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All the ideas for 'Precis of 'Limits of Abstraction'', 'Of Miracles' and 'Mathematics and Indispensibility'

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6 ideas

2. Reason / D. Definition / 2. Aims of Definition
10528 Definitions concern how we should speak, not how things are [Fine,K]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle
10529 If Hume's Principle can define numbers, we needn't worry about its truth [Fine,K]
10530 Hume's Principle is either adequate for number but fails to define properly, or vice versa [Fine,K]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / e. Ontological commitment problems
9558 All scientific tests will verify mathematics, so it is a background, not something being tested [Sober]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
10527 An abstraction principle should not 'inflate', producing more abstractions than objects [Fine,K]
28. God / B. Proving God / 3. Proofs of Evidence / e. Miracles
7636 It can't be more rational to believe in natural laws than miracles if the laws are not rational [Ishaq on Hume]