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Single Idea 12154
[filed under theme 6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / d. Counting via concepts
]
Full Idea
If we list the words 'bull', 'bull' and 'cow', it is often said that there are three 'word tokens' but only two 'word types', but Geach says there are not two kinds of object to be counted, but two different ways of counting the same object.
Gist of Idea
Are 'word token' and 'word type' different sorts of countable objects, or two ways of counting?
Source
report of Peter Geach (Reference and Generality (3rd ed) [1980]) by John Perry - The Same F II
Book Ref
'Metaphysics - An Anthology', ed/tr. Sosa,E. /Kim,J. [Blackwell 1999], p.93
A Reaction
Insofar as the notion that a 'word type' is an 'object', my sympathies are entirely with Geach, to my surprise. Geach's point is that 'bull' and 'bull' are the same meaning, but different actual words. Identity is relative to a concept.
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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