Read on its own, it seems to present you with two options; of course that’s not what it’s meant to do, but that understanding is based on the (statistical) norm.

Of course, if you aren’t struck by its oddness at all, then your idiolect is, by my lights, pretty unusual.

In this case the relevant dialect is not “spoken English” (In which btw I think you would never ever hear the construction “no food or no drinks”), but rather “posted notice English”, the subset of the language that you see on signs. In this dialect there are two correct usages: “No food or drinks”, and “No food no drinks”. (This second may also be represented as “NO food drinks” where “NO” is twice the point size of the other words, and the other words are on two lines next to it.)

Another funny NJ sign: if you’re driving down rte. 9W from Nyack, when you hit Bergen County the sign says “Welcome to New Jersey/ Wipers on/ Lights on”—the first several times I saw it I thought it meant you had to keep your wipers and lights on at all times in the state.

True or False:
I rarely hear voices in my head.

Either way, the reader can bring in one, but it makes a difference who gets to choose. (It’s the difference between additive conjunction and additive disjunction in linear logic.)

A language is the spoken language.

I’ve not come across many natural languages where multiple negatives reduce to a single negative. Dialectal English maybe: “we don’t sell no beers to no bears.” And perhaps also Old English. But in Japanese, shinakereba naranai (do-NEG-COND be-NEG) means “should”, and in Chinese—my native tongue—bu4 ke3 bu4 cha2 (not can not study) means “must be studied”. Oops.

Why not? The sign is perfectly sensible. Only someone who attempts to parse the sentence as a mathematical statement will have trouble comprehending it. Everyone else who is a literate native English speaker will comprehend it as intended.

Smug put-downs of supposed misuse of language (like those on exhibit here) are the sophomoric equivalent of criticizing the innacuracy of Star Trek physics. In a deep sense, it’s a category error. I am beginning to believe that I could tolerate an analytic philosopher (of the linguistic philosopher subspeciality or inclination) who comes with substantial linguistics credentials. But the armchair variety? Not so much. Well, really, not at all.

Here’s something that will blow your minds: in natural language, double negatives are usually intensifiers and do not reduce to a positive. Wow! Isn’t that amazing?

Intellectual rigor is not essentially the metaphorical equivalent of a carefully wielded scalpel. It’s first and foremost the metaphorical equivalent of wielding the most appropriate tool.

I’d apologize for my ill-temper, but I expect better around these parts.

And, this has nothing to do with boolean algebra, but I can’t resist: “TRESPASSERS WILL BE PERSECUTED”.