A Paradox
In the famous aporia, a Cretan declares all Cretans to be liars. It is a simple statement, but also a vertiginous one. To postulate that language cannot communicate meaning, to give another example, is to postulate the meaninglessness of your postulation. Other familiar forms of the problem include the arguments against argumentation and the negation of everything including, ex hypothesi, negation. It is probable that all such statements equally pointless—but I think I may have found one exception.
Consider for a moment the old saw: “There is an exception to every rule.” This statement is itself a rule. One might object, then, that it falls into the same trap: If true, there must be an exception to it and the rule invalidates itself. And there is but it does not. The reason is that this rule is the exception to itself. At the risk of tautology, I will formulate the rule in its implied form: There is an exception to every rule, including the rule that there is an exception to every rule, to which there is no exception. Consider those words carefully. So formulated, this rule appears to be a paradox that, paradoxically, does not involve contradiction. |