Combining Texts

All the ideas for 'reports', 'Introduction to Zermelo's 1930 paper' and 'Epistemology Naturalized'

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13 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
The first-order ZF axiomatisation is highly non-categorical [Hallett,M]
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
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
The General Continuum Hypothesis and its negation are both consistent with ZF [Hallett,M]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Mathematics reduces to set theory (which is a bit vague and unobvious), but not to logic proper [Quine]
10. Modality / A. Necessity / 8. Transcendental Necessity
Even the gods cannot strive against necessity [Pittacus, by Diog. Laertius]
13. Knowledge Criteria / C. External Justification / 9. Naturalised Epistemology
You can't reduce epistemology to psychology, because that presupposes epistemology [Maund on Quine]
We should abandon a search for justification or foundations, and focus on how knowledge is acquired [Quine, by Davidson]
If we abandon justification and normativity in epistemology, we must also abandon knowledge [Kim on Quine]
Without normativity, naturalized epistemology isn't even about beliefs [Kim on Quine]
Epistemology is a part of psychology, studying how our theories relate to our evidence [Quine]
19. Language / A. Nature of Meaning / 1. Meaning
Inculcations of meanings of words rests ultimately on sensory evidence [Quine]
19. Language / E. Analyticity / 4. Analytic/Synthetic Critique
In observation sentences, we could substitute community acceptance for analyticity [Quine]