Combining Texts

All the ideas for 'fragments/reports', 'Review of Parsons (1983)' and 'On the Question of Absolute Undecidability'

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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]

6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics

18198

Mathematics is part of science; transfinite mathematics I take as mostly uninterpreted [Quine]

9. Objects / E. Objects over Time / 8. Continuity of Rivers

579	Cratylus said you couldn't even step into the same river once [Cratylus, by Aristotle]

13. Knowledge Criteria / D. Scepticism / 1. Scepticism

578	Cratylus decided speech was hopeless, and his only expression was the movement of a finger [Cratylus, by Aristotle]