Combining Philosophers

All the ideas for Pindar, Nicolas Malebranche and Peter Koellner

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10 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]
8. Modes of Existence / B. Properties / 8. Properties as Modes
16669 Everything that exists is either a being, or some mode of a being [Malebranche]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / j. Ethics by convention
6017 Nomos is king [Pindar]
26. Natural Theory / C. Causation / 9. General Causation / d. Causal necessity
12726 In a true cause we see a necessary connection [Malebranche]
2594 A true cause must involve a necessary connection between cause and effect [Malebranche]