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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 5 ideas from 'Reference and Generality (3rd ed)'

Are 'word token' and 'word type' different sorts of countable objects, or two ways of counting? [Geach, by Perry]
We should abandon absolute identity, confining it to within some category [Geach, by Hawthorne]
Denial of absolute identity has drastic implications for logic, semantics and set theory [Wasserman on Geach]
Leibniz's Law is incomplete, since it includes a non-relativized identity predicate [Geach, by Wasserman]
Identity is relative. One must not say things are 'the same', but 'the same A as' [Geach]