Combining Texts

All the ideas for '27: Book of Daniel', 'What are Sets and What are they For?' and 'A Completeness Theorem in Modal Logic'

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15 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 / 3. Types of Set / b. Empty (Null) Set

14239

The empty set is usually derived from Separation, but it also seems to need Infinity [Oliver/Smiley]

14240

The empty set is something, not nothing! [Oliver/Smiley]

14241

We don't need the empty set to express non-existence, as there are other ways to do that [Oliver/Smiley]

14242

Maybe we can treat the empty set symbol as just meaning an empty term [Oliver/Smiley]

4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets

14243

The unit set may be needed to express intersections that leave a single member [Oliver/Smiley]

5. Theory of Logic / G. Quantification / 6. Plural Quantification

14234

If you only refer to objects one at a time, you need sets in order to refer to a plurality [Oliver/Smiley]

14237

We can use plural language to refer to the set theory domain, to avoid calling it a 'set' [Oliver/Smiley]

5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth

14245

Logical truths are true no matter what exists - but predicate calculus insists that something exists [Oliver/Smiley]

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics

14246

If mathematics purely concerned mathematical objects, there would be no applied mathematics [Oliver/Smiley]

6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory

14247

Sets might either represent the numbers, or be the numbers, or replace the numbers [Oliver/Smiley]

29. Religion / D. Religious Issues / 2. Immortality / a. Immortality

7482	Resurrection developed in Judaism as a response to martyrdoms, in about 160 BCE [Anon (Dan), by Watson]