[Top] [All Lists]

Re: [ontolog-forum] standard ontology

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Christopher Menzel <cmenzel@xxxxxxxx>
Date: Wed, 11 Feb 2009 13:21:05 -0600
Message-id: <76AAF8DF-E16F-447D-94E3-B86A4C6C207B@xxxxxxxx>
On Feb 11, 2009, at 10:41 AM, Chris Partridge wrote:
> PatH,
> Last time you raised the question of numbers, and I responded, Chris  
> Menzel told me off for raising something NOT relevant.    (01)

Really?  I find that hard to believe.  Given my own proclivities,  
that'd be the pot calling the kettle black. :-)    (02)

>>> 1. Are there certain things like e.g. numbers and possible worlds?
>>> 2. Are they abstract or concrete?
>>> Even the first may be controversial, but even if you agree that  
>>> these things exist, whether they are considered abstract or not is  
>>> a different question (and arguably more controversial).
>> Whether they exist or not, I think  you have to say that numbers  
>> are not concrete. You can't weigh seven.
> As I think you must know there is a Fregean concept of number (where  
> 2 is the set of all sets with two members).  This Fregean proposal  
> has modern supporters - e.g. Crispin Wright 
>http://en.wikipedia.org/wiki/Crispin_Wright    (03)

It is quite misleading to express the thesis in terms of sets, as it  
is easy to show in modern Zermelo-Fraenkel set theory that there is no  
set of all 2-element sets.  Frege's account, famously, ended in  
failure due to Russell's paradox.  Modern reconstructions show that  
arithmetic can in fact be reconstructed in second-order logic a la  
Frege by the addition of "Hume's Principle": that the number of Fs =  
the number of Gs iff there is a bijection between the Fs and the Gs.   
The issues here are very subtle and extremely interesting.  A masterly  
account of both the history and the logic of Frege's account by Edward  
Zalta can be found in the Stanford Encyclopedia of Philosophy:    (04)

   http://plato.stanford.edu/entries/frege-logic    (05)

> There is debate about whether sets are abstract - David Lewis asks  
> why we cannot say the set of cars in the car park is located in the  
> car park -    (06)

Are you sure Lewis asked that?    (07)

> and if it is located, it cannot be abstract. Hence, there is an  
> account of numbers that says they are not abstract.    (08)

That, of course, is a complete non sequitur.  Even ignoring the fact  
that your proposed definition of "number" above doesn't work, all  
Lewis's (?) question shows is that sets of *concrete* objects might be  
considered concrete.  But, on the "Fregean" definition of number you  
propose, for it to follow that, say, the number 2 is concrete, you'd  
need *all* 2-element sets are concrete, not just 2-element sets whose  
elements are themselves concrete.    (09)

-chris    (010)

Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/  
Config Subscr: 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 join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J
To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx    (011)

<Prev in Thread] Current Thread [Next in Thread>