Combining Philosophers

All the ideas for Oswald Veblen, Tim Black and Michael Hallett

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7 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]

5. Theory of Logic / A. Overview of Logic / 2. History of Logic

10247

We have no adequate logic at the moment, so mathematicians must create one [Veblen]

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 / 1. Justification / a. Justification issues

19729

'Modal epistemology' demands a connection between the belief and facts in possible worlds [Black,T]

13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / b. Gettier problem

19728

Gettier and lottery cases seem to involve luck, meaning bad connection of beliefs to facts [Black,T]