Combining Texts

All the ideas for 'The Roots of Reference', 'The Nature of Musical Expression' and 'Introduction to Zermelo's 1930 paper'

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7 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]

8. Modes of Existence / C. Powers and Dispositions / 3. Powers as Derived

14296

Dispositions are physical states of mechanism; when known, these replace the old disposition term [Quine]

21. Aesthetics / B. Nature of Art / 4. Art as Expression

12165

Romantics say music expresses ideas, or the Will, or intuitions, or feelings [Scruton]

21. Aesthetics / C. Artistic Issues / 4. Emotion in Art

12164

Expressing melancholy is a good thing, but arousing it is a bad thing [Scruton]