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Re: The Codex

Posted By: Forrest (cache1.avtel.net)
Date: 3/27/2000 at 11:00 a.m.

In Response To: Re: The Codex (SiliconDream =PN=)

: What's paradoxical about the "Every rule"
: statement? It's not self-contradictory.

Yes it is. It can be inferred from the statement "Every rule has an exception, except this one" that this rule has no exceptions. But "except this one" IS an exception! Therefore every rule, including this one, has an exception. But that contradicts the statement itself, which says that it has no exceptions. So the rule is the exception to itself, while claiming that it has no exceptions.

Now that I think about it, the opposite statement "Every rule has an exception, including this one" would be equally paradoxical. "Every rule has an exception" implies that there is an exception to that rule too, meaning that in some case, there is a rule without an exception, so the original statement is false. But if it's false, then that rule COULD have an exception, meaning that it could be true... in which case you come back to the same conclusion that it's false. Which leads to the possibility that it's true, in which case it's false... and so on. The very truth of the statement proves itself false. But then it was never true to prove itself false in the first place. So it could be true. In which case it's false.

See the paradox?

The only way out of it is to declare the statement innacurate but not entirely false; the correct phrasing would be "MOST rules have exceptions, but some, such as this one, don't". Then it's just up to whether most rules really do have exceptions or not to determine if that statement is true or false; if it's false, then it could be rephrased "Many..." or "Some..." instead of "Most".

You can't get out of a loop from within the loop; but if you can move up and beyond the loop, change it so it's no longer a loop at all, or simply stop bothering with it, then you can get out of it. Fortunately our brains can preemptively multitask and self-rewrite, so if we get stuck in a logical loop we can just kill that task, or change it so it's not a loop anymore.

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