Combining Texts

All the ideas for 'Conspectus libelli (book outline)', 'Alfred Tarski: life and logic' and 'Against Euthanasia'

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18 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]
9. Objects / B. Unity of Objects / 1. Unifying an Object / b. Unifying aggregates
12699 A body would be endless disunited parts, if it did not have a unifying form or soul [Leibniz]
9. Objects / C. Structure of Objects / 2. Hylomorphism / d. Form as unifier
12700 Form or soul gives unity and duration; matter gives multiplicity and change [Leibniz]
10. Modality / D. Knowledge of Modality / 2. A Priori Contingent
12736 If we understand God and his choices, we have a priori knowledge of contingent truths [Leibniz, by Garber]
17. Mind and Body / A. Mind-Body Dualism / 3. Panpsychism
12698 Every body contains a kind of sense and appetite, or a soul [Leibniz]
25. Social Practice / F. Life Issues / 2. Euthanasia
4050 We only allow voluntary euthanasia to someone who is both sane and crazed by pain [Kamisar]
4051 People will volunteer for euthanasia because they think other people want them dead [Kamisar]