Yes-no questions in mathematics and in Chinese

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From Daniel Sterman:

There’s an old joke about computer programmers (or mathematicians, or logicians). Ask them “Is X right or wrong?” and they’ll answer “Yes”. Because, indeed, either X is right or it is wrong.

Well, a few months ago, most of my team’s operations were transferred to a team based in Shanghai, and they seem to be doing something similar. Whenever I ask a question that offers two alternatives (“Is it A or is it B?”), they always answer with a single, solitary yes or no.

The occasional “no” responses prove that they’re not giving me the Mathematician’s Answer. But I of course have to ask each time, “Yes to which one?” or “No to which one?”. It drives me crazy.

I haven’t yet had the opportunity to analyze the responses I’ve been getting, but I theorize that there is something about the Chinese language (I assume Mandarin in this case) or about Chinese culture that leads to this phenomenon. Perhaps the structure of A-or-B questions, when translated into Chinese, implies something along the lines of “Tell me if it’s B, and if it’s not I will assume it’s A”, or vice versa. Or perhaps the Mandarin words for Yes and No strongly imply “…to that last thing you just said” rather than, as it is in English, “to all that you just said”.

Is my theory correct? If not, do you know of any linguistic or cultural influence that could be causing this?

I will let others speak for computer programming, mathematics, and logic, but we certainly do have yes-no questions in Sinitic languages.  As for Sinitic, I will focus on Mandarin as representative.

In Mandarin, yes–no questions usually have an A-not-A form, and the reply is generally an echo response.

Here are three example sets of yes-no questions in Mandarin with their affirmative and negative responses:

Q: 你要不要吃桔子? Nǐ yào bú yào chī júzi? ("You want or not want eat orange?") — "Do you want (to eat) an orange?"

A: 要。 Yào. ("Want.") — "Yes."  (I.e., "Yes, I want [to eat] an orange.")

N: 不要。 Bú yào. ("Not want.") — "No."  (I.e., "No, I do not want [to eat] an orange.")

Q: 他在不在慢跑? Tā zài bú zài màn pǎo? ("He is or not jog?") — "Is he jogging?"

A: 在(慢跑)。 zài (màn pǎo). ("Is (jog).") — "Yes." (I.e., "Yes, he is jogging.")

N: 不在(慢跑)。 Bu zài (màn pǎo) ("Not is (jog).") — "No." (I.e., "No, he is not jogging.")

In addition, yes-no questions are often formed by adding the particle "吗" (ma for "yes or no?") to the end of a sentence, in which case the answer can be "是的" (shì de for "is [so]") or "不是" (bu shì for "not is [so]"), or "对" (duì for "right") or "不对" (bu duì for "not right"):

Q: 你不上课吗? Nǐ bu shàng kè ma? ("You not go-to class yes-or-no?") — "Don't you have a class?" OR "Aren't you going to class?"

A: 对。 Duì. ("Right.") or 是的。 Shì de. ("Is (so).") — "Right / yes."  (I.e., "No, I do not have a class." OR "No, I am not going to class.")

N: 不对。 Bu duì. ("Not right.") or 不是。 "Bu shì. ("Not is (so).") — "Wrong / no." (I.e., "Right / Yes, I do have a class." OR "Right / yes, I am going to class.")

Source (VHM:  the brief explanations following the dashes are by me; the rewordings  inside the parentheses of the A and N answers convert the full answer to the English way of thinking.)

N.B.:  In the last set of answers, duì 对 may also be thought of as "correct" and shì 是 has the meaning of "is so / thus / this way / as posited" — this is a very ancient use of shì 是; the opposite with which it is often paired is fēi 非 "is not so / thus / this way / as posited".  Early Chinese philosophical discussions on shìfēi 是非 are about "right and wrong".

For many more examples of "Yes-no questions with 'ma'", see this article on Chinese Grammar Wiki.

Half a century after beginning the study of Mandarin, I still find the third type of q & a to be rather mind-boggling.  I suppose that many Language Log readers feel as though their own mind is about to burst as they try to make sense of how "yes" and "no" play out in the Chinese responses.

The whole business is difficult even for native Chinese speakers, as is revealed by the fact that several of the informants who replied to my question about the grammar of the third set cautioned that it is "tricky".  To show how the Chinese and English usage radically differ, I'll simply quote the following responses from native speakers of Mandarin who also know English well (the notes in square brackets are explanatory / clarifying additions by VHM):

1. A graduate student in Sinology:

I think the interpretations for the answers should be opposite.
你不上课吗? ("Aren't you going to class?")
对。Right (Yes, I am not going to class.)
不对. Not Right (No, I am going to class)

2. From a senior language lecturer:

[1st answer:] — Correct. (i.e. “Correct, I do not have a class.” OR “ I am not going to class”)

[2nd answer:]  I would never reply “不对/不是”for this question. I would say““不,我上课。” (“No, I do have a class.” OR “No, I am going to class”)  Just a simple “” is not clear enough.

