Chris
>
> 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.
>
> 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.
>
> > But not absolutely meaningless. However, I have already agreed
> > numbers pose problems.
>
> 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. (01)
If you look further up the discussion, you will see that this comment was in
the context of trying to deny the existence of abstract objects. Pat offered
numbers as his favourite example of abstract objects. If you see no problem
in making numbers (integers, rationals, reals, transfinite ...) concrete, I
am interested. To repeat Pat's question, Where is the number one located? (02)
>
> Chris Menzel
>
>
Chris (03)
_________________________________________________________________
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 (04)
|