Combining Texts

All the ideas for 'fragments/reports', 'Abstraction Reconsidered' and 'On the Introduction of Transfinite Numbers'

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14 ideas

1. Philosophy / D. Nature of Philosophy / 4. Divisions of Philosophy
Six parts: dialectic, rhetoric, ethics, politics, physics, theology [Cleanthes, by Diog. Laertius]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
Von Neumann treated cardinals as a special sort of ordinal [Neumann, by Hart,WD]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
A von Neumann ordinal is a transitive set with transitive elements [Neumann, by Badiou]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / g. Von Neumann numbers
For Von Neumann the successor of n is n U {n} (rather than {n}) [Neumann, by Maddy]
Von Neumann numbers are preferred, because they continue into the transfinite [Maddy on Neumann]
Each Von Neumann ordinal number is the set of its predecessors [Neumann, by Lavine]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
Abstraction from objects won't reveal an operation's being performed 'so many times' [Geach]
15. Nature of Minds / C. Capacities of Minds / 5. Generalisation by mind
If concepts are just recognitional, then general judgements would be impossible [Geach]
17. Mind and Body / A. Mind-Body Dualism / 8. Dualism of Mind Critique
Bodies interact with other bodies, and cuts cause pain, and shame causes blushing, so the soul is a body [Cleanthes, by Nemesius]
17. Mind and Body / E. Mind as Physical / 1. Physical Mind
The soul suffers when the body hurts, creates redness from shame, and pallor from fear [Cleanthes]
18. Thought / D. Concepts / 3. Ontology of Concepts / b. Concepts as abilities
For abstractionists, concepts are capacities to recognise recurrent features of the world [Geach]
18. Thought / E. Abstraction / 8. Abstractionism Critique
The abstractionist cannot explain 'some' and 'not' [Geach]
Only a judgement can distinguish 'striking' from 'being struck' [Geach]
28. God / B. Proving God / 3. Proofs of Evidence / b. Teleological Proof
The ascending scale of living creatures requires a perfect being [Cleanthes, by Tieleman]