Combining Philosophers

All the ideas for Thrasymachus, Isaiah and Peter Koellner

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10 ideas

1. Philosophy / D. Nature of Philosophy / 2. Invocation to Philosophy

7493	Let us reason together, saith the Lord [Isaiah]

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]

27. Natural Reality / E. Cosmology / 1. Cosmology

7608	The world is established, and cannot be moved [Isaiah]

28. God / A. Divine Nature / 1. God

7343	Beside me there is no God [Isaiah]

28. God / C. Attitudes to God / 3. Deism

1558	Clearly the gods ignore human affairs, or they would have given us justice [Thrasymachus]