Combining Texts

All the ideas for 'Without Immediate Justification', 'On Certainty' and 'Introduction to Zermelo's 1930 paper'

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12 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]
13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / a. Agrippa's trilemma
8851 Coherentists say that regress problems are assuming 'linear' justification [Williams,M]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / a. Foundationalism
3597 Foundations need not precede other beliefs [Wittgenstein]
8849 Traditional foundationalism is radically internalist [Williams,M]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / b. Basic beliefs
8853 Basic judgements are immune from error because they have no content [Williams,M]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / c. Empirical foundations
8855 Sensory experience may be fixed, but it can still be misdescribed [Williams,M]
13. Knowledge Criteria / C. External Justification / 10. Anti External Justification
8852 In the context of scepticism, externalism does not seem to be an option [Williams,M]
13. Knowledge Criteria / D. Scepticism / 6. Scepticism Critique
3596 Total doubt can't even get started [Wittgenstein, by Williams,M]
19. Language / A. Nature of Meaning / 10. Denial of Meanings
4721 If you are not certain of any fact, you cannot be certain of the meaning of your words either [Wittgenstein]