Because of the fallacy of induction?
Nick
Nicholas S. Thompson
Emeritus Professor of Psychology and Ethology,
Clark University (nthomp...@clarku.edu)
http://home.earthlink.net/~nickthompson/naturaldesigns/
http://www.cusf.org [City University of Santa Fe]
----- Original Message -----
From: Russ Abbott
To: The Friday Morning Applied Complexity Coffee Group
Sent: 4/24/2010 10:48:21 PM
Subject: [FRIAM] Why are there theorems?
I have what probably seems like a strange question: why are there theorems? A
theorem is essentially a statement to the effect that some domain is structured
in a particular way. If the theorem is interesting, the structure characterized
by the theorem is hidden and perhaps surprising. So the question is: why do so
many structures have hidden internal structures?
Take the natural numbers: 0, 1, 2, 3, 4, ... It seems so simple: just one
thing following another. Yet we have number theory, which is about the
structures hidden within the naturals. So the naturals aren't just one thing
following another. Why not? Why should there be any hidden structure?
If something as simple as the naturals has inevitable hidden structure, is
there anything that doesn't? Is everything more complex than it seems on its
surface? If so, why is that? If not, what's a good example of something that
isn't.
-- Russ Abbott
______________________________________
Professor, Computer Science
California State University, Los Angeles
cell: 310-621-3805
blog: http://russabbott.blogspot.com/
vita: http://sites.google.com/site/russabbott/
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