We have used the concept of Mu in our logic since the start, but we didn’t always have a name for it. The name ended up coming from the koan Joshu’s Dog from The Gateless Gate;
A monk asked Joshu, a Chinese Zen master: “Has a dog Buddha-nature or not?”
Joshu answered: “Mu.”
Recently I found out that we weren’t the only people to do this, and infact mu is the standard word for the concept, also taken from Joshu’s dog koan! Take a look at this: http://en.wikipedia.org/wiki/Mu_(negative)
Mu means not applicable, moot, invalid. It means the statement is incapable of being true or false. This is invariably because one or more or the premises or prerequisites for that statement being true are false. We call this shai, the Second Law of Logic. It states “If any statement is impossible to disprove, it is false.” So Mu can be considered at the same time as falsifiability, anything which whether it is true or false, would have no observable effect on the world is mu. There are different ways a concept can be Mu. There is the classical example used to demonstrate Mu of asking a bachelor “Have you stopped beating your wife yet?” The answer is mu, because the premises of the question are false. But there is another type of mu. Suppose the argument “There is a dog over there. I have a satchel. Therefore you are a piñata.” In this case, the answer is also mu, but while all of the individual statements may be true (and I would question the person who talks to piñatas), there is no relation between them. We call this latter type of mu ‘taim’. Furthermore, this sort argument is not even unsound necessarily although it very likely does seem to be the case. There is no way of actually “knowing” this however based on the logic of the statement, hence it being deemed mu.
We aren’t the only ones to use this concept, in computer programming it is called null, in mathematics its called the null set and it is also used allot in Buddhist logic. It is a third value of logic along with true and false, and the answer to most paradoxes.
For more info on this sort of logic you should check out http://en.wikipedia.org/wiki/Multi-valued_logic and http://plato.stanford.edu/entries/logic-manyvalued/
For more Buddhist koans check out http://www.thezensite.com/ZenTeachings/Teishos/Tarrant_koan_mu.html
-Both Civilsavage and Mouse