You must have had something else in mind.

That’s a very kind way of saying “your brain must have been turned off”. (-:O

]]>Of course, any constant function is idempotent, as is the identity. And if *P* is any proposition, then and are both idempotent. If , then the former is constant at **0** and the latter is the identity; while if , then the former is the identity and the latter is constant at **1**. Of course, with excluded middle we can construct other idempotents, like sending *X* to **0** if it is empty and to **1** if it is inhabited. Can we construct any nonidentity, nonconstant idempotents on the universe without using classical axioms? Can we derive a taboo from the assumption of a nonidentity, nonconstant idempotent on the universe?