Combining Philosophers

All the ideas for Speussipus, Peter Koellner and Carl Ginet

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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]
9. Objects / B. Unity of Objects / 2. Substance / c. Types of substance
594 Speusippus suggested underlying principles for every substance, and ended with a huge list [Speussipus, by Aristotle]
13. Knowledge Criteria / A. Justification Problems / 1. Justification / a. Justification issues
8836 Must all justification be inferential? [Ginet]
8837 Inference cannot originate justification, it can only transfer it from premises to conclusion [Ginet]
28. God / C. Attitudes to God / 5. Atheism
2632 Speusippus said things were governed by some animal force rather than the gods [Speussipus, by Cicero]