Combining Philosophers

All the ideas for Jonathan Barnes, Peter Koellner and James Baillie

expand these ideas     |    start again     |     specify just one area for these philosophers

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 / D. Assumptions for Logic / 4. Identity in Logic
3299 In logic identity involves reflexivity (x=x), symmetry (if x=y, then y=x) and transitivity (if x=y and y=z, then x=z) [Baillie]
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]
18. Thought / E. Abstraction / 8. Abstractionism Critique
9073 Abstraction from an ambiguous concept like 'mole' will define them as the same [Barnes,J]
9074 Abstraction cannot produce the concept of a 'game', as there is no one common feature [Barnes,J]
9072 Defining concepts by abstractions will collect together far too many attributes from entities [Barnes,J]