Combining Texts

All the ideas for 'Science and Method', 'Alfred Tarski: life and logic' and 'The Virtues and Human Nature'

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19 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
10147 The Axiom of Choice is consistent with the other axioms of set theory [Feferman/Feferman]
10148 Axiom of Choice: a set exists which chooses just one element each of any set of sets [Feferman/Feferman]
10149 Platonist will accept the Axiom of Choice, but others want criteria of selection or definition [Feferman/Feferman]
10150 The Trichotomy Principle is equivalent to the Axiom of Choice [Feferman/Feferman]
10146 Cantor's theories needed the Axiom of Choice, but it has led to great controversy [Feferman/Feferman]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
10158 A structure is a 'model' when the axioms are true. So which of the structures are models? [Feferman/Feferman]
10162 Tarski and Vaught established the equivalence relations between first-order structures [Feferman/Feferman]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
10160 Löwenheim-Skolem says if the sentences are countable, so is the model [Feferman/Feferman]
10159 Löwenheim-Skolem Theorem, and Gödel's completeness of first-order logic, the earliest model theory [Feferman/Feferman]
5. Theory of Logic / K. Features of Logics / 4. Completeness
10161 If a sentence holds in every model of a theory, then it is logically derivable from the theory [Feferman/Feferman]
5. Theory of Logic / K. Features of Logics / 7. Decidability
10156 'Recursion theory' concerns what can be solved by computing machines [Feferman/Feferman]
10155 Both Principia Mathematica and Peano Arithmetic are undecidable [Feferman/Feferman]
6. Mathematics / A. Nature of Mathematics / 2. Geometry
10245 One geometry cannot be more true than another [Poincaré]
20. Action / B. Preliminaries of Action / 1. Intention to Act / a. Nature of intentions
23146 Motives produce intentions, which lead to actions [Driver]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / a. Nature of virtue
23147 Good intentions are not necessary for virtue [Driver]
23144 Virtue should be defined by consequences, not by states of mind [Driver]
23148 Virtues are character traits or dispositions which produce good consequences for others [Driver]
23150 Control of pregnancy and knowledge of paternity have downgraded chastity [Driver]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
23149 If generosity systematically turned recipients into parasites, it wouldn't be a virtue [Driver]