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In the SEP article on negation, they say:

Where we do not find negation is in the one place propositional logic would lead us to look, sentence- or clause-peripheral position, as an external one-place connective interpreted as “it is not the case that”. (Horn 1989 takes apparent instances of external negation in English and elsewhere to represent the metalinguistic use of negation, discussed in §1.10 below, while Bar-Asher Siegal 2015 presents evidence for the existence of a semantic external negation operator in Jewish Babylonian Aramaic.)

I checked the indicated section, which didn't seem to cover the use of the word "no." But so take some declarative question:

  1. Do you want to go to Xanadu?
  2. No, I don't want to go to Xanadu (maybe I don't want to go anywhere!).
  3. No, I want to go to not-Xanadu (I want to go somewhere besides Xanadu/I want to go to Shangri-La).

Oddly or not, "no" as used requires inserting a "not" into the negated proposition, and the double negation on the phrasing level is a single negation on the interpretation level. So one might just as well not use "no"? I also considered "no" for imperatives:

  1. Go to the store?
  2. No, go to the library.

I would tend to read a speaker A of (4) as holding, "Go to the store," to be directed by the B-speaker of (5) at A. Maybe A is hard of hearing and is asking B to clarify some instruction. When B denies (4), they are not issuing a command to themselves; they are not disagreeing with/rejecting directions for themselves but for A. But we can also ask such questions of ourselves: "Spend my afternoon reading?" "No, spend my afternoon exercising..."

Is, "No," an example of the kind of natural-language negation that the SEP article says is not to be found? Or is this issue addressed in the cited [Horn1989]?

EDIT: I don't know if I'm reading the article correctly. I take, "English doesn't have a sentence-level negation," to mean that, for some sentence A, ~A as "Not A," isn't the kind of thing English-speakers would almost ever say, and/or isn't a faithful use of the word "Not" in English as such. Which is why "No" seems like a counterexample to that claim, albeit one that implicitly transfers "not" across the sentence/predicate threshold.

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  • Preliminary examination of NO yields only trivial results, as suggested by the OP itself. Negation however is a powerful item in our toolkit, but comes at a cost - much like everything friggin' thing in our world I guess. At times negation seems so nonphilosophical, I would even go so far as to accuse it of being blatantly antiphilosophical. May 20, 2023 at 13:53

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"No" is not a one-place connective, so it doesn't even fulfill the syntactic requirement of being a sentence-level negation. It is either a one-word sentence or a counting word pretty much equivalent to zero.

As to semantics, the examples you gave are not examples of "no" modifying the following sentence, they are examples of "no" being used as a one-word proposition, an answer to the question that preceded the "no". What comes after the "no" in your examples are redundancies or additional details, not parameters to a "no" operator.

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  • The SEP article on questions says that for some reason, "Most authors require answers to be sentences or propositions, so that answers to a question are the kind of thing that is true or false. Tichy (1978) is a striking exception and argues that answers can be of any logical type," incl. single words/noun-phrases. But so why would a one-word sentence, "No," fail to count as a negation of a previous possible sentence? May 20, 2023 at 14:28
  • Or if, instead of asking questions, we had someone say, "The moon is blue," and then someone says, "No," to that. This would lead to, "The moon is not blue," or a positive claim about another color. But so I still don't see how the initial, "No," fails to negate the original sentence. I mean, imagine, "The moon is blue," and then, "No, the moon is blue." Would that make sense? May 20, 2023 at 14:31
  • @KristianBerry, do you know what a one-place connective is? My answer assumes you do, but these responses seem to indicate otherwise. I didn't say that "no" doesn't negate a sentence; I said that it's not a one-place connective, which is exactly what the SEP quote says doesn't exist. May 20, 2023 at 14:39
  • Isn't a one-place connective an operator that attaches to one sentence to yield a new sentence? May 20, 2023 at 14:47
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    @KristianBerry, yes, in a sense it's a trivial point, or at least it's a point about syntax rather than meaning or truth. They aren't saying that you cannot negate a sentence, just that there is no specific syntactic operator of the form "not X" to negate a sentence X. In English, of course, you can't say "not I'm hungry" like you can in propositional logic. May 20, 2023 at 18:31

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