Combining Philosophers

All the ideas for Hermarchus, Arnauld / Nicole and Feferman / Feferman

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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
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]
7. Existence / C. Structure of Existence / 7. Abstract/Concrete / b. Levels of abstraction
10502 We can rise by degrees through abstraction, with higher levels representing more things [Arnauld,A/Nicole,P]
12. Knowledge Sources / B. Perception / 3. Representation
18258 We can only know the exterior world via our ideas [Arnauld,A/Nicole,P]
14. Science / D. Explanation / 2. Types of Explanation / k. Explanations by essence
16784 Forms make things distinct and explain the properties, by pure form, or arrangement of parts [Arnauld,A/Nicole,P]
15. Nature of Minds / C. Capacities of Minds / 3. Abstraction by mind
10499 We know by abstraction because we only understand composite things a part at a time [Arnauld,A/Nicole,P]
15. Nature of Minds / C. Capacities of Minds / 5. Generalisation by mind
10501 A triangle diagram is about all triangles, if some features are ignored [Arnauld,A/Nicole,P]
15. Nature of Minds / C. Capacities of Minds / 6. Idealisation
10500 No one denies that a line has width, but we can just attend to its length [Arnauld,A/Nicole,P]
25. Social Practice / F. Life Issues / 6. Animal Rights
6005 Animals are dangerous and nourishing, and can't form contracts of justice [Hermarchus, by Sedley]