Exception paradox: if every rule has an exception (this is the false premise), then there must be an exception to the rule that every rule has an exception.
From the logical point of view, this can be taken as a proof that the sentence "every rule has an exception" is false - a simple example of a proof technique known as reductio ad absurdum. More formally,
- Every rule has an exception. (Statement)
- "Every rule has an exception" has an exception. (By 1)
- There exists some rule R without exception. (By 2)
- Since R is a rule, by the first statement it must have an exception. But as stated in 3, it does not have an exception - an apparent contradiction.
Yet again, the rule may be true, as well as false; in particular, if the rule R is "Every rule has an exception". Such a rule has no domain to restrict it, and so its truth and falsehood need not conflict, as they do not compete on any domain.
Read more about Exception Paradox: Variations On The Paradox
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