Again there are two concepts in Sanskrit (01)
1. Innumerable - (Asankhya) e.g. the numbers are too many to count, such
as the stars in the universe? (02)
2. Infinite (Ananta) where the numbers (as well as any other metrology
item - Unit) are limitless or exceed the concept of limit. (03)
Quoting -Ravi's approximate translation, concept is deeper than my
English abilities. (04)
"This is Complete! That is Complete! From the Complete comes
(springs-up!) Complete -is so said! If you take away Complete (or whole
number) from the Complete what remains is Complete." -recursive and
infinite concept! (05)
If we trace back, the concept of Whole Number (and real numbers) and
Decimals originated from Sanskrit (At least 3000 BC) although these came
back recently to the West via mid-east and are know as Arabic numerals
(0-9). FOr 1 and 2 above, in practice the dimensions of space-time enter
as many physicists would agree. (06)
The Difficulty or challenge of understanding count-ability: whether in
discrete or in continuous worlds - is limited by our sense-mind complex
and psychologists and scientists have to work together to present some
alternatives and cognitive concepts that can be harmonized by
Mathematics - mother of all natural sciences - and described as
meaningful(?) mathematical limits, if any! We mortal physicists get away
with calling difficult areas with Greek symbols (infinity) and describe
other limits (infinitesimal!) as singularities - nearing zero. (07)
Thanks. (08)
Ravi (09)
(Dr. Ravi Sharma) Senior Enterprise Architect (010)
Vangent, Inc. Technology Excellence Center (TEC) (011)
8618 Westwood Center Drive, Suite 310, Vienna VA 22182
(o) 703-827-0638, (c) 313-204-1740 www.vangent.com (012)
-----Original Message-----
From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of John F.
Sowa
Sent: Thursday, February 07, 2008 7:18 PM
To: Pat Hayes
Cc: [ontolog-forum]
Subject: Re: [ontolog-forum] Axiomatic ontology (013)
Pat, (014)
I wasn't advocating that we go back to pre-Cantorian set theory. (015)
But I was trying to distinguish two directions Avril was suggesting:
the indefensible idea of trying to set a finite upper bound to the
integers and the more defensible (but unlikely to be adopted) idea of
going back to 19th c. math. (016)
> Attained? We don't need to attain it in order to speak of it.
> Obviously there is a sense in which no infinity can be 'attained'
> in a finite universe. (017)
I was summarizing the way a 19th century mathematician would talk,
not advocating it. (018)
PH> Ack(Ack(5,5),5) can be constructed in a finite number of steps. (019)
Yes. A 19th-century mathematician would be quite happy to accept
functions whose values grow very large very quickly. I definitely
do *not* support Avril's finite upper bound, and neither would
any mathematician since the ancient Greeks (or even earlier). (020)
PH> On the whole, I think that the mathematicians have done a fairly
> good job and we would all be better off leaving it to them, and
> focusing on matters of more direct importance to our engineering. (021)
I agree. But they have developed an abundance of theories, many
of which have not been fully evaluated for possible applications. (022)
My recommendation to Avril would be to avoid trying to stop any
mathematicians from following their own inclinations. A more
useful approach would be to show how some approaches that have
been overlooked have important applications. (023)
As one example, I believe that Peirce's proof procedure has
important advantages for many purposes. Another example is the
application of 19th century geometric algebra to modern physics
by David Hestenes. (024)
John (025)
_________________________________________________________________
Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/
Subscribe/Config:
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 Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx (026)
_________________________________________________________________
Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/
Subscribe/Config: 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 Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx (027)
|