Nick and I had an off-list discussion that may speak to some of the
recent posts.
Begin forwarded message:
From: Owen Densmore <[email protected]>
Date: July 13, 2009 10:38:08 AM MDT
To: [email protected]
Cc: John Kennison <[email protected]>, Owen Densmore <[email protected]
>
Subject: Re: Cauchy sequence - Wikipedia, the free encyclopedia
On Jul 12, 2009, at 10:30 PM, Nicholas Thompson wrote:
http://en.wikipedia.org/wiki/Cauchy_sequence
Sorry. I dont know why this came up. I see that it's some nice
mathematics,but I dont see its relevance.
The sub-theme was "Bridging the Gap" .. in this case between
philosophy and mathematics. In the above case, the CS is a
delightful example of bridging the gap between the CONtinuous and
disCRETE in Don Knuth's Concrete Mathematics .. a topic we've
discussed in the past.
Or possibly more formally, applying the epsilon/delta idea to both
the continuous and discrete as discussed in the book we read last
summer, Journey Through Genius.
While I have your attention, is a mathematical proof a kind of
algorithm?
Although they share a step-wise approach, I think not.
Do you agree, that mathematical proofs are very rigorous arguments?
Not arguments as in a way to resolve disagreements. But arguments
as a line of thought. Certainly rigorous.
Is a symbolic logical proof an example of mathematics?
I'd say yes, but others might be more comfortable separating math
and logic.
Or of Philosophy?
See the word comfortable above.
Was Bertrand Russel a mathematician or a philosopher?
Both. Wittgenstein studied under him, so the Both applies to him
too, as it does for Kant and others.
Since I think of mathematics as a kind of tremendously rigorous
extension of the art of argument from philosophy, I would expect
that most of these questions are bad questions.
No, but you do feel argument is a sort of sport, not unlike
wrestling! This is really more key that you might imagine.
Mathematicians and scientists, even though they do have
disagreements, generally argue/discuss means to an end (solving a
problem, creating a proof) rather than argue right and wrong.
You can take this on the list, if you like. I think your answers
would be interesting to list members, but I am leery of being
called on the carpet for starting another philosophical discussion.
I have cc'ed my mathematician friend John Kennison to see what he
might say.
Nicholas S. Thompson
Emeritus Professor of Psychology and Ethology,
Clark University ([email protected])
http://home.earthlink.net/~nickthompson/naturaldesigns/
============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org
