non-negation story problem

I've just realized that the issue of double negatives is actually a math problem.

English teachers insist that putting two negatives together causes them to cancel out. In other languages, putting two negatives together intensifies or modifies the negation, rather than, um, negating it.

I once, as a young linguistics student, had an argument with an elementary school teacher of my parents' long acquaintance, on this very issue. It was impossible to convince him that two negatives could augment each other. He insisted that they 'logically' cancelled each other out.

It is a bad idea to tell me that I'm being illogical.

It's one of those pointless things that burrs in your memory. Then, last night, having drunk one crap Bellini and half a crap margarita slush at Earl's (yes, we all knew that resolution would quietly fall to bits -- but I'm still drinking less coffee) I was flipping through the dictionary and revisited i, which as you know is the square root of minus one. In school they told us that it was called an imaginary number, and that that was a silly name because it wasn't really imaginary.

Thoughts began to accrue under my pen. "i am the square root of negative one." Which sounded like a damn good opening for a story about someone with low self-esteem.

Negation is a slippery thing, much less robust than, er, positivization. Both -1 squared and 1 squared work out to 1, but it's only by inventing this number i that we can find a creature that in multiplying itself doesn't negate its own negation.

And it occurred to me that the reason English Language Authorities have decided that "not not blue" means "blue" is that they're reading the negatives as multiplied by each other, rather than added.

Which actually isn't particularly logical. You could as easily read it as addition.

A) Not not blue : (-1)(-1)(blue), or +1 blue
OR
B)Not not blue : (-1 + -1) (blue), or -2 blue

We're still treating the operation of modifiers on the adjective as multiplication, only because otherwise we get difficult semantic ideas like:

C)Not not blue : -1 + -1 + blue, or -2 + blue

And I'm not sure what (-2 + blue) would translate back to, unless we assign 'blue' an absolute value, although I'd like to try to figure it out.

So maybe my bugbear teacher had a point by analogy within the mechinery of the English language. After all, if we modify the negation, that acts like multiplication:

D) Very not blue : (X)(-1)(blue), or -1X blue, not
E) Very not blue : X + -1 (blue), or (X-1)blue, which would translate to "Not as not blue as just plain not blue."

But there's still no particular reason to assume that identical modifiers should act together amongst themselves like multiplication instead of addition. It all depends which parallel gramamtical process you make your analogy on. Once you go to another language, you'd have to look at how its machinery works before you could decide if the rules about negatives were consistent with it. Which I rather think they would be, brains being what they are. You couldn't work from English assumptions, Mr. Teacher Guy.

Before this, I'd always approached the distinction slightly differently, as the difference between:

not (not blue)
and
not, not blue

{rf}