Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'works' and 'works'

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9 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 / 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]

9. Objects / C. Structure of Objects / 8. Parts of Objects / a. Parts of objects

8249	Class membership is not transitive, unlike being part of a part of the whole [Lesniewski, by George/Van Evra]

11. Knowledge Aims / A. Knowledge / 4. Belief / d. Cause of beliefs

20945

Belief is no more rational than is tasting and smelling [Hamann]

28. God / A. Divine Nature / 2. Divine Nature

7666	God is not a mathematician, but a poet [Hamann, by Berlin]