Does double negation turn “neither” into “either”?

Peter Guess posted tongue twister with a construct where something occurs that creates what looks like a paradox to me.

neither either...or...or nor neither...nor...nor are either particularly wrong or strictly right

stripping of tonguetwisting:

Neither A nor B are either X or Y.

like in:

-- You have a van and a truck. Do you have any red or yellow cars?
-- Neither the van nor the truck are either red or yellow. They are both blue.

(meaning both A and B are not X, and they are not Y too.)

But following the common, intuitive usage of:

A is neither X nor Y.

this would seem like the sentence should read

Neither A nor B are neither X nor Y.

What rule is applied here that the negative (neither X nor Y) turns into a positive (either X or Y)? Is the double negation unrolling double-"neither" back into "either"?

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Btw: Neither ... is, at least in this context. – Kris Oct 10 '12 at 13:40

Let's simplify it down by turning one of the "multiple choices" into a single value. Like we could say, "Neither the van nor the truck is red." That's pretty clear and unambiguous. The van is not red and the truck is not red.

"Neither" is basically short for "not either". So let's go back to "Neither the van nor the truck is neither red nor yellow." Let's drop the yellow. Now, "neither" is a "negating word", so if there was only one option, it would have to be replaced with "not" or something similar. That would leave us with the analogous sentence, "Neither the van nor the truck is not red." I think that means that both ARE red, but it's a contorted sentence, at best unclear.

So going back to the two-by-two case, I think it follows that if you negate both sides, you turn it into either one of those "double negative equals a positive" cases or just a jumbled mess. You have to make just one side or the other negative. That is, either:

Neither the van nor the truck is either red or yellow.

Or

Both the van and the truck are neither red nor yellow.

Or maybe better still:

The van is neither red nor yellow. The same thing goes for the truck.

:-)

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Well done. BTW, there is also the construction “Neither the van nor the truck is red nor yellow.” That sounds a bit old-fashioned though. – tchrist Oct 10 '12 at 14:05

Logically you are trying to say

(A and B) are not (C or D).

The way I see it

'(A and B) are not'

becomes

Neither A nor B is

leaving only the (C or D)

which becomes simply

C or D

Putting the 2 together you get

Neither A nor B is C or D

Or something like it.

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-1: This answer doesn't make any sense at all. Whatever happened to OP's X and Y? You can't just rephrase OP's text substituting A for X and B for Y! Obviously A and B are things which can have attributes, whereas X and Y are the attribute values themselves. – FumbleFingers Oct 10 '12 at 23:02
I agree, I really should have used different letters for the second A or B so I will change them to C or D. – Alan Gee Oct 11 '12 at 7:03
Okay, I've removed the downvote. I still don't see any good reason for switching OP's X/Y to C/D. I'd also say that you need to be careful converting English to formal logic. Bracketing (A and B) suggests you're analysing something like "Jack and Jill are neither a married couple nor siblings", which isn't OP's structure at all. Logically, I think all we have is A is not C and A is not D and B is not C and B is not D. – FumbleFingers Oct 11 '12 at 12:46