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All the ideas for 'Precis of 'Limits of Abstraction'', 'Intuitionism and Formalism' and 'The Making of a Philosopher'

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11 ideas

2. Reason / D. Definition / 2. Aims of Definition
Definitions concern how we should speak, not how things are [Fine,K]
4. Formal Logic / E. Nonclassical Logics / 7. Paraconsistency
Our dislike of contradiction in logic is a matter of psychology, not mathematics [Brouwer]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
Scientific laws largely rest on the results of counting and measuring [Brouwer]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle
If Hume's Principle can define numbers, we needn't worry about its truth [Fine,K]
Hume's Principle is either adequate for number but fails to define properly, or vice versa [Fine,K]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
Intuitionists only accept denumerable sets [Brouwer]
Neo-intuitionism abstracts from the reuniting of moments, to intuit bare two-oneness [Brouwer]
15. Nature of Minds / B. Features of Minds / 2. Unconscious Mind
If all mental life were conscious, we would be unable to see things, or to process speech [McGinn]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
An abstraction principle should not 'inflate', producing more abstractions than objects [Fine,K]
19. Language / A. Nature of Meaning / 3. Meaning as Speaker's Intention
If meaning is speaker's intentions, it can be reduced to propositional attitudes, and philosophy of mind [McGinn]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
Intuitonists in mathematics worried about unjustified assertion, as well as contradiction [Brouwer, by George/Velleman]