Combining Texts

All the ideas for 'fragments/reports', 'Scientific Attitude and Fallibilism' and 'Introduction to Zermelo's 1930 paper'

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13 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 / 4. Using Numbers / c. Counting procedure
14775 Numbers are just names devised for counting [Peirce]
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 / 4. Mathematical Empiricism / c. Against mathematical empiricism
14776 That two two-eyed people must have four eyes is a statement about numbers, not a fact [Peirce]
11. Knowledge Aims / B. Certain Knowledge / 3. Fallibilism
14770 Reasoning is based on statistical induction, so it can't achieve certainty or precision [Peirce]
12. Knowledge Sources / A. A Priori Knowledge / 3. Innate Knowledge / a. Innate knowledge
14774 Innate truths are very uncertain and full of error, so they certainly have exceptions [Peirce]
12. Knowledge Sources / E. Direct Knowledge / 3. Inspiration
14771 Only reason can establish whether some deliverance of revelation really is inspired [Peirce]
14773 A truth is hard for us to understand if it rests on nothing but inspiration [Peirce]
14772 If we decide an idea is inspired, we still can't be sure we have got the idea right [Peirce]
15. Nature of Minds / C. Capacities of Minds / 2. Imagination
14769 Only imagination can connect phenomena together in a rational way [Peirce]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
468 Musical performance can reveal a range of virtues [Damon of Ath.]