Ideas from 'Abstraction Reconsidered' by Peter Geach [1983], by Theme Structure

[found in 'Knowledge and Mind' (ed/tr Ginet,C/Shoemaker,S) [OUP 1983,0-19-503148-2]].

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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'
15. Nature of Minds / C. Capacities of Minds / 5. Generalisation by mind
If concepts are just recognitional, then general judgements would be impossible
18. Thought / D. Concepts / 3. Ontology of Concepts / b. Concepts as abilities
For abstractionists, concepts are capacities to recognise recurrent features of the world
18. Thought / E. Abstraction / 8. Abstractionism Critique
The abstractionist cannot explain 'some' and 'not'
Only a judgement can distinguish 'striking' from 'being struck'