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3 ideas
| 17518 | Counting 'coin in this box' may have coin as the unit, with 'in this box' merely as the scope [Ayers] |
| Full Idea: If we count the concept 'coin in this box', we could regard coin as the 'unit', while taking 'in this box' to limit the scope. Counting coins in two boxes would be not a difference in unit (kind of object), but in scope. | |
| From: M.R. Ayers (Individuals without Sortals [1974], 'Counting') | |
| A reaction: This is a very nice alternative to the Fregean view of counting, depending totally on the concept, and rests more on a natural concept of object. I prefer Ayers. Compare 'count coins till I tell you to stop'. |
| 17516 | If counting needs a sortal, what of things which fall under two sortals? [Ayers] |
| Full Idea: If we accepted that counting objects always presupposes some sortal, it is surely clear that the class of objects to be counted could be designated by two sortals rather than one. | |
| From: M.R. Ayers (Individuals without Sortals [1974], 'Realist' vii) | |
| A reaction: His nice example is an object which is both 'a single piece of wool' and a 'sweater', which had better not be counted twice. Wiggins struggles to argue that there is always one 'substance sortal' which predominates. |
| 16150 | One is, so numbers exist, so endless numbers exist, and each one must partake of being [Plato] |
| Full Idea: If one is, there must also necessarily be number - Necessarily - But if there is number, there would be many, and an unlimited multitude of beings. ..So if all partakes of being, each part of number would also partake of it. | |
| From: Plato (Parmenides [c.364 BCE], 144a) | |
| A reaction: This seems to commit to numbers having being, then to too many numbers, and hence to too much being - but without backing down and wondering whether numbers had being after all. Aristotle disagreed. |