Combining Philosophers

All the ideas for Samuel Alexander, T Adorno / M Horkheimer and Feferman / Feferman

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17 ideas

1. Philosophy / H. Continental Philosophy / 5. Critical Theory
Adorno and Horkheimer subjected the Enlightenment to 'critical theory' analysis [Adorno/Horkheimer, by Finlayson]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
Cantor's theories needed the Axiom of Choice, but it has led to great controversy [Feferman/Feferman]
The Axiom of Choice is consistent with the other axioms of set theory [Feferman/Feferman]
The Trichotomy Principle is equivalent to the Axiom of Choice [Feferman/Feferman]
Axiom of Choice: a set exists which chooses just one element each of any set of sets [Feferman/Feferman]
Platonist will accept the Axiom of Choice, but others want criteria of selection or definition [Feferman/Feferman]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
A structure is a 'model' when the axioms are true. So which of the structures are models? [Feferman/Feferman]
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
Löwenheim-Skolem says if the sentences are countable, so is the model [Feferman/Feferman]
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
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
'Recursion theory' concerns what can be solved by computing machines [Feferman/Feferman]
Both Principia Mathematica and Peano Arithmetic are undecidable [Feferman/Feferman]
7. Existence / A. Nature of Existence / 6. Criterion for Existence
To be is to have causal powers [Alexander,S]
17. Mind and Body / A. Mind-Body Dualism / 6. Epiphenomenalism
Epiphenomenalism makes the mind totally pointless [Alexander,S]
Epiphenomenalism is like a pointless nobleman, kept for show, but soon to be abolished [Alexander,S]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / b. Rational ethics
De Sade said it was impossible to rationally argue against murder [Adorno/Horkheimer]