Combining Texts

All the ideas for 'The Value of Science', 'What is innate and why' 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]

18. Thought / B. Mechanics of Thought / 4. Language of Thought

2605	If everything uses mentalese, ALL concepts must be innate! [Putnam]

2606	No machine language can express generalisations [Putnam]

26. Natural Theory / D. Laws of Nature / 11. Against Laws of Nature

15877

The aim of science is just to create a comprehensive, elegant language to describe brute facts [Poincaré, by Harré]