One of my favourite German words, as well as one that lots of German learners find hard to grasp the meaning of, is doch. It took me so long to get to grips with this word that now any chance to use it is a delicious treat.
Like many German words, doch is difficult because, as well as standing on its own, it's often deployed as a particle. It's one of those frustrating tiny words that get thrown into German sentences like confetti, changing the whole meaning in some unquantifiable fashion, of which native speakers tell us, "Well, it's hard to explain exactly what that means..."
A few years ago, I finally found a memorable and concise definition for doch, though I can't remember where I saw this. Doch is "a positive answer to a negative question." It's a missing word in the English language that fills an annoying gap.
Here are some examples to make it clearer what I mean.
A positive answer to a positive question might be something like this: "Did you take the bins out?" "Yes." It's clear what's going on here. A negative answer to a positive question is also clear: "Did you feed the cats?" "No."
A negative question, in this framing, would be something like the following: "We don't have any chores to do today, right?"
If I reply with yes, am I saying that the speaker is correct, or that we do in fact have chores? English-speakers have to clear up this ambiguity with a longer answer. In German, one can just say, "Doch."
A stranger in the Berlin railway station once called out to me in German, as we rode the escalators in opposite directions, "Cool hair! But that's not your natural colour?" "Doch!" It was bright blue at the time. I was very happy, not only to know the punchline to the joke and laugh with a stranger, but for the perfect excuse to use this word. (I was also rather punchy because I was getting off an overnight train at 6 a.m., and most interactions would have made me laugh right then.)
Knowing this definition of doch makes it easier to see the work it does when plunked in the middle of a sentence.
Er ist doch nicht gekommen: He didn't come, though. He still didn't come. Nevertheless, he didn't come.
Ich habe so viel geschrieben, doch ich bin noch nicht mit meinem Aufsatz fertig: I've written so much but I'm still not finished with my essay.
This blog post gives many more examples and goes into detail about the different uses of doch. I feel, though, that everything falls into place once you understand the chief definition of the word. The nicest thing about living in a German-speaking region is that I can use it even in English conversations. Everyone understands what I mean and exchanges have a lovely, logical flow.
One last question remains open: do we need a word for a negative answer to a negative question? I actually think that no suffices for both situations, but perhaps there are languages that have one?