Combining Philosophers

All the ideas for Hermarchus, Dean W. Zimmerman and Feferman / Feferman

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18 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]
8. Modes of Existence / D. Universals / 3. Instantiated Universals
10197 An immanent universal is wholly present in more than one place [Zimmerman,DW]
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
10198 If only two indiscernible electrons exist, future differences must still be possible [Zimmerman,DW]
10199 Discernible differences at different times may just be in counterparts [Zimmerman,DW]
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]
27. Natural Reality / D. Time / 1. Nature of Time / g. Growing block
14610 Neither 'moving spotlight' nor 'growing block' views explain why we care what is present or past [Zimmerman,DW]
27. Natural Reality / D. Time / 2. Passage of Time / e. Tensed (A) series
14608 A-theorists, unlike B-theorists, believe some sort of objective distinction between past, present and future [Zimmerman,DW]