### Ideas from 'Reference and Generality (3rd ed)' by Peter Geach [1980], by Theme Structure

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###### 6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / d. Counting via concepts
 12154 Are 'word token' and 'word type' different sorts of countable objects, or two ways of counting?
 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. From: report of Peter Geach (Reference and Generality (3rd ed) [1980]) by John Perry - The Same F II 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.
###### 9. Objects / A. Existence of Objects / 6. Nihilism about Objects
 8969 We should abandon absolute identity, confining it to within some category
 Full Idea: Geach argued that the notion of absolute identity should be abandoned. ..We can only grasp the meaning of a count noun when we associate it with a criterion of identity, expressed by a particular relative identity sortal. From: report of Peter Geach (Reference and Generality (3rd ed) [1980]) by John Hawthorne - Identity A reaction: In other words, identity needs categorisation. Hawthorne concludes that Geach is wrong. Geach clearly has much common usage on his side. 'What's that?' usually invites a categorisation. Sameness of objects seems to need a 'respect'.
###### 9. Objects / F. Identity among Objects / 3. Relative Identity
 16075 Denial of absolute identity has drastic implications for logic, semantics and set theory
 Full Idea: Geach's denial of absolute identity has drastic implications for logic, semantics and set theory. He must deny the axiom of extensionality in set theory, for example. From: comment on Peter Geach (Reference and Generality (3rd ed) [1980]) by Ryan Wasserman - Material Constitution 6 A reaction: I'm beginning to think we have two entirely different concepts here - the logicians' and mathematicians' notion of when two things are identical, and the ordinary language concept of two things being 'the same'. 'We like the same music'.
 12152 Identity is relative. One must not say things are 'the same', but 'the same A as'
 Full Idea: Identity is relative. When one says 'x is identical with y' this is an incomplete expression. It is short for 'x is the same A as y', where 'A' represents some count noun understood from the context of utterance. From: Peter Geach (Reference and Generality (3rd ed) [1980], p.39), quoted by John Perry - The Same F I A reaction: Perry notes that Geach's view is in conscious opposition to Frege, who had a pure notion of identity. We say 'they are the same insofar as they are animals', but not 'they are the same animal'. Perfect identity involves all possible A's.
###### 9. Objects / F. Identity among Objects / 8. Leibniz's Law
 16073 Leibniz's Law is incomplete, since it includes a non-relativized identity predicate
 Full Idea: Geach rejects the standard formulation of Leibniz's Law as incomplete, since it includes a non-relativized identity predicate. From: report of Peter Geach (Reference and Generality (3rd ed) [1980]) by Ryan Wasserman - Material Constitution 6 A reaction: Not many people accept Geach's premiss that identity is a relative matter. I agree with Wiggins on this, that identity is an absolute (and possibly indefinable). The problem with the Law is what you mean by a 'property'.