Combining Texts

All the ideas for 'fragments/reports', 'On the Question of Absolute Undecidability' and 'Essays on Active Powers 3: Princs of action'

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11 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]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
Musical performance can reveal a range of virtues [Damon of Ath.]
22. Metaethics / C. The Good / 1. Goodness / g. Consequentialism
If an attempted poisoning results in benefits, we still judge the agent a poisoner [Reid]
23. Ethics / B. Contract Ethics / 2. Golden Rule
We shouldn't do to others what would be a wrong to us in similar circumstances [Reid]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / b. Basis of virtue
To be virtuous, we must care about duty [Reid]
23. Ethics / C. Virtue Theory / 3. Virtues / e. Honour
Every worthy man has a principle of honour, and knows what is honourable [Reid]