"Isn't it hot?"
I absolutely don't get it. The way I see it both "Isn't it hot?" and "Is it hot?" are kind of the same question, but there seems to be a significant detail in Japanese - when [hot] is negated and thus the meaning changes completely. あつい is [hot], あつくない is [not hot]. So, wouldn't "あついですか？" be "Isn't/Is it [hot]?", and "あつくないですか？" translate as the OPPOSITE of that - "Isn't/Is it [not hot]?"
Thats actually not correct. I've spoken to several Japanese speakers and "あつくないですか?" is specifically asking if its "not hot", not "isn't it hot". They're expecting a "yes" if you're cool, and a "no" if you are actually hot, which is the opposite of what you'd expect with "isn't it hot" in english. Duo has mistranslated all of these "isnt ___?" questions to make them opposite in English from what a Japanese speaker would ask. "Isn't" in English assumes the negative and seeks a positive answer to confirm the negative, the only thing that exists in Japanese like that is "ね" at the end of the sentence.
This should be translated as "is it not hot?", since that'll make both Japanese and English responses of はい/yes mean the same thing, rather than the opposite as Duo translates it.
No, either you haven't understood what I said, or you haven't understood how Japanese use Yes and No.
In English we answer yes or no based on the fact itself: It isn't hot, is it? Yes (it is hot) / No (it is not hot).
In Japanese we answer yes or no based on what the counterparty says: あつくないですか。はい (What you said is right. It's not hot) / いえ (What you said is wrong. It is hot indeed).
I would disagree with your English statement. I had a lengthy discussion with another poster about it, and it seems that your way of thinking and where you were raised determines the colloquialization of "isn't". To me, "is it not hot" doesn't colloquialize, to which I'd say "yes, it's not hot" or "no, it is hot", which uses a logical argument. I'm being asked if (not hot) is true or false. This doesn't maintain the case when you use "isn't it hot?", where isn't is colloquialized to become "is it hot?" Which is what the original poster was commenting on.
My response was from asking someone using Japanese everyday, on what the speaker was looking for, wether they were colloquializing the 暑くない or not, just as in English. Through another lengthy discussion, it seems some Japanese colloquialize it, while others don't. From my understanding, 暑くない is the equavalent of (not hot) as a singular state of being in English. When you ask "is it (not hot)" you preserve the entire state in your response (assuming non-colloquialized), which becomes "yes, it's (not hot)" or "no, it's not (not hot)", the later of which becomes "no, it is hot".
That's my understanding with the issue of using "isn't" as a colloquailized string, which may or may not happen in English, and may or may not happen in Japan. Essentially this entire line of questions becomes nearly impossible to derive the true meaning without additional context on both English & Japanese sides.
You're confusing "It isn't , is it?" and "Isn't it ?" These have fundamentally different meanings. Say you were driving the car and you had a passenger. Worried that they might be hot and that you might need to turn on the A/C, you ask the question "It isn't hot, is it?" to them to confirm that they are indeed not hot and you do not need to turn on the A/C. If they answer "no, it isn't", you have received confirmation that no, you do not need to turn on the A/C, because your passenger isn't hot. If they answer "yes, it's hot", then you decide you have to turn on the A/C because your passenger is hot. When asking this question, you are expecting the possibility of either "yes" or "no".
However, "Isn't it hot?" isn't used in the same way. Let's say you and a friend were on summer vacation and it's really hot. You ask your friend, "Isn't it hot?", expecting to recieve confirmation that it is indeed objectively hot. The answer you are expecting is "yes", or "yes, it's hot", which would mean you were correct and it is hot. You do not expect the "no" answer from your friend from this somewhat redudant question, you are fully expecting your friend to echo back that it is indeed hot.
When you use an adjective in a negative question in Japanese, you think that the adjective has its positive meaning and are looking for confirmation. If you say 暑くないですか (atsukunai desu ka), you think that it is hot and are looking to the listener to agree with you.
In my dialect of English, "isn't it ~?" carries the same connotation. When Stevie Wonder sang "isn't she lovely?" he thought the muse of his song was lovely and was looking for confirmation.
If you're worried about how to answer such a question in Japanese, just agree with the person and say 暑いです (atsui desu), thereby maintaining the 和.
You gotta be careful about this though, because while it is often colloquailized to mean "isn't it?", it's not always - for both Japanese and English.
If we're eating soup and you get a disgusted look on your face, I'd ask "What? Is it not hot?" And I'd expect a reply of "Yes, it's not hot (and therefore disgusting)."
I've also discovered it tends to highly depend on the person asking and their background. Those with more literary backgrounds tend to colloquailize all the time, where as those with a more mathematical/engineering background, like myself, tend to focus on the logic of the question and not colloquailize the phrase.
All in all, it's just really confusing, and there's no clear answer.
I was explaining the Japanese and why duolingo chose the English interpretation that it did. I appreciate that you've put a lot of thought into it and that not everyone speaks English the way that I do. I also understand that I make a lot of mistakes in Japanese, but it's never not been my experience to have someone ask me 暑くないですか (atsukunai desu ka) and not expect me to answer 暑いです (atsui desu). (Please enjoy all those negatives.)
In your example, the person is asking the question because they think that the soup isn't hot enough, whereas if a Japanese person asked me 熱くないですか (atsukunai desu ka), they would usually be asking the question because they thought the soup was (too) hot. I understand that your goal is to get the same answer to the question, but for me the intent behind the questions is completely different so they don't mean the same thing at all.
I expect that "is it not hot" has already been added to the database of answers, so everyone can answer the Japanese-to-English questions the way that they want. I know I'm not going to change your mind on "isn't it hot?" being the best answer for the English-to-Japanese questions, but there are certain other English translations on this site that I don't agree with, and the most important thing is that even if we have to type answers we don't agree with to pass the question, that in the end we've understood the Japanese.
I do appreciate your feedback - lord knows some of these questions need more feedback. I'm of the camp that there is no real "best translation" available, so it's not that "isn't it hot?" is good or bad. As you've said, it's one of many possible ones. I was just providing a friendly reminder, not to you, but to anyone else who may stumble across our posts, that it's slightly more complicated than "answer opposite of what you think" as I've heard it said. There's 4 different sides, 2 different perspectives of delivery and 2 different perspectives of receiving. I was just alerting people to be mindful that there are other ways to interpret this. I know I was on 1 specific side of the camp when I first came across this question, and didn't consider that anyone else could be right, logically. Turns out I was misguided, and acknowledge that. I'd just like others to be mindful and even if they don't understand it, it's not technically wrong either way. This is what my math brain hates the most about languages - 1 + 1 should always be 2... Not 3 when you're sick, or maybe 1 when I'm wearing a purple hat. Math is very concrete, and language is anything but.
As I understand it, ATUKUNAI DESU KA would be a request for information - say, if your roommate went out wearing a tee-shirt and then came back a couple of minutes later and, to your surprise, changed into a sweatshirt. ATUI DESU NE would be a request for agreement - say, if while walking down the road you stopped to loosen your collar and mop your brow, and just then a friend came along also mopping his brow. In English you might say "Isn't it hot?" in either case, but the given Japanese translation wouldn't suit them both. Correct?
I think in your first example you are thinking of using あつくないのですか, where the の asks for more information.
あついですね - I think it's hot. I'm making a statement, but feel free to chime in and agree with me.
あつくないですか - I think it's hot. Don't you agree? I'm asking what you think, but I think you will agree with me.
あついですか - Is it hot? I'm asking because I don't know the answer.
あつくないのですか - I think it's hot, but it seems like you don't think it's hot. Isn't it hot??