Combining Philosophers

All the ideas for Paul M. Pietroski, Geoffrey Gorham and Feferman / Feferman

expand these ideas     |    start again     |     specify just one area for these philosophers

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]
14. Science / A. Basis of Science / 6. Falsification
22190 If a theory is more informative it is less probable [Gorham]
22189 Why abandon a theory if you don't have a better one? [Gorham]
14. Science / B. Scientific Theories / 1. Scientific Theory
22192 Is Newton simpler with universal simultaneity, or Einstein simpler without absolute time? [Gorham]
22194 Structural Realism says mathematical structures persist after theory rejection [Gorham]
22195 Structural Realists must show the mathematics is both crucial and separate [Gorham]
14. Science / B. Scientific Theories / 3. Instrumentalism
22197 Theories aren't just for organising present experience if they concern the past or future [Gorham]
22196 For most scientists their concepts are not just useful, but are meant to be true and accurate [Gorham]
14. Science / D. Explanation / 2. Types of Explanation / d. Consilience
22193 Consilience makes the component sciences more likely [Gorham]
19. Language / B. Reference / 5. Speaker's Reference
21650 No language is semantically referential; it all occurs at the level of thought or utterance [Pietroski, by Hofweber]
26. Natural Theory / A. Speculations on Nature / 1. Nature
22198 Aristotelian physics has circular celestial motion and linear earthly motion [Gorham]