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Re: [ontolog-forum] Ontological Assumptions of FOL

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Christopher Menzel <cmenzel@xxxxxxxx>
Date: Tue, 20 Mar 2007 11:45:36 -0500
Message-id: <721DD516-09EB-4866-8201-4B448F611461@xxxxxxxx>
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)

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