Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'talk' and 'Intro to 'Philosophical Essays''

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9 ideas

1. Philosophy / D. Nature of Philosophy / 1. Philosophy

9786	Philosophers working like teams of scientists is absurd, yet isolation is hard [Cartwright,R]

2. Reason / A. Nature of Reason / 6. Coherence

9784	A false proposition isn't truer because it is part of a coherent system [Cartwright,R]

2. Reason / A. Nature of Reason / 9. Limits of Reason

1403	A rational donkey would starve to death between two totally identical piles of hay [Buridan, by PG]

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]