Combining Texts

All the ideas for 'fragments/reports', 'Fallibilism' and 'Introduction to Zermelo's 1930 paper'

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8 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]

11. Knowledge Aims / B. Certain Knowledge / 3. Fallibilism

19701

Fallibilism is consistent with dogmatism or scepticism, and is not alternative to them [Dougherty]

19700

It is best to see the fallibility in the reasons, rather than in the agents or the knowledge [Dougherty]

19702

We can't normally say that we know something 'but it might be false' [Dougherty]

13. Knowledge Criteria / E. Relativism / 2. Knowledge as Convention

1556	By nature people are close to one another, but culture drives them apart [Hippias]