Combining Texts

All the ideas for 'Prologue to Ordinatio', 'Philosophy without Intuitions' and 'Introduction to Zermelo's 1930 paper'

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8 ideas

2. Reason / E. Argument / 7. Thought Experiments

20183

So-called 'though experiments' are just philosophers observing features of the world [Cappelen]

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]

11. Knowledge Aims / A. Knowledge / 4. Belief / c. Aim of beliefs

9100	Our intellect only assents to what we believe to be true [William of Ockham]

12. Knowledge Sources / E. Direct Knowledge / 2. Intuition

20182

The word 'intuitive' often plays not role at all in arguments, and can be removed [Cappelen]

15. Nature of Minds / C. Capacities of Minds / 3. Abstraction by mind

9101	Abstractive cognition knows universals abstracted from many singulars [William of Ockham]