3. From a senior language lecturer:

If you answered : 对 d ("right.") or 是的  shì de ("is [so]").  It means 'No, I am NOT going to class.'

If you answered : 不对 bu duì ("not correct") or 不是 bu shì ("not [so]").  It means 'Yes, I NEED to go to class.'

4. From a senior language lecturer:

When the answer is 对 (Right!) or 是的 (Is so), the person is actually saying "your assumption is right. I don't have a class or I am not going to class."

On the contrary, when the answer is 不对 or 不是, the person is saying  "your assumption is not right. I do have a class or I am going to class.

In other words, in Chinese, the answer YES or NO is not reflecting the fact the answerer is going to class or not but to the questioner's assumption when he/she asks the question. This is exactly opposite to English so we always have to remind students so that they won't get confused.

5. From a graduate student in cultural studies:

This is one of the most famous brain teasers that appears in English tests of Chinese high schools.

I think the English and Chinese modes of thinking in this case are fundamentally different.

When a Chinese is replying to the question "你不上课吗?", his/her answer is aimed at the whole sentence:

对/是/Yes is an affirmation of the speculation that "你不上课"(the replier is actually not going to class);

不对/不是/No is the negation of “你不上课”(the replier is going to class).

However, in the English language, the answer is only contingent on the key word "上课", no matter how the question is phrased:

If the replier does go to class, he/she answers 对/是/Yes.

If the replier does not go to class, he/she answers 不对/不是/No.

I can hardly tell which mode of thinking is more complex. It's just habit.


6. A graduate student in Egyptology:

I think the "yes" or "no" answer for the negative interrogative in Chinese is different from that in English. The Chinese answer "是" ["is so"] or "不" ["is not so"] is a reaction to the question itself, not the reality.

Question — 你不去上课吗?  Don't you have a class?

Positive answer — 对,我不去上课。 No [lit., "correct"] , I don't have a class.

Negative answer — 不,我去上课。Yes [lit., "no"], I have a class.

I know this is very confusing. I had to pay much attention to this grammatical difference between Chinese and English because I made myself misunderstood by others many, many times. Even worse, many people like to use rhetorical and negative questions!

I believe rhetorical and negative questions are the most difficult in any language. Ancient Egyptians sometimes used double negative rhetorical questions in literature, which are always chosen as grammar questions in our exams!

"Yes, we have no bananas!"  I've seen suggested several places on the web that Frank Silver and Irving Cohn, who wrote a song with that as the title, heard this sentence of "broken English" in New York city in 1922 from a Greek immigrant greengrocer.  Is there an underlying basis for this in Greek grammar?

[Thanks to Maiheng Dietrich, Melvin Lee, Liwei Jiao, Fangyi Cheng, Yixue Yang, and Jing Wen]


  1. Avinor said,

    February 10, 2017 @ 9:23 pm

    But what about the "A or B" questions that were the subject of the original question? How are they expressed in Mandarin?

  2. Chris C. said,

    February 10, 2017 @ 9:38 pm

    That third type is even a tad difficult in English, isn't it? "You didn't feed the cat, did you?" is only ambiguously answered by "Yes" — as least as far as my literalist brain is concerned — and is only really clear with an answer like "Yes, I did."

    I came to very much appreciate the French "Si" when I was learning that language in high school.

  3. satkomuni said,

    February 10, 2017 @ 9:56 pm

    Two things: "The occasional “no” responses prove that they’re not giving me the Mathematician’s Answer." They do no such thing; if neither A nor B is true, then in logic "A or B" is false; the "or" is inclusive. But as to the main point, Chinese (MSM) uses a "还是" construction to ask the kind of question OP is asking about: "你喜欢肉丸子还是狮子头?" (Do you like/prefer tight meatballs [A] or huge, loosely packed, starchy yet watery meatballs in brown, potato-starch-thickened gravy [B]? lit. "You ike A or B?"), just like english, is an exclusively exclusive "or", and cannot be answered with a simple "Yes" or "No", so I don't think we're barking up the right tree here.

  4. liuyao said,

    February 10, 2017 @ 10:12 pm

    Likewise it is driving Chinese who come to US (and those who have to converse with them) crazy. (It reminds me questions of the type "Do you mind…" I think Americans are not careful when they answer "sure" or "yeah".)

