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Re: [ontolog-forum] form and content

 To: "[ontolog-forum] " , "John F. Sowa" "[ontolog-forum]" "Avril Styrman" Fri, 11 Dec 2009 12:44:00 +0200 <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) ```
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