Combining Texts

All the ideas for 'reports', 'Introduction to Zermelo's 1930 paper' and 'The Raft and the Pyramid'

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11 ideas

2. Reason / A. Nature of Reason / 6. Coherence

8797	The negation of all my beliefs about my current headache would be fully coherent [Sosa]

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]

10. Modality / A. Necessity / 8. Transcendental Necessity

3016	Even the gods cannot strive against necessity [Pittacus, by Diog. Laertius]

12. Knowledge Sources / E. Direct Knowledge / 1. Common Sense

8794	There are very few really obvious truths, and not much can be proved from them [Sosa]

13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / e. Pro-foundations

8796	A single belief can trail two regresses, one terminating and one not [Sosa]

13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / f. Foundationalism critique

8799	If mental states are not propositional, they are logically dumb, and cannot be foundations [Sosa]

8795	Mental states cannot be foundational if they are not immune to error [Sosa]

13. Knowledge Criteria / C. External Justification / 2. Causal Justification

8798	Vision causes and justifies beliefs; but to some extent the cause is the justification [Sosa]