A dialetheia is a

true contradiction - a statement such that both the statement and its

negation are true. People who can stomach this idea, and believe there are such things, are called

dialetheists - which doesn't imply anything about their

religion: the word breaks down as

**di-** (

two) -

**aletheia** (old Greek for

truth - see

*aletheia* where it is explained rather well).

A commonly given example is the 'liar paradox'
(*Epimenides paradox*, 'this sentence is false', etc.) The reasoning may go as follows: if it's true, it's false; if false then true; hence assuming either its truth or falsity implies both its truth *and* its falsity - it comes out the same.

Disregarding the falsities, both the statement and its contradiction may be said (by brave dialetheists, anyway) to be true.

For this idea to be any use in logic, we must use a deductive system where a true contradiction does not let you immediately prove all statements (*ie.* the *Ex Falso Quodlibet* rule, which is valid in the 'normal' propositional calculus, does not hold) otherwise the acceptance of one dialetheia would enable us to prove any
arbitrary statement, making our 'logic' trivial - any statement can be proved in it!

Fortunately help is to hand, in the form of paraconsistent logics and the related (and gloriously named) field of inconsistent mathematics^{1}.

Paraconsistent logics which accomodate this logical
'feature' include many-valued logic(s) where statements can evaluate to *true*, *false*, or *both true and false* (to {T}, {F} or {T,F}) and worse.

The most plausible type of dialetheia I've found is *not* drawn from maths or logic. It's a quote from an obscure book called *The third wor*d war*. The original goes (as well as I can remember):

*Words mean anything these days*
*Words do not mean anything these days*

If that seems too

self-referential or

general to be plausible, how about:

*Moral terms mean anything these days*
*Moral terms do not mean anything these days*

Perhaps these are a special brand of dialetheia, such that the statement

*means the same thing* as its contradiction. I doubt even paraconsistent logics have a

theory for that, yet.

1. **I swear I am not making this up**. If you don't believe me, have a look at:
`
http://plato.stanford.edu/entries/mathematics-inconsistent/.
`