Can we not go there

[넥서스샤프]

1. Can we not go there?
2. Can't we go there?

3. Are we able not to go there?
4. Aren't we able to go there?
I'd like to know if #1 means #3 and #2 does #4.
Thank you in advance for your help.

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This seems rather complex. Let me see. Here is what I think:

Sentence #1, in general, could actually mean two things, depending on how you think about it.

If you think of it as ‘Can we not go there?’ (let's call it ‘sentence #1.1’), then the speaker is asking if it is true that they cannot go there. It is like he received some sort of information that they cannot go there, and he is confirm‎ing it (asking in the negative form because he thinks it is the most likely result). The word ‘not’ affects the verb ‘can’. In this case, the sentence has the same meaning as sentence #2: ‘Can't we go there?’.

But, if you think of it as ‘Can we not go there?’ (let's call it ‘sentence #1.2’), then the speaker is asking if it is possible for them not to go there. It feels like he does not want to go there, and asking ‘Can we please not go there?’. The word ‘not’ affects the verb ‘to go’.

Considering the context of your dialogue, it seems that this second interpretation is the correct one. Anne does not want to go there: and ‘to go there’ means ‘to talk about it’. Upon being asked whether or not she will tell her mother that her boyfriend is four years younger than she, Anne asks Sophie not to talk about it: she does not want to discuss the issue.

Sentences #2 and #4 mean the same thing. As I said before, both also have the same meaning as sentence #1.1.

Sentence #3, just as it is (let's call it ‘sentence #3.2), means the same as sentence #1.2 (the word ‘not’ affects the verb ‘to go’). But, if you rewrote it as ‘Are we not able to go there?’ (let's call it ‘sentence #3.1), then it would mean the same as sentence #1.1 (the word ‘not’ affects the verb ‘to be [able to]’).

To summarise:

Sentences #1.1, #2, #3.1 and #4 mean the same thing. The word ‘not’ affects the verb ‘can’ or ‘to be [able to]’. It is being asked if indeed it is not possible to go there — that is, if it is impossible to go.

Sentences #1.2 (the one used in the text) and #3.2 mean the same thing. The word ‘not’ affects the verb ‘to go [there]’. It is being asked if it is possible for them not to go there — that is, to refuse to go even if it is possible to go.

I know, it is confusing. Even I was rather confused as I was thinking about this. But I believe that this is the correct answer (though I may be wrong). I hope this has been helpful!