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Old 01-03-2012, 02:54 PM
The Hamster King The Hamster King is offline
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Quote:
Originally Posted by whc.03grady View Post
What's more, I don't see how empirical results can trump principles of logic or reasoning.
You have it exactly backwards. It's the success of logic in explaining empirical results that justifies its use.

Depending on the axioms you pick as your starting point, you can construct a wide range of different mathematical systems. You can create a system where 1+1=3 or where TRUE & TRUE = FALSE, if you want.

Now, some of these systems happen to be useful in modelling the behavior of the universe. Systems where 1+1=2 and TRUE & TRUE = TRUE fall into this category.

The reason we trust these systems is because they do a good job of explaining what we observe. However, if we observe things that violate the predictions, then the systems must change.