how to understand "...whether he could not somehow turn Jones’s misfortune to his own"
I was reading the "animal farm", and I saw a sentence:
'"each of them was secretly wondering whether he could not somehow turn Jones’s misfortune to his own "
I don't understand why it's '"...whether he could not...'"
I prefer "...whether he could..." or "whether he could or not..."?

Question

how to understand  "...whether he could not somehow turn Jones’s misfortune to his own"
I was reading the "animal farm", and I saw a sentence:
'"each of them was secretly wondering  whether he could not somehow turn Jones’s misfortune to his own "
I don't understand why it's '"...whether he could not...'"
I prefer "...whether he could..." or "whether he could or not..."?

Answer

It means the same as 'if he could'. 
To be honest, I don't know exactly why we say it like that, and I am now curious as to how the grammar works,  BUT it is certainly a structure that we use.

Answer

You could have "whether he could" or "whether he could not". The first is a more neutral style.  The second adds a shade of drama and intrigue.  You might have seen this in questions e.g.

"Will you have a cream cake?  I bought them fresh today." (neutral)

"Won't you have a cream cake?  You know how nice they are.  Go on!"  (with the intention of persuading the other to eat one)

Answer

Mr Gary
this