Combining Texts

All the ideas for 'works', 'Manuscript remains' and 'Introduction to Zermelo's 1930 paper'

expand these ideas     |    start again     |     specify just one area for these texts

---

11 ideas

1. Philosophy / D. Nature of Philosophy / 1. Philosophy

21916

Philosophers can't be religious, and don't need to be; philosophy is perilous but free [Schopenhauer]

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

8717	Hilbert wanted to prove the consistency of all of mathematics (which realists take for granted) [Hilbert, by Friend]

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]

6. Mathematics / C. Sources of Mathematics / 7. Formalism

10113

The grounding of mathematics is 'in the beginning was the sign' [Hilbert]

10115

Hilbert substituted a syntactic for a semantic account of consistency [Hilbert, by George/Velleman]

6. Mathematics / C. Sources of Mathematics / 8. Finitism

10116

Hilbert aimed to prove the consistency of mathematics finitely, to show infinities won't produce contradictions [Hilbert, by George/Velleman]

20. Action / B. Preliminaries of Action / 2. Willed Action / a. Will to Act

21924

As the subject of willing I am wretched, but absorption in knowledge is bliss [Schopenhauer]

22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / b. Rational ethics

21915

To deduce morality from reason is blasphemy, because it is holy, and far above reason [Schopenhauer]