Combining Texts

All the ideas for 'Barcan Formulae', 'works' and 'What is Cantor's Continuum Problem?'

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9 ideas

4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5

7791	The simplest of the logics based on possible worlds is Lewis's S5 [Lewis,CI, by Girle]

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

15380

Barcan:nothing comes into existence; Converse:nothing goes out; Both:domain is unchanging [Vervloesem]

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets

8679	We perceive the objects of set theory, just as we perceive with our senses [Gödel]

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / o. Axiom of Constructibility V = L

9942	Gödel proved the classical relative consistency of the axiom V = L [Gödel, by Putnam]

5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / a. Set theory paradoxes

18062

Set-theory paradoxes are no worse than sense deception in physics [Gödel]

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis

10868

The Continuum Hypothesis is not inconsistent with the axioms of set theory [Gödel, by Clegg]

13517

If set theory is consistent, we cannot refute or prove the Continuum Hypothesis [Gödel, by Hart,WD]

6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism

10271

Basic mathematics is related to abstract elements of our empirical ideas [Gödel]

10. Modality / A. Necessity / 2. Nature of Necessity

11002

Equating necessity with informal provability is the S4 conception of necessity [Lewis,CI, by Read]