    As to the original A-or-B type question, the Chinese equivalent would be less ambiguous (logically). "Do you want apple or orange?" would be 你想要苹果还是橘子? (You want apple or rather orange?)

    I'd suggest you use more "rather" in your questions.

  5. Jean-Michel said,

    February 10, 2017 @ 10:27 pm

    @Chris C.: Questions like that are something a lot of ESL learners (not just Chinese-speakers) struggle with. Coincidentally this Chinese-language article on the subject showed up on my Twitter timeline a few weeks ago, and suggests that it's better to just rephrase such questions, even if a nuance gets lost in the process. ("Did you feed the cat?" doesn't have the skeptical tone of "You didn't feed the cat, did you?", but it's simpler to answer.) Of course this advice doesn't help if you're on the receiving end of the query.

  6. WSM said,

    February 10, 2017 @ 10:49 pm

    in technical contexts, for instance when discussing boolean true/false values, it's simply 是/否

  7. hanmeng said,

    February 10, 2017 @ 11:40 pm

    Yes, we have no bananas.

    BTW, isn't a 桔子 actually a mandarin (or tangerine), rather than an orange?

  8. Jonathan Smith said,

    February 11, 2017 @ 12:29 am

    To the original question, Mandarin uses two different words in "Is it A or [is it rather] B?", where or = hai2shi4 還是, and "Is it [A or B]?" (i.e., the "mathematician's interpretation"), where or = 或[者]). Whether this is material to the misunderstandings Daniel is experiencing I don't know.

  9. Colin Mclarty said,

    February 11, 2017 @ 1:44 am

    I wonder whether Daniel Sterman is asking his questions in the form "Is it A 或者 B?" If he is, than I believe Jonathan Smith is right. But if Daniel Sterman is already using the form "Is it A 還是 B?" then I do not understand why people would answer "Yes." I just never ask about two alternatives at once in my own poor Chinese. But I would like to know which form of question Daniel is using

  10. Gregory Kusnick said,

    February 11, 2017 @ 2:39 am

    Because, indeed, either X is right or it is wrong.

    Not so. X could be incoherent and undecidable, or "not even wrong" in Pauli's memorable phrase.

  11. Tim Taylor said,

    February 11, 2017 @ 7:35 am

    I once had occasion to text someone asking 这个礼拜不上课吗?The answer was 嗯. Stupidly I turned up. There was no class.

  12. Su-Chong Lim said,

    February 11, 2017 @ 10:52 am

    The third question is actually phrased logically such that "Is it true that you are not going to class?" would be a more accurate literal translation. Or in more colloquial English "You're not going to class, right?"

    Seen through this logical lens, the answers "Right/Yeah" or "Wrong/No, I am" in English would correspond to the 对 or 不对 in Chinese, and be unambiguous. Although I have to admit, colloquially, "No" would be regarded as somewhat incomplete an answer, which is why I added the "I am" to my response example.

  13. Avinor said,

    February 11, 2017 @ 11:13 am

    Jonathan Smith: Could it be that Chinese early on in their English studies learn that "or means 或 (huò)" and this sticks so well that they always land in the "mathematical interpretation" of an A or B question?

  14. Luís said,

    February 11, 2017 @ 11:47 am

    Poor Daniel can't catch a break. His question was yet again misunderstood.

  15. Victor Mair said,

    February 11, 2017 @ 12:36 pm

    I will write a separate post on choice-type questions. Perhaps that will help to clarify matters somewhat.

  16. Daniel Sterman said,

    February 11, 2017 @ 1:45 pm

    @Colin Mclarty
    I am asking my questions in English, over the company's IM system. The Shanghai team (none of whom are native English speakers) are also answering in English. So they read my question, translate it in their heads into Chinese, formulate their answer in Chinese, and then translate it in their heads into English to answer me.

    I've had "No" responses that indeed meant "neither of your options are correct". But I've also had several that meant "one of your options is incorrect", and (just as with the "Yes" responses) I've had to ask which one is meant.

    However, those are much rarer. It is possible that those instances were unique for some other reason, and as Jonathan Smith and Avinor said, they actually are giving me the Mathematician's Yes in most cases.. I will try liuyao's advice and use "rather" the next time I have something to ask them, and see if that works.

    It is certainly possible that there is, in fact, nothing linguistic going on here, but I submitted my question to Professor Mair in the hopes that there was – and that I could therefore apply what I learned from the answer to phrase my two-option questions more carefully, as with liuyao's suggestion.

    @Victor Mair
    I look forward to the follow-up post, and appreciate the effort you put into this.

  17. John Rohsenow said,

    February 11, 2017 @ 1:53 pm

    cf. Japanese "Hai!": 'it is so (what you said)'.

