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Single Idea 17518

[filed under theme 6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / d. Counting via concepts ]

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.

Gist of Idea

Counting 'coin in this box' may have coin as the unit, with 'in this box' merely as the scope

Source

M.R. Ayers (Individuals without Sortals [1974], 'Counting')

Book Ref

-: 'Canadian Journal of Philosophy' [-], p.139

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'.

The 12 ideas with the same theme [grouping by concept for counting]:

17438 Our concepts decide what is countable, as in seeing the leaves of the tree, or the foliage [Frege, by Koslicki]
17427 Frege's 'isolation' could be absence of overlap, or drawing conceptual boundaries [Frege, by Koslicki]
17437 Non-arbitrary division means that what falls under the concept cannot be divided into more of the same [Frege, by Koslicki]
17426 A concept creating a unit must isolate and unify what falls under it [Frege]
17428 Frege says counting is determining what number belongs to a given concept [Frege, by Koslicki]
12154 Are 'word token' and 'word type' different sorts of countable objects, or two ways of counting? [Geach, by Perry]
17518 Counting 'coin in this box' may have coin as the unit, with 'in this box' merely as the scope [Ayers]
17516 If counting needs a sortal, what of things which fall under two sortals? [Ayers]
17529 Maybe the concept needed under which things coincide must also yield a principle of counting [Wiggins]
17530 The sortal needed for identities may not always be sufficient to support counting [Wiggins]
13867 Instances of a non-sortal concept can only be counted relative to a sortal concept [Wright,C]
17434 We struggle to count branches and waves because our concepts lack clear boundaries [Koslicki]