Combining Texts

All the ideas for 'Croce and Collingwood', 'The Concept of Dread (/Anxiety)' and 'On the Question of Absolute Undecidability'

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15 ideas

4. Formal Logic / F. Set Theory ST / 1. Set Theory
Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner]
'Reflection principles' say the whole truth about sets can't be captured [Koellner]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
We have no argument to show a statement is absolutely undecidable [Koellner]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
There are at least eleven types of large cardinal, of increasing logical strength [Koellner]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
Arithmetical undecidability is always settled at the next stage up [Koellner]
20. Action / B. Preliminaries of Action / 2. Willed Action / d. Weakness of will
Socrates neglects the gap between knowing what is good and doing good [Kierkegaard, by Carlisle]
21. Aesthetics / A. Aesthetic Experience / 1. Aesthetics
By 1790 aestheticians were mainly trying to explain individual artistic genius [Kemp]
21. Aesthetics / B. Nature of Art / 4. Art as Expression
Expression can be either necessary for art, or sufficient for art (or even both) [Kemp]
We don't already know what to express, and then seek means of expressing it [Kemp]
The horror expressed in some works of art could equallly be expressed by other means [Kemp]
23. Ethics / F. Existentialism / 3. Angst
Anxiety is not a passing mood, but a response to human freedom [Kierkegaard, by Carlisle]
The ultimate in life is learning to be anxious in the right way [Kierkegaard]
Ultimate knowledge is being anxious in the right way [Kierkegaard]
Anxiety is staring into the yawning abyss of freedom [Kierkegaard]