Exception paradox: if every rule

Rule

Rule, ruler, ruling usually refers to standards for activities. They may refer to:- Human activity :* Business rule, a rule pertaining to the structure or behavior internal to an organization* Game rules, rules that define how a game is played...

 has an exception

Exception

Exception may refer to:* An action that is not part of ordinary operations or standards* Exception handling, in programming languages** or a programming interrupt itself of which exception handling is meant to deal with....

 (this is the false premise

False premise

A false premise is an incorrect proposition that forms the basis of a logical syllogism. Since the premise is not correct, the conclusion drawn may be in error...

), 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

Mathematical proof

In mathematics, a proof is a convincing demonstration that some mathematical statement is necessarily true. Proofs are obtained from deductive reasoning, rather than from inductive or empirical arguments. That is, a proof must demonstrate that a statement is true in all cases, without a single...

 that the sentence "every rule has an exception" is false - a simple example of a proof technique known as reductio ad absurdum

Reductio ad absurdum

In logic, proof by contradiction is a form of proof that establishes the truth or validity of a proposition by showing that the proposition's being false would imply a contradiction...

. 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 - an apparent contradiction.

Variations on the Paradox

• The liar paradox
  Liar paradox
  In philosophy and logic, the liar paradox or liar's paradox , is the statement "this sentence is false"...
  
  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.