Combining Texts

All the ideas for 'Philosophical Grammar', 'Universals and Particulars' 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 / 1. Mathematics

18281

In mathematics everything is algorithm and nothing is meaning [Wittgenstein]

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 / D. Universals / 6. Platonic Forms / c. Self-predication

4442	Most thinkers now reject self-predication (whiteness is NOT white) so there is no Third Man problem [Armstrong]

21. Aesthetics / A. Aesthetic Experience / 2. Aesthetic Attitude

6606	Consider: "Imagine this butterfly exactly as it is, but ugly instead of beautiful" [Wittgenstein]