Combining Philosophers

All the ideas for Tom Clark, Jim Baggott and Feferman / Feferman

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20 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]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / d. Purpose of consciousness
4741 A very powerful computer might have its operations restricted by the addition of consciousness [Clark,T]
27. Natural Reality / A. Classical Physics / 2. Thermodynamics / a. Energy
24162 Planck introduced the idea that energy can be quantized [Baggott]
27. Natural Reality / B. Modern Physics / 2. Electrodynamics / b. Fields
21731 Fields can be 'scalar', or 'vector', or 'tensor', or 'spinor' [Baggott]
21730 A 'field' is a property with a magnitude, distributed across all of space and time [Baggott]
27. Natural Reality / B. Modern Physics / 2. Electrodynamics / c. Electrons
24163 Free electrons have clouds of virtual particles, arising from field interaction [Baggott]
27. Natural Reality / B. Modern Physics / 4. Standard Model / a. Concept of matter
24161 Thermodynamics sees nature as a continuous flow of energy, as radiation and as substance [Baggott]
27. Natural Reality / B. Modern Physics / 4. Standard Model / b. Standard model
21732 The current standard model requires 61 particles [Baggott]
27. Natural Reality / B. Modern Physics / 4. Standard Model / c. Particle properties
24160 Particle measurements don't seem to reflect their reality [Baggott]