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Tuesday, April 29, 11:59:09pmLogin ] [ Main index ] [ Post a new message ] [ Search | Check update time | Archives: 1234[5]678910 ]
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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