"Both," "neither," "either," and the slippery plural

I recently made this claim on Facebook:
You might see a sentence like "I have an aversion to figs," or "I have an aversion for figs." Neither of these are ungrammatical, but "aversion to" is quite a bit more common, so it seems more natural.
And while nobody balked at the point about "aversion to" or "aversion for," there was a comment—can you see it coming?—about using "neither" as if it were plural ("neither of these are" as opposed to "neither of these is").

And for the record, I didn't mean to do that. I like to keep it simple: "either" is singular, and "neither" is singular. However, there is a more nuanced usage point here that allows for "neither" as a plural. Here is what I wrote on Facebook:
Indeed, I meant to write "neither of these is ungrammatical," since I see either and neither as singular. However, in the case of neither there is a school of thought that allows for a plural sense, especially when used as a negation of both. That is the case here, where the meaning is identical to "Both of these are grammatical." A plural sense is retained even when both changes to neither.

As Webster's Dictionary of English Usage points out, that is what Shakespeare did in these lines from Cymbaline:

Theristes' body is as Ajax'
When neither are alive
Which is to say that "neither are alive" is identical in meaning to "both are dead," so "neither" is acceptable as a plural when it is the opposite of "both" and not a negation of "either." Webster's goes on to provide several examples of such usage from many edited sources by professional writers.

However, it is completely safe and sane to just stick with the "'neither' is singular" guideline, which is what I tend to do. Still, in the heat of the moment--speech and unedited writing especially--it is easy to see how the plural verb shows up. Also, while I do have a high opinion of myself—ahem—I don't think Shakespeare needs my writing tips.

See also the usage note in the entry at Dictionary.com.
So there you have it, a lucky instance where I did not follow my own personal style guide but still managed to fall within the parameters of standard usage. It happens. You can read the whole Webster's explanation here.

I do like to keep it simple in such instances and remember to use is rather than are, but I'm not perfect; and by the way, neither are you.

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