Combining Texts

All the ideas for 'Tractatus', 'Introduction to Zermelo's 1930 paper' and 'No Understanding without Explanation'

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8 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]

9. Objects / E. Objects over Time / 10. Beginning of an Object

16706

Generation is when local motions aggregate to become a single subject [Nicholas of Autrecourt]

11. Knowledge Aims / A. Knowledge / 2. Understanding

14369

Understanding is a precondition, comes in degrees, is active, and holistic - unlike explanation [Strevens]

14365

Scientific understanding is always the grasping of a correct explanation [Strevens]

14368

We may 'understand that' the cat is on the mat, but not at all 'understand why' it is there [Strevens]