From: Mark Steven Heyman (markheyman@infoproconsulting.com)
Date: Thu Nov 18 2004 - 16:27:11 GMT
Hi Scott, SM...
Scott Roberts wrote:
>[Scott:] Please tell me how sense experience verifies that no ratio
>of integers is the square root of 2.
sm:
The answer is that none of the answers that you can come up with to
that mathematical question have quality. You are looking for an
answer that fulfils a harmony, you know when you have found that
harmony because you sense it, even before you have fully committed
the answer to mathematical expression.
msh adds:
I would suggest another way of looking at it, which, I think, fits in
with what Simon is saying here. My idea is that mathematics is
rooted in empiricism, but then rationality allows us to draw from
math all sorts of strictly non-empirical conclusions, where by
"strictly" I mean not verifiable through any of the five senses.
That is, mathematics, grounded in experience, allows us to verify
that no ratio of integers may be used to represent root 2.
Scott, thanks for pointing me to the Copleston Annotations.
Later,
Mark Steven Heyman (msh)
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