Combining Texts

All the ideas for 'fragments/reports', 'Of the original contract' and 'Alfred Tarski: life and logic'

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21 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
10159 Löwenheim-Skolem Theorem, and Gödel's completeness of first-order logic, the earliest model theory [Feferman/Feferman]
10160 Löwenheim-Skolem says if the sentences are countable, so is the model [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]
9. Objects / E. Objects over Time / 8. Continuity of Rivers
579 Cratylus said you couldn't even step into the same river once [Cratylus, by Aristotle]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
578 Cratylus decided speech was hopeless, and his only expression was the movement of a finger [Cratylus, by Aristotle]
20. Action / C. Motives for Action / 5. Action Dilemmas / a. Dilemmas
21103 Moral questions can only be decided by common opinion [Hume]
24. Political Theory / A. Basis of a State / 3. Natural Values / b. Natural equality
21099 People must have agreed to authority, because they are naturally equal, prior to education [Hume]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / c. Social contract
21100 The idea that society rests on consent or promises undermines obedience [Hume]
20495 We no more give 'tacit assent' to the state than a passenger carried on board a ship while asleep [Hume]
21101 The people would be amazed to learn that government arises from their consent [Hume]
25. Social Practice / A. Freedoms / 7. Freedom to leave
6703 Poor people lack the knowledge or wealth to move to a different state [Hume]
25. Social Practice / C. Rights / 4. Property rights
21102 We all know that the history of property is founded on injustices [Hume]