[Top] [All Lists]

Re: [ontolog-forum] form and content

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>, "John F. Sowa" <sowa@xxxxxxxxxxx>
Cc: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "Avril Styrman" <Avril.Styrman@xxxxxxxxxxx>
Date: Fri, 11 Dec 2009 12:44:00 +0200
Message-id: <20091211124400.18121ph2ezr92pgw@xxxxxxxxxxxxxxxxxxx>
Hi all,    (01)

just a short notion about the used terminology.    (02)

> Theoretically, Peano's axioms define the common notion of number.  But
> the number of applications that use integers of arbitrary size (e.g.,
> the infinite precision Bignum in LISP) are extremely limited.  The
> overwhelming choice for applications is to use integers modulo some
> suitable upper value:  2^1, 2^8, 2^16, 2^32, or 2^64.    (03)

Always when it is said that a real-life application uses something  
infinite, it in fact uses only the potential infinite. However, also  
the 'infinite' in potential infinity is quite misleading, and could be  
replaced with "as much as can be taken" or something similar.    (04)

Also, the notion "arbitrary natural number" only meditates away the  
problems of the transfinite collection of natural numbers. It does not  
matter whether Peano's class of naturals or the set theoretic omega is  
thought of. Consider the class/set/aggregate or whatever sort of  
completed totality that contains each and every one of the infinitely  
many natural numbers, where infinite especially means never ending but  
still completed all the way through. This sort of a collection is  
called transfinite. If you select "just some" number n from that  
collection, in the way that all numbers have an equal possibility of  
getting selected, then the selected number n is so big, that it does  
not fit in a microchip that is of the size of the known part of  
Universe, that is, with probability 1. The number n is called  
arbitrary natural number in the transfinitist parlance. The problem  
with n is that n is that n is in practice very close to transfinite.  
Then again, if an arbitrary number is not selected randomly, then what  
is the meaning of "just some number"?    (05)

To conclude, when the term arbitrary is used with real-life  
applications, it always means a randomly selected number from within  
some finite range of numbers. The upper limit can be vague, such as  
the greatest number that fits in a microchip that is of the size of  
the known part of Universe, but it is still always finite.    (06)

-Avril    (07)

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    (08)

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