|From:||FERENC KOVACS <f.kovacs@xxxxxxxxxxxxxx>|
|Date:||Fri, 11 Dec 2009 11:41:20 +0000 (GMT)|
Thanks for that!
----- Original Message -----
From: "Avril Styrman" <Avril.Styrman@xxxxxxxxxxx>
Cc: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
Sent: Friday, December 11, 2009 10:44 AM
Subject: Re: [ontolog-forum] form and content
> Hi all,
> just a short notion about the used terminology.
>> 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.
> 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.
> 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"?
> 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.
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