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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 15 ideas from 'Individuals without Sortals'

17511 Recognising continuity is separate from sortals, and must precede their use [Ayers]
17510 Speakers need the very general category of a thing, if they are to think about it [Ayers]
17509 Some say a 'covering concept' completes identity; others place the concept in the reference [Ayers]
17521 You can't have the concept of a 'stage' if you lack the concept of an object [Ayers]
17522 We use sortals to classify physical objects by the nature and origin of their unity [Ayers]
17523 Sortals basically apply to individuals [Ayers]
17520 Events do not have natural boundaries, and we have to set them [Ayers]
17519 To express borderline cases of objects, you need the concept of an 'object' [Ayers]
17518 Counting 'coin in this box' may have coin as the unit, with 'in this box' merely as the scope [Ayers]
17514 Temporal 'parts' cannot be separated or rearranged [Ayers]
17512 If diachronic identities need covering concepts, why not synchronic identities too? [Ayers]
17513 If there are two objects, then 'that marble, man-shaped object' is ambiguous [Ayers]
17515 Seeing caterpillar and moth as the same needs continuity, not identity of sortal concepts [Ayers]
17517 Could the same matter have more than one form or principle of unity? [Ayers]
17516 If counting needs a sortal, what of things which fall under two sortals? [Ayers]