Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'A Completeness Theorem in Modal Logic' and 'On Fate ('De fato')'

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13 ideas

4. Formal Logic / D. Modal Logic ML / 1. Modal Logic

10163

Propositional modal logic has been proved to be complete [Kripke, by Feferman/Feferman]

4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / a. Systems of modal logic

10760

With possible worlds, S4 and S5 are sound and complete, but S1-S3 are not even sound [Kripke, by Rossberg]

4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula

16189

The variable domain approach to quantified modal logic invalidates the Barcan Formula [Kripke, by Simchen]

15132

The Barcan formulas fail in models with varying domains [Kripke, by Williamson]

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 / D. Assumptions for Logic / 1. Bivalence

21677

How can the not-true fail to be false, or the not-false fail to be true? [Cicero]

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]

19. Language / F. Communication / 1. Rhetoric

21667

Oratory and philosophy are closely allied; orators borrow from philosophy, and ornament it [Cicero]

22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / g. Moral responsibility

21678

If desire is not in our power then neither are choices, so we should not be praised or punished [Cicero]