Combining Philosophers

All the ideas for Moses Schönfinkel, Niccolo Machiavelli and Feferman / Feferman

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22 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 / E. Structures of Logic / 4. Variables in Logic
17699 Variables are auxiliary notions, and not part of the 'eternal' essence of logic [Schönfinkel]
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]
23. Ethics / B. Contract Ethics / 3. Promise Keeping
7127 If men are good you should keep promises, but they aren't, so you needn't [Machiavelli]
24. Political Theory / B. Nature of a State / 3. Constitutions
6309 The principle foundations of all states are good laws and good armies [Machiavelli]
24. Political Theory / C. Ruling a State / 2. Leaders / c. Despotism
6306 People are vengeful, so be generous to them, or destroy them [Machiavelli]
6305 To retain a conquered state, wipe out the ruling family, and preserve everything else [Machiavelli]
6308 A sensible conqueror does all his harmful deeds immediately, because people soon forget [Machiavelli]
25. Social Practice / E. Policies / 1. War / a. Just wars
6307 A desire to conquer, and men who do it, are always praised, or not blamed [Machiavelli]
25. Social Practice / E. Policies / 2. Religion in Society
7486 Machiavelli emancipated politics from religion [Machiavelli, by Watson]
19813 All legislators invoke God in support of extraordinary laws, because their justification is not obvious [Machiavelli]
7126 Rulers should preserve the foundations of religion, to ensure good behaviour and unity [Machiavelli]