Combining Texts

All the ideas for 'Alfred Tarski: life and logic', 'Ambitious, yet modest, Metaphysics' and 'Aristotle and Kant on the Source of Value'

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20 ideas

1. Philosophy / E. Nature of Metaphysics / 5. Metaphysics beyond Science
16415 Esoteric metaphysics aims to be top science, investigating ultimate reality [Hofweber]
1. Philosophy / E. Nature of Metaphysics / 7. Against Metaphysics
16413 Science has discovered properties of things, so there are properties - so who needs metaphysics? [Hofweber]
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 / G. Quantification / 1. Quantification
16416 The quantifier in logic is not like the ordinary English one (which has empty names, non-denoting terms etc) [Hofweber]
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]
22. Metaethics / B. Value / 1. Nature of Value / f. Ultimate value
18228 An end can't be an ultimate value just because it is useless! [Korsgaard]
18225 If we can't reason about value, we can reason about the unconditional source of value [Korsgaard]
22. Metaethics / C. The Good / 1. Goodness / b. Types of good
18224 Goodness is given either by a psychological state, or the attribution of a property [Korsgaard]
23. Ethics / C. Virtue Theory / 3. Virtues / g. Contemplation
18233 Contemplation is final because it is an activity which is not a process [Korsgaard]
18226 For Aristotle, contemplation consists purely of understanding [Korsgaard]