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Single Idea 8772
[filed under theme 18. Thought / E. Abstraction / 8. Abstractionism Critique
]
Full Idea
The number-concepts just cannot be got by concentrating on the number and abstracting from the kind of things being counted.
Gist of Idea
We can't acquire number-concepts by extracting the number from the things being counted
Source
Peter Geach (Mental Acts: their content and their objects [1957], §8)
Book Ref
Geach,Peter: 'Mental Acts: Their content and their objects' [RKP 1971], p.28
A Reaction
This point is from Frege - that if you 'abstract away' everything apart from the number, you are simply left with nothing in experience. The objection might, I think, be met by viewing it as second-order abstraction, perhaps getting to a pattern first.
The
27 ideas
from Peter Geach
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10731
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For abstractionists, concepts are capacities to recognise recurrent features of the world
[Geach]
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10732
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If concepts are just recognitional, then general judgements would be impossible
[Geach]
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10733
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The abstractionist cannot explain 'some' and 'not'
[Geach]
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10734
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Only a judgement can distinguish 'striking' from 'being struck'
[Geach]
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10735
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Abstraction from objects won't reveal an operation's being performed 'so many times'
[Geach]
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22489
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'Good' is an attributive adjective like 'large', not predicative like 'red'
[Geach, by Foot]
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2567
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You can't define real mental states in terms of behaviour that never happens
[Geach]
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2568
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Beliefs aren't tied to particular behaviours
[Geach]
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8769
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If someone has aphasia but can still play chess, they clearly have concepts
[Geach]
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8770
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'Abstractionism' is acquiring a concept by picking out one experience amongst a group
[Geach]
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8771
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'Or' and 'not' are not to be found in the sensible world, or even in the world of inner experience
[Geach]
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8772
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We can't acquire number-concepts by extracting the number from the things being counted
[Geach]
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8773
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Abstractionists can't explain counting, because it must precede experience of objects
[Geach]
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8774
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The numbers don't exist in nature, so they cannot have been abstracted from there into our languages
[Geach]
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8775
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A big flea is a small animal, so 'big' and 'small' cannot be acquired by abstraction
[Geach]
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8776
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We cannot learn relations by abstraction, because their converse must be learned too
[Geach]
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8778
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Blind people can use colour words like 'red' perfectly intelligently
[Geach]
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8777
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If 'black' and 'cat' can be used in the absence of such objects, how can such usage be abstracted?
[Geach]
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8779
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We can form two different abstract concepts that apply to a single unified experience
[Geach]
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8780
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Attributes are functions, not objects; this distinguishes 'square of 2' from 'double of 2'
[Geach]
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8781
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The mind does not lift concepts from experience; it creates them, and then applies them
[Geach]
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11910
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Being 'the same' is meaningless, unless we specify 'the same X'
[Geach]
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8969
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We should abandon absolute identity, confining it to within some category
[Geach, by Hawthorne]
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16075
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Denial of absolute identity has drastic implications for logic, semantics and set theory
[Wasserman on Geach]
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12154
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Are 'word token' and 'word type' different sorts of countable objects, or two ways of counting?
[Geach, by Perry]
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16073
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Leibniz's Law is incomplete, since it includes a non-relativized identity predicate
[Geach, by Wasserman]
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12152
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Identity is relative. One must not say things are 'the same', but 'the same A as'
[Geach]
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