Natural number and set
If, following the path indicated by our considerations so far, we proceed to define the concept of natural number, we must begin with the description of the state of affairs in which numbers are first given, the "model' of numbers; next, we must isolate numbers by abstracting them from that state of affairs. This latter is the process of counting, about which we can make two preliminary remarks: (1) any arbitrary objects may be counted, thus insights about the number concept gained by descriptively analysing the counting process hold independently of what we happen to be counting; (2) no new property accrues to objects through being counted. The second point needs some elucidation.
Kaufmann, F. (1978). Natural number and set, in The infinite in mathematics, Dordrecht, Springer, pp. 68-90.
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