  18. TR said,

    February 11, 2017 @ 2:17 pm

    The English situation might be clarified by reviving the old four-form (yea, nay, yes, no) system.

  19. AntC said,

    February 11, 2017 @ 3:44 pm

    Thank you Victor, that explains a lot. It seems to me at the core is English over-politeness/diffidence obscuring what a speaker is really asking.

    When a Chinese is replying to the question "你不上课吗?", his/her answer is aimed at the whole sentence:

    However, in the English language, the answer is only contingent on the key word "上课", no matter how the question is phrased: …

    "Would you pass the salt" in English is not a question about your attitude to salt-passing.

    If your original questioner is in a position of authority over "his team", this would combine with the Chinese culture of 'face' to render direct communication almost impossible. I've learnt from experience: don't ask A-or-B questions; don't use "whether"; don't use polite forms like "would"/"could" you/"I wonder"/"is it possible" …; don't use tag questions (which have opposite polarity to the main sentence).

    When Victor's informants said it was "tricky", I think all the trickiness is in the English.

    Of course still be polite/respectful. Just don't mix up the polite phrases in the same sentence as 'business'.

  20. DWalker07 said,

    February 11, 2017 @ 8:25 pm

    In a work setting, I would not answer a question "is it A or is it B" with either "Yes", or "No", because each of those answers is completely unhelpful.

    I have had an ESL coworker say something like "I do not know that" when he meant to say "I did not know that" about something that I just informed him of. It's kinda maddening. Is this difficult for ESL speakers?

    I don't speak his language as well as he speaks English, but …..

  21. Ashley said,

    February 11, 2017 @ 8:51 pm

    This reminds me of my years living in Japan. Often I would ask someone either or questions like "Which would you like the, chocolate or vanilla cake?" or "Should we go out to eat or stay in?" etc and often I would get an answer of 'yes' or 'no'. I couldn't understand why I wasn't getting a straight answer.
    There is a Japanese form for 'Which would you like ___ or ___" so I didn't think there was misunderstanding there. I think sometimes there is a hesitancy to state a firm preference without knowing how it would inconvenience the others.
    Anyone have any thoughts ?

  22. Bruce said,

    February 11, 2017 @ 9:06 pm

    I was counselled from almost from my first Mandarin lesson not to pose a negative question to a Chinese speaker since it doesn't readily conform to any of the best question alternatives that Dr Mair presents.

    For that matter, a negative question in English has its history of problems, and at least in an American or Canadian context (not sure about British or other regions), conventional syntax has evolved:

    Q: Aren't you going to class today?
    A: Nope (affirmation)
    A: Sure am (denying premise)
    whereas plain
    are both unclear

    I like French which has the word "si" as part of its regular lexicon to deny a negative premise, for instance the following example from Wiktionnaire:

    Vous n’allez pas voir ce spectacle ? — Si, nous y allons.

  23. philip said,

    February 12, 2017 @ 5:28 am

    At the risk of being banned from Language Log, I will state the following: there is no single word for 'yes' or 'no' in Irish (in answer to a question containing a verb).

    So maybe we are like the Mandarin language?
    Examples: Did you enjoy the play, Mrs Lincoln?
    Answers: Enjoyed [yes]; didn't enjoy [no].

    Bad speakers of Irish often end up asking questions of the A or B type in an incorrect form mirroring English syntax to which good speakers of Irish can only give what sound like a facetious answer:
    Q: Is the play set in the day-time or the night-time?
    A: Is set/is not set
    Q: Do you want tea or coffee?
    A: Want/don't want.

  24. BZ said,

    February 13, 2017 @ 12:59 pm

    In my idiolect questions such as "aren't you going to class?" cannot be answered "yes". "No" means "I'm not going to class". If you want to say the opposite, it will not be a one-word answer, something like "I am" would be the shortest.

  25. Silas S. Brown said,

    February 20, 2017 @ 7:58 am

    Problems can occur when anybody thinks "yes" is a word you say when you didn't quite understand the question but you don't want to look rude.

    I once found myself alone on the London Underground at a station which I was not familiar with and which was not staffed, and my eyesight is not good enough to read the signs. I asked a passerby if the platform we were standing on is "northbound". He said "yes". So I boarded the train, and next thing I knew I was in completely the wrong part of London because that had been the southbound platform I was on.

    And I know someone whose immigrant parents got into trouble with the UK's TV License enforcement officers. In the UK you have to pay for the privilege of owning a TV, and if you don't pay, the enforcement officers might visit you to check that you don't own a TV, and fine you or take you to court if you admit to owning one without paying. Apparently these officers had asked on the doorstep "do you have a TV?" and they'd said "yes, yes" without understanding the question, with predictable results.

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