Proper yes/no answer to a question posed in negative form

Question

Should the question, "Does anyone not understand this?" be answered yes or no, if one does understand?

Answer 1

Assuming that this is addressed to a group, the normal response is for those who do understand to remain silent, and for anyone who does not understand to say something like "I don't understand", thus removing any ambiguity.

Questions like this are fraught with ambiguity. The dangers of a strictly logical approach are illustrated by this joke:

Five pure logicians are in a restaurant. The waiter asks "Does anyone want a drink?". The first logician says: "I don't know.". The second, third and fourth also say "I don't know.". The last logician says "No."

Answer 2

In response to the question:

Does anyone not understand this?

If you answer:

• "yes": You are saying that you are one of the people who does not understand. That is, there is at least one person who does not understand, which is you. There may or may not be other people who do or don't understand, but that is irrelevant to your answer. (Minor note: OK, technically you could be speaking on behalf of someone else. You might answer, "Yes, there is someone who does not understand this. That person is John. I understand this, but John does not. I'm speaking up for him." However, this is not the most typically response, because usually when a speaker asks "Does anyone...", the speaker is expecting each person to speak only for himself/herself.)

• "no": You are saying that "not understanding" does not apply to you or anyone else who hears the question. If your goal is to indicate that you understand (i.e. just to speak for yourself), it would be more logical to avoid speaking at all. Answering this question with "no" means that you can answer on behalf of the group. That is, if you say "no," it does not mean "I understand"; it means "There are no people in this group of listeners who does not understand, i.e. everyone in this group of listeners does understand."

Finally, it's worth noting that this question is in fact easily misunderstood (as evidenced by the fact that it's being asked on this Stack Exchange). Thus, while it's grammatically correct and perhaps even appropriate in some circumstances, it would be preferably (in the interest of clarity) to reword the question to something like:

Please raise your hand if you had trouble understanding this.

Who does not understand this?

One more side note: It is tempting to try to rewrite this as:

Does everyone understand this?

But as anyone who has taught or dealt with large groups knows, people who don't understand are often unlikely to speak up loudly. If the question is asked, "Does everyone understand this?" and 95% of the audience responds, "Yes, we understand," it is unlikely that the lone person who doesn't understand will be willing to speak up (for fear of social rejection), and also unlikely that the speaker would be able to hear the response (because of the noise generated by all of the affirmative answers).