Combining Texts

All the ideas for '04: Gospel of St John', 'Alfred Tarski: life and logic' and 'Moral Thinking: Its Levels,Method and Point'

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19 ideas

2. Reason / A. Nature of Reason / 2. Logos
In the beginning was the Word, and the Word was with God, and the word was God [John]
3. Truth / A. Truth Problems / 2. Defining Truth
Jesus said he bore witness to the truth. Pilate asked, What is truth? [John]
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]
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]
The Trichotomy Principle is equivalent to the Axiom of Choice [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 Theorem, and Gödel's completeness of first-order logic, the earliest model theory [Feferman/Feferman]
Löwenheim-Skolem says if the sentences are countable, so is the model [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]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / i. Prescriptivism
Hare says I acquire an agglomeration of preferences by role-reversal, leading to utilitarianism [Hare, by Williams,B]
If we have to want the preferences of the many, we have to abandon our own deeply-held views [Williams,B on Hare]
If morality is to be built on identification with the preferences of others, I must agree with their errors [Williams,B on Hare]
A judgement is presciptive if we expect it to be acted on [Hare]
23. Ethics / B. Contract Ethics / 8. Contract Strategies
By far the easiest way of seeming upright is to be upright [Hare]