Combining Philosophers

All the ideas for Rescher,N/Oppenheim,P, Peter Koellner and Correia,F/Schnieder,B

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12 ideas

1. Philosophy / E. Nature of Metaphysics / 1. Nature of Metaphysics
Using modal logic, philosophers tried to handle all metaphysics in modal terms [Correia/Schnieder]
2. Reason / B. Laws of Thought / 2. Sufficient Reason
Why do rationalists accept Sufficient Reason, when it denies the existence of fundamental facts? [Correia/Schnieder]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner]
'Reflection principles' say the whole truth about sets can't be captured [Koellner]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
We have no argument to show a statement is absolutely undecidable [Koellner]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
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
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
Arithmetical undecidability is always settled at the next stage up [Koellner]
7. Existence / C. Structure of Existence / 1. Grounding / a. Nature of grounding
Is existential dependence by grounding, or do grounding claims arise from existential dependence? [Correia/Schnieder]
7. Existence / C. Structure of Existence / 1. Grounding / c. Grounding and explanation
Grounding is metaphysical and explanation epistemic, so keep them apart [Correia/Schnieder]
7. Existence / D. Theories of Reality / 8. Facts / a. Facts
The identity of two facts may depend on how 'fine-grained' we think facts are [Correia/Schnieder]
9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
A whole must have one characteristic, an internal relation, and a structure [Rescher/Oppenheim]