Combining Texts

All the ideas for 'The Logic of Boundaryless Concepts', 'Elusive Knowledge' and 'Introduction to Zermelo's 1930 paper'

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11 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 / 3. Value of Logic

9390	Logic guides thinking, but it isn't a substitute for it [Rumfitt]

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]

9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects

9389	Vague membership of sets is possible if the set is defined by its concept, not its members [Rumfitt]

11. Knowledge Aims / A. Knowledge / 4. Belief / a. Beliefs

12899

The timid student has knowledge without belief, lacking confidence in their correct answer [Lewis]

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

12897

To say S knows P, but cannot eliminate not-P, sounds like a contradiction [Lewis]

13. Knowledge Criteria / A. Justification Problems / 1. Justification / b. Need for justification

12898

Justification is neither sufficient nor necessary for knowledge [Lewis]

13. Knowledge Criteria / C. External Justification / 6. Contextual Justification / a. Contextualism

12895

Knowing is context-sensitive because the domain of quantification varies [Lewis, by Cohen,S]

19562

We have knowledge if alternatives are eliminated, but appropriate alternatives depend on context [Lewis, by Cohen,S]