Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Contributions to Philosophy' and 'Internal and External Reasons'

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8 ideas

4. Formal Logic / F. Set Theory ST / 1. Set Theory

17884

Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner]

17893

'Reflection principles' say the whole truth about sets can't be captured [Koellner]

5. Theory of Logic / K. Features of Logics / 5. Incompleteness

17894

We have no argument to show a statement is absolutely undecidable [Koellner]

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity

17890

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

17887

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

17891

Arithmetical undecidability is always settled at the next stage up [Koellner]

20. Action / C. Motives for Action / 3. Acting on Reason / c. Reasons as causes

9284	Reasons are 'internal' if they give a person a motive to act, but 'external' otherwise [Williams,B]

23. Ethics / F. Existentialism / 4. Boredom

20767

Culture is now dominated by boredom, so universal it is unnoticed [Heidegger, by Aho]