Combining Texts

All the ideas for 'The Case for Closure', 'works' and 'Mathematical Thought from Ancient to Modern Times'

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6 ideas

2. Reason / D. Definition / 1. Definitions

15927

Definition just needs negation, known variables, conjunction, disjunction, substitution and quantification [Weyl, by Lavine]

5. Theory of Logic / K. Features of Logics / 1. Axiomatisation

17606

Axioms reveal the underlying assumptions, and reveal relationships between different areas [Kline]

11. Knowledge Aims / B. Certain Knowledge / 2. Common Sense Certainty

19553

Commitment to 'I have a hand' only makes sense in a context where it has been doubted [Hawthorne]

13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / c. Knowledge closure

19551

How can we know the heavyweight implications of normal knowledge? Must we distort 'knowledge'? [Hawthorne]

19552

We wouldn't know the logical implications of our knowledge if small risks added up to big risks [Hawthorne]

19554

Denying closure is denying we know P when we know P and Q, which is absurd in simple cases [Hawthorne]