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2 ideas
| 18256 | Quantity is inconceivable without the idea of addition [Frege] |
| Full Idea: There is so intimate a connection between the concepts of addition and of quantity that one cannot begin to grasp the latter without the former. | |
| From: Gottlob Frege (Rechnungsmethoden (dissertation) [1874], p.2), quoted by Michael Dummett - Frege philosophy of mathematics 22 'Quantit' | |
| A reaction: Frege offers good reasons for making cardinals prior to ordinals, though plenty of people disagree. |
| 12154 | 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. |