Single Idea 9974

[catalogued under 6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism]

Full Idea

If there are ten sheep and ten dogs, the number is the same (because it does not differ by a numerical difference), but it is not the same ten (because the objects it is predicated of are different - dogs in one instance, horses in the other).

Gist of Idea

Ten sheep and ten dogs are the same numerically, but it is not the same ten

Source

Aristotle (Physics [c.337 BCE], 224a2-14)

Book Reference

Aristotle: 'Physics', ed/tr. Waterfield,Robin [OUP 1996], p.117


A Reaction

Mega! Abstract objects are unique, and can't be 'added' to themselves. I think we need 'units' here, because 2+2 adds four units, so each 2 refers to something different. '2' must refer to something other than itself.

Related Idea

Idea 8311 If 2 is a particular, then adding particulars to themselves does nothing, and 2+2=2 [Lowe]