
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
10894 A sentence-set is 'satisfiable' if at least one truth-assignment makes them all true [Zalabardo]
10901 Some formulas are 'satisfiable' if there is a structure and interpretation that makes them 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]
7. Existence / A. Nature of Existence / 3. Being / c. Becoming
21899 There is no being beyond becoming [Deleuze]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / a. Nature of virtue
22402 Most people think virtues can be displayed in bad actions [Foot]
23145 Virtues are intended to correct design flaws in human beings [Foot, by Driver]
22401 Actions can be in accordance with virtue, but without actually being virtuous [Foot]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / b. Basis of virtue
22398 Virtues are corrective, to resist temptation or strengthen motivation [Foot]
23. Ethics / C. Virtue Theory / 3. Virtues / b. Temperance
22403 Temperance is not a virtue if it results from timidity or excessive puritanism [Foot]
23. Ethics / C. Virtue Theory / 3. Virtues / d. Courage
22400 Courage overcomes the fears which should be overcome, and doesn't overvalue personal safety [Foot]