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Ideas for 'fragments/reports', 'Review of Bob Hale's 'Abstract Objects'' and 'Reference and Generality (3rd ed)'

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2 ideas

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / d. Counting via concepts
Are 'word token' and 'word type' different sorts of countable objects, or two ways of counting? [Geach, by Perry]
     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.
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
Platonism claims that some true assertions have singular terms denoting abstractions, so abstractions exist [Williamson]
     Full Idea: The Fregean argument for platonism is that some true assertions contain singular terms which denote abstract objects if they denote anything; since the assertions are true, the singular terms denote.
     From: Timothy Williamson (Review of Bob Hale's 'Abstract Objects' [1988])
     A reaction: I am perplexed that anyone would rest their view of reality on such an argument. The obvious comparison would be with true remarks about blatantly fictional characters, or blatantly invented concepts such as 'checkmate'.