Combining Texts

All the ideas for 'What Price Bivalence?', 'Introduction to Zermelo's 1930 paper' and 'Principles of Theoretical Logic'

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7 ideas

4. Formal Logic / C. Predicate Calculus PC / 1. Predicate Calculus PC

17750

The first clear proof of the consistency of the first order predicate logic was in 1928 [Hilbert/Ackermann, by Walicki]

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

17833

The first-order ZF axiomatisation is highly non-categorical [Hallett,M]

17834

Non-categoricity reveals a sort of incompleteness, with sets existing that the axioms don't reveal [Hallett,M]

4. Formal Logic / F. Set Theory ST / 7. Natural Sets

17837

Zermelo allows ur-elements, to enable the widespread application of set-theory [Hallett,M]

5. Theory of Logic / D. Assumptions for Logic / 1. Bivalence

19043

Bivalence applies not just to sentences, but that general terms are true or false of each object [Quine]

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

17836

The General Continuum Hypothesis and its negation are both consistent with ZF [Hallett,M]

7. Existence / D. Theories of Reality / 10. Vagueness / d. Vagueness as linguistic

19042

Terms learned by ostension tend to be vague, because that must be quick and unrefined [Quine]