Combining Texts

All the ideas for 'fragments/reports', 'Either/Or: a fragment of life' and 'Alfred Tarski: life and logic'

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22 ideas

1. Philosophy / D. Nature of Philosophy / 7. Despair over Philosophy
22087 Philosophy fails to articulate the continual becoming of existence [Kierkegaard, by Carlisle]
3. Truth / A. Truth Problems / 8. Subjective Truth
5651 Traditional views of truth are tautologies, and truth is empty without a subject [Kierkegaard, by Scruton]
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]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
468 Musical performance can reveal a range of virtues [Damon of Ath.]
23. Ethics / F. Existentialism / 2. Nihilism
22090 For me time stands still, and I with it [Kierkegaard, by Carlisle]
23. Ethics / F. Existentialism / 4. Boredom
9305 The plebeians bore others; only the nobility bore themselves [Kierkegaard]
23. Ethics / F. Existentialism / 5. Existence-Essence
5650 Reason is just abstractions, so our essence needs a subjective 'leap of faith' [Kierkegaard, by Scruton]
23. Ethics / F. Existentialism / 6. Authentic Self
22095 There are aesthetic, ethical and religious subjectivity [Kierkegaard, by Carlisle]
23. Ethics / F. Existentialism / 7. Existential Action
20747 What matters is not right choice, but energy, earnestness and pathos in the choosing [Kierkegaard]
24. Political Theory / D. Ideologies / 7. Communitarianism / b. Against communitarianism
22091 Kierkegaard prioritises the inward individual, rather than community [Kierkegaard, by Carlisle]
29. Religion / D. Religious Issues / 1. Religious Commitment / e. Fideism
22088 Faith is like a dancer's leap, going up to God, but also back to earth [Kierkegaard, by Carlisle]