Exception paradox

Homies 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 homie law, 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.

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.