Combining Texts

All the ideas for 'fragments/reports', 'Introduction to Zermelo's 1930 paper' and 'Deriving Kripkean Claims with Abstract Objects'

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8 ideas

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]

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]

9. Objects / A. Existence of Objects / 2. Abstract Objects / a. Nature of abstracta

10558

Abstract objects are actually constituted by the properties by which we conceive them [Zalta]

18. Thought / E. Abstraction / 2. Abstracta by Selection

10557

Abstract objects are captured by second-order modal logic, plus 'encoding' formulas [Zalta]

25. Social Practice / E. Policies / 5. Education / b. Education principles

13304

Learned men gain more in one day than others do in a lifetime [Posidonius]

27. Natural Reality / D. Time / 1. Nature of Time / d. Time as measure

20820

Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus]