Combining Texts

All the ideas for 'reports', 'On the Question of Absolute Undecidability' and 'Letters to Foucher'

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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]

8. Modes of Existence / C. Powers and Dispositions / 4. Powers as Essence

13095

Essence is primitive force, or a law of change [Leibniz]

10. Modality / A. Necessity / 8. Transcendental Necessity

3016	Even the gods cannot strive against necessity [Pittacus, by Diog. Laertius]

26. Natural Theory / C. Causation / 9. General Causation / d. Causal necessity

2117	The connection in events enables us to successfully predict the future, so there must be a constant cause [Leibniz]