On Mar 19, 2007, at 5:25 PM, Chris Partridge wrote:
> ...
> A number of points:
> 3) If one has a Fregean notion of number, then as the set of all
> (actual and possible?) sets with 17 members would have an infinite
> number of members – working out the density would be difficult, if
> not impossible. (01)
This is a red herring. All that the Fregean (or, for that matter,
*any* set theoretic) representation of the numbers buys you is a
class of well-defined objects that collectively model the axioms of
Peano Arithmetic; they provide a convenient answer to the question,
"What are the numbers?". You don't actually have to "manipulate"
them in any sense that requires that they themselves be represented
in a computer, you just *do* arithmetic. (02)
> But not absolutely meaningless. However, I have already agreed
> numbers pose problems. (03)
Why? Arithmetic is undecidable, of course, but so is first-order
logic, so I take it that that is not the sort of problem you have in
mind. If anything, because the ontology of the numbers -- a.k.a.
Peano Arithmetic -- is universally agreed upon, they pose far fewer
problems than most domains. (04)
Chris Menzel (05)
_________________________________________________________________
Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/
Subscribe/Config: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/
Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
Shared Files: http://ontolog.cim3.net/file/
Community Wiki: http://ontolog.cim3.net/wiki/
To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx (06)
|