Combining Philosophers

All the ideas for Anaxarchus, Peter Koellner and Paul M. Churchland

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12 ideas

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]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius]
17. Mind and Body / E. Mind as Physical / 3. Eliminativism
Folk psychology may not be reducible, but that doesn't make it false [Kirk,R on Churchland,PM]
Eliminative materialism says folk psychology will be replaced, not reduced [Churchland,PM]
18. Thought / A. Modes of Thought / 4. Folk Psychology
If folk psychology gives a network of causal laws, that fits neatly with functionalism [Churchland,PM]
Many mental phenomena are totally unexplained by folk psychology [Churchland,PM]
Folk psychology never makes any progress, and is marginalised by modern science [Churchland,PM]