Combining Texts

All the ideas for 'Socrates: Ironist and Moral Philosopher', 'Metaphysics: contemporary introduction' and 'Alfred Tarski: life and logic'

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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]
8. Modes of Existence / B. Properties / 13. Tropes / b. Critique of tropes
4483 If abstract terms are sets of tropes, 'being a unicorn' and 'being a griffin' turn out identical [Loux]
8. Modes of Existence / D. Universals / 1. Universals
4481 Austere nominalists insist that the realist's universals lack the requisite independent identifiability [Loux]
4477 Universals come in hierarchies of generality [Loux]
8. Modes of Existence / E. Nominalism / 1. Nominalism / a. Nominalism
4482 Austere nominalism has to take a host of things (like being red, or human) as primitive [Loux]
8. Modes of Existence / E. Nominalism / 1. Nominalism / c. Nominalism about abstracta
4478 Nominalism needs to account for abstract singular terms like 'circularity'. [Loux]
9. Objects / A. Existence of Objects / 5. Individuation / c. Individuation by location
4480 Times and places are identified by objects, so cannot be used in a theory of object-identity [Loux]
25. Social Practice / D. Justice / 3. Punishment / b. Retribution for crime
1658 In early Greece the word for punishment was also the word for vengeance [Vlastos]