Combining Philosophers

All the ideas for Stilpo, Feferman / Feferman and Lawrence M. Krauss

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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 / 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]
7. Existence / C. Structure of Existence / 2. Reduction
21110 An understanding of the most basic physics should explain all of the subject's mysteries [Krauss]
7. Existence / C. Structure of Existence / 6. Fundamentals / c. Monads
21105 In 1676 it was discovered that water is teeming with life [Krauss]
27. Natural Reality / B. Modern Physics / 1. Relativity / a. Special relativity
21109 Space itself can expand (and separate its contents) at faster than light speeds [Krauss]
27. Natural Reality / B. Modern Physics / 1. Relativity / b. General relativity
21104 General Relativity: the density of energy and matter determines curvature and gravity [Krauss]
27. Natural Reality / B. Modern Physics / 2. Electrodynamics / d. Quantum mechanics
21107 Uncertainty says that energy can be very high over very short time periods [Krauss]
27. Natural Reality / B. Modern Physics / 4. Standard Model / e. Protons
21106 Most of the mass of a proton is the energy in virtual particles (rather than the quarks) [Krauss]
27. Natural Reality / C. Space / 2. Space
21112 Empty space contains a continual flux of brief virtual particles [Krauss]
27. Natural Reality / E. Cosmology / 3. The Beginning
21108 The universe is precisely 13.72 billion years old [Krauss]
27. Natural Reality / E. Cosmology / 10. Multiverse
21111 It seems likely that cosmic inflation is eternal, and this would make a multiverse inevitable [Krauss]
28. God / C. Attitudes to God / 5. Atheism
3029 Stilpo said if Athena is a daughter of Zeus, then a statue is only the child of a sculptor, and so is not a god [Stilpo, by Diog. Laertius]