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'
                        Full Idea: For an understanding of arithmetic the grasp of an operation's being performed 'so many times' is quite indispensable; and abstraction of a feature from groups of nuts cannot give us this grasp.
                        From: Peter Geach (Abstraction Reconsidered [1983], p.170)
                        A reaction: I end up defending the empirical approach to arithmetic because remarks like this are so patently false. Geach seems to think we arrive ready-made in the world, just raring to get on with some counting. He lacks the evolutionary perspective.
15. Nature of Minds / C. Capacities of Minds / 5. Generalisation by mind
If concepts are just recognitional, then general judgements would be impossible
                        Full Idea: If concepts were nothing but recognitional capacities, then it is unintelligible that I can judge that cats eat mice when neither of them are present.
                        From: Peter Geach (Abstraction Reconsidered [1983], p.164)
                        A reaction: Having observed the importance of recognition for the abstractionist (Idea 10731), he then seems to assume that there is nothing more to their concepts. Geach fails to grasp levels of abstraction, and cross-reference, and generalisation.
18. Thought / D. Concepts / 3. Ontology of Concepts / b. Concepts as abilities
For abstractionists, concepts are capacities to recognise recurrent features of the world
                        Full Idea: For abstractionists, concepts are essentially capacities for recognizing recurrent features of the world.
                        From: Peter Geach (Abstraction Reconsidered [1983], p.163)
                        A reaction: Recognition certainly strikes me as central to thought (and revelatory of memory, since we continually recognise what we cannot actually recall). Geach dislikes this view, but I see it as crucial to an evolutionary view of thought.
18. Thought / E. Abstraction / 8. Abstractionism Critique
The abstractionist cannot explain 'some' and 'not'
                        Full Idea: The abstractionist cannot give a logically coherent account of the features that are supposed to be reached by discriminative attention, corresponding to the words 'some' and 'not'.
                        From: Peter Geach (Abstraction Reconsidered [1983], p.167)
                        A reaction: I understand 'some' in terms of mereology, because that connects to experience, and 'not' I take to derive more from psychological experience than from the physical world, building on thwarted expectation, which even animals experience.
Only a judgement can distinguish 'striking' from 'being struck'
                        Full Idea: To understand the verb 'to strike' we must see that 'striking' and 'being struck' are different, but necessarily go together in event and thought; only in the context of a judgment can they be distinguished, when we think of both together.
                        From: Peter Geach (Abstraction Reconsidered [1983], p.168)
                        A reaction: Geach seems to have a strange notion that judgements are pure events which can precede all experience, and are the only ways we can come to understand experience. He needs to start from animals (or 'brutes', as he still calls them!).