FOM: Alice, Bob and Carol
Dean Buckner
Dean.Buckner at btopenworld.com
Thu Apr 11 15:45:35 EDT 2002
wiman lucas raymond <lrwiman at ilstu.edu> wrote:
> > 7. So, isn't that all there is to say about number?
>
> In some senses, yes, that is all there is to say about a number. A
> number
> is an intuitively obvious idea, something that even a chimpanzee can
> grasp.
It's doubtful whether animals can understand language, and therefore
doubtful whether they can understand the proposition expressed by "Alice and
Bob are different people". If they can understand its meaning then, well,
I'd say they have the concept of number.
[skip]
> >From which I conclude all the Fregean stuff is absolutely irrelevant
> either
> >to our ideas about number, or to facts about it.
>
> Whoa, that's quite a leap. I find it very dubious to say that Peano
> arithmetic has nothing whatever to do with number theory (the facts about
>numbers), and number theory definitely relates to the real world.
We're confusing "Frege stuff" with "Peano stuff". By "Frege stuff" I mean
the idea that any collection of objects has a common property that defines
it as a collection, that this property has a number, and that this number
consists in being equinumerous with a concept such as "identical with 0",
"identical with 0 or 1", "identical with 0 or 1 or 2" or another concept in
that "series". This is junk. By "Peano stuff" I mean the axioms and the
stuff that follows from it. That's not junk. And you can get from my stuff
to
PA.
Dean Buckner
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