Combining Texts

All the ideas for 'Precis of 'Limits of Abstraction'', 'On Platonism in Mathematics' and 'Evidentialism'

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9 ideas

2. Reason / D. Definition / 2. Aims of Definition
10528 Definitions concern how we should speak, not how things are [Fine,K]
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
10304 Very few things in set theory remain valid in intuitionist mathematics [Bernays]
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]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
10303 Restricted Platonism is just an ideal projection of a domain of thought [Bernays]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
10306 Mathematical abstraction just goes in a different direction from logic [Bernays]
11. Knowledge Aims / A. Knowledge / 4. Belief / c. Aim of beliefs
19525 If the only aim is to believe truths, that justifies recklessly believing what is unsupported (if it is right) [Conee/Feldman]
13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / c. Knowledge closure
19524 We don't have the capacity to know all the logical consequences of our beliefs [Conee/Feldman]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
10527 An abstraction principle should not 'inflate', producing more abstractions than objects [Fine,K]