Combining Philosophers

All the ideas for Hermarchus, Feferman / Feferman and Stephen Boulter

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21 ideas

1. Philosophy / E. Nature of Metaphysics / 4. Metaphysics as Science
22138 Science rests on scholastic metaphysics, not on Hume, Kant or Carnap [Boulter]
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]
8. Modes of Existence / D. Universals / 2. Need for Universals
22134 Thoughts are general, but the world isn't, so how can we think accurately? [Boulter]
10. Modality / A. Necessity / 6. Logical Necessity
22150 Logical possibility needs the concepts of the proposition to be adequate [Boulter]
14. Science / A. Basis of Science / 3. Experiment
22139 Experiments don't just observe; they look to see what interventions change the natural order [Boulter]
14. Science / B. Scientific Theories / 1. Scientific Theory
22136 Science begins with sufficient reason, de-animation, and the importance of nature [Boulter]
15. Nature of Minds / C. Capacities of Minds / 1. Faculties
22135 Our concepts can never fully capture reality, but simplification does not falsify [Boulter]
19. Language / E. Analyticity / 3. Analytic and Synthetic
22152 Aristotelians accept the analytic-synthetic distinction [Boulter]
22. Metaethics / B. Value / 1. Nature of Value / b. Fact and value
22156 The facts about human health are the measure of the values in our lives [Boulter]
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]