Combining Texts

All the ideas for 'Space and Time', 'A Completeness Theorem in Modal Logic' and 'The Identity of Indiscernibles'

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9 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 / 4. Axioms for Sets / j. Axiom of Choice IX

10196

The Axiom of Choice needs a criterion of choice [Black]

9. Objects / A. Existence of Objects / 5. Individuation / b. Individuation by properties

10194

Two things can only be distinguished by a distinct property or a distinct relation [Black]

9. Objects / F. Identity among Objects / 5. Self-Identity

10193

The 'property' of self-identity is uselessly tautological [Black]

9. Objects / F. Identity among Objects / 7. Indiscernible Objects

10195

If the universe just held two indiscernibles spheres, that refutes the Identity of Indiscernibles [Black]

27. Natural Reality / C. Space / 6. Space-Time

14014

Space alone, and time alone, will fade away, and only their union has an independent reality [Minkowski]