Combining Philosophers

All the ideas for Rescher,N/Oppenheim,P, Peter Koellner and Alfred North Whitehead

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12 ideas

1. Philosophy / C. History of Philosophy / 2. Ancient Philosophy / c. Classical philosophy
European philosophy consists of a series of footnotes to Plato [Whitehead]
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 / G. Quantification / 2. Domain of Quantification
With 'extensive connection', boundary elements are not included in domains [Whitehead, by Varzi]
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 / B. Change in Existence / 2. Processes
In Whitehead 'processes' consist of events beginning and ending [Whitehead, by Simons]
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]
26. Natural Theory / C. Causation / 1. Causation
Whitehead held that perception was a necessary feature of all causation [Whitehead, by Harré/Madden]
27. Natural Reality / C. Space / 3. Points in Space
Whitehead replaced points with extended regions [Whitehead, by Quine]