| Subject: In fact.... |
Author:
Duane
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Date Posted: 09/11/04 2:42am
In reply to:
Damoclese
's message, "I think" on 09/10/04 10:22am
In fact, I think I ought to mention this (or, rather, explicitly state it)
The Tristam Shandy paradox was created to prove one thing:
Set theory cannot be used to describe our natural world.
Our understanding of the universe is the basis of all reality for us. Mathematics is an abstraction - a tool created by us to help us understand reality.
Based on the axioms of set theory, Tristam Shandy DOES illustrate a paradox. There's no question about that. So the real question is this:
Given that a man-made abstraction disagrees with our best understanding of reality, which do we throw out?
The answer is clear: we throw out the "tool". In this case, that tool is NOT set theory, but it is the assumption that set theory can be used to understand our natural world.
Imagine a carpenter, building a house. He tries to nail together some wood into a house frame, and after hammering and hammering, his hammer suddenly breaks. The carpenter looks at the splintered handle of his hammer, and says one of the two things:
"Whoops. Better fix my hammer. Or maybe get a new one"
OR
"Well, I guess that houses can't be built using hammers and nails. Better give up."
Clearly, the first choice is reasonable. But Wade (and a few others) would have you believe that we should give up on trying to build houses.
Duane
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