Combining Philosophers

All the ideas for Critolaus, Pindar and Peter Koellner

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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]

22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / j. Ethics by convention

6017	Nomos is king [Pindar]

22. Metaethics / C. The Good / 2. Happiness / b. Eudaimonia

5996	Critolaus redefined Aristotle's moral aim as fulfilment instead of happiness [Critolaus, by White,SA]