: 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.
Ah, but you forget the true meaning of "exception." An exception is an occurrence in reality which violates the rule. It's *not* an occurrence of the word "except" within the rule. The statement "No bipeds have complex languages, except humans," is (always) as far as we know, true. It has no exceptions. So the rule "every rule has an exception, except this one" isn't a paradox. This rule does indeed have no exception. It applies correctly to all other rules, and to itself.
: 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?
Yes, this one *is* genuinely paradoxical. But you can pare it down some--just make it "This rule has an exception." That's equivalent to "This sentence is false." Your "Every rule, including this one, has an exception" is equivalent to "All sentences are false," which is a stronger assertion than you need to make in order to produce a 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".
Again, you can leave out the second part--"This rule has no exceptions" is equivalent to "This sentence is true," and is tautologically true and therefore unnecessary. Just say, "Most rules have exceptions."
: 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.
Your brain, maybe; I got the economy model. I lose an IQ point every year, as more and more of my mind becomes devoted to logical paradoxes...
--SiliconDream
