Combining Texts

All the ideas for 'The Gettier Problem', 'Introduction to 'New Pragmatists'' and 'Introduction to Zermelo's 1930 paper'

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6 ideas

2. Reason / A. Nature of Reason / 5. Objectivity

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Modern pragmatism sees objectivity as possible, despite its gradual evolution [Misak]

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 / b. Gettier problem

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A Gettier case is a belief which is true, and its fallible justification involves some luck [Hetherington]