[FOM] Count Calculus

Dean Buckner Dean.Buckner at btopenworld.com
Tue Jun 17 16:42:21 EDT 2003

I repeat the point I made to Harvey in earlier posting.  If the "count
calculus" is to make philosophical sense, it has to reflect the way we
actually ascribe number.
And we can ascribe number simply by making a statement of identity, such as
"Those people we met last night were Alice and Bob"

(*) S = a, b.

This states that the number of S is two, by asserting an identity between
what is referred to by "S", a term whose meaning does not include the number
of things it refers to, and the term "a,b", which does specify the number of
things referred to (simply by listing them individually).

> We can require that the intended interpretation of the counts be
> the natural numbers.

If we are going to be faithful to ordinary use, we don't count numbers.  We
count objects, and counting consists simply in listing the objects out by
name.  Obviously it's convenient to use ordinal names ("the first X", "the
second X", and so on), which give us a supply of names, and also help us to
remember how many objects we have listed).  But these numeral-names are not
essential to the logic of number.

 A number is what is referred to by a list.

> However, infinite extensions may get counted.

I may be very stupid, but if we allow "infinite extensions" to get counted,
don't we then have to specify whether any term we use refers to an infinite
number of things or not?  Then we have to define the terms "finite",
"infinite".  How do we do that?


Dean Buckner

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