Understanding 心を開く開けないを話し合う

Question

そもそも士道はまだ、映像越しでしか六喰と話をしていないのである。これで心を開く開けないを話し合うのは滑稽というものだ。

Source: 「デート・ア・ライブ」

Could you please explain the grammar of the bold part? Why can two verbs be connected directly like that? And why is there not a の before を?

Answer 1

There is a mostly colloquial expression putting a verb's dictionary form and its negative together, such as するしない (there seems to be a JLPT idiom するしないにかかわらず which employs this form, but it can be used independently), which equates to either するかしないか "whether V or not V", or するとかしないとか "to V and/or not to V", "such as V-ing and not V-ing".

The latter sense needs some understanding of connotation. People are usually not really interested in whether to do it or not when they say it, but they use it casually to refer to some discussion or conversation around the topic of "V-ing".

りんごの皮をむくむかない whether to peel or not to peel an apple
同窓生の顔を覚えているいないの話題 a topic like how much you remember old classmates' faces
cf. 言った言わない（の話） he said she said

Now when you look at your example, it has a small grammatical prickle. When you use this construction you expect the verb forms to be the same except for the negation. However,

これで心を開く開けないを話し合うのは滑稽というものだ。

開く has multiple possible synonymous readings, but there is no exact match for this specific combination. It should be:

• 心を開【ひら】く開【ひら】かない
• 心を開【あ】ける開【あ】けない
• 心を開【ひら】ける開【ひら】けない (potential forms)

This may be the writer's slip of the pen, or their particular writing style I don't know. If I can assume it to be the same as 心を開く開かない above, the sentence can be translated like:

It's just ridiculous at this point to have a talk about things like opening up your heart (or not).