Combining Texts

All the ideas for 'fragments/reports', 'Introduction to Zermelo's 1930 paper' and 'The Nature of Existence vol.2'

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16 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
The first-order ZF axiomatisation is highly non-categorical [Hallett,M]
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
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
The General Continuum Hypothesis and its negation are both consistent with ZF [Hallett,M]
7. Existence / B. Change in Existence / 1. Nature of Change
How could change consist of a conjunction of changeless facts? [McTaggart, by Le Poidevin]
Change is not just having two different qualities at different points in some series [McTaggart]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
27. Natural Reality / D. Time / 1. Nature of Time / b. Relative time
For McTaggart time is seen either as fixed, or as relative to events [McTaggart, by Ayer]
27. Natural Reality / D. Time / 1. Nature of Time / i. Denying time
A-series time positions are contradictory, and yet all events occupy all of them! [McTaggart, by Le Poidevin]
Time involves change, only the A-series explains change, but it involves contradictions, so time is unreal [McTaggart, by Lowe]
27. Natural Reality / D. Time / 2. Passage of Time / a. Experience of time
There could be no time if nothing changed [McTaggart]
27. Natural Reality / D. Time / 2. Passage of Time / d. Time series
The B-series can be inferred from the A-series, but not the other way round [McTaggart, by Le Poidevin]
A-series uses past, present and future; B-series uses 'before' and 'after' [McTaggart, by Girle]
A-series expressions place things in time, and their truth varies; B-series is relative, and always true [McTaggart, by Lowe]
The B-series must depend on the A-series, because change must be explained [McTaggart, by Le Poidevin]
27. Natural Reality / G. Biology / 3. Evolution
Archelaus said life began in a primeval slime [Archelaus, by Schofield]