Exception paradox  

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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,

1. Every rule has an exception. (Statement)
2. "Every rule has an exception" has an exception. (By 1)
3. There exists some rule R without exception. (By 2)
4. Since R is a rule, by the first statement it must have an exception. But by 3, it does not have an exception - a contradiction.

Or, in another view:

1. Every rule has an exception. (Statement)
2. "Every rule has an exception" has an exception. (By 1)
3. There exists some rule R without exception. (By 2)
4. Since R is a rule, by the first statement it must have an exception. Therefore, the statement should be the only rule that doesn't have an exception, what could be called a contradiction.
5. The rule itself represents its own exception, because it should be the only rule without an exception.

In this last point of view there isn't a contradiction but a systematic interpretation. This is a reason why it could not be considered a real paradox. Otherwise, the sentence could be read: "Every other rule, except this one, has an exception." This is a hermeneutic rule, saving the meaning, and represents a common technique applied on legal and constitutional norms, by extracting from the different interpretations of the statement the possible one, even if implicit.

Variations on the Paradox

• The liar paradox has similar self-reference, with the added twist that rejecting it leads to another paradox.
• If everything is possible, then it is possible for anything to be impossible.
• The only rule is that there are no rules.
• The only thing certain is that there is nothing certain.
• If everything has an opposite, then the opposite of there being an opposite to everything, is that there is not an opposite to everything.
• If everything should be taken in moderation, then moderation should itself be taken moderately, meaning that not everything would be taken in moderation.