Combining Texts

All the ideas for 'Science and Method', 'The Putney Debates' and 'Introduction to Zermelo's 1930 paper'

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6 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 / 2. Geometry

10245

One geometry cannot be more true than another [Poincaré]

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]

24. Political Theory / B. Nature of a State / 2. State Legitimacy / c. Social contract

23215

Even the poorest have a life to lead, and so should consent to who governs them [-]