Wednesday, August 22, 2007

The Exception Paradox

From Wikipedia's article:

Exception paradox: if every rule has an exception, then there must be an exception to the rule that every rule has an exception.

It is not a true paradox, but serves as an explanation and simple example for the resolution of the paradox without the solution of continuity for the applicability to the classical logic.

If every rule has an exception, the exception to this rule would be the existence of a rule with no exception. However, the nonexistence of this exception would make the sentence false. But the existence of one would turn false the "every" from "every rule". If the phrase does not carry any exception, therefore, for not having exception to this rule of the "nonexistence of exception", its proper existence would imply in the (maybe partial) invalidation of its postulate, for the lack of exception.

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