Combining Texts

All the ideas for 'fragments/reports', 'Introduction to Zermelo's 1930 paper' and 'The Theory of Knowledge'

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10 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]

5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives

23476

Logical constants seem to be entities in propositions, but are actually pure form [Russell]

23477

We use logical notions, so they must be objects - but I don't know what they really are [Russell]

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

18273

Logical truths are known by their extreme generality [Russell]

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 / 8. Facts / d. Negative facts

22315

There can't be a negative of a complex, which is negated by its non-existence [Potter on Russell]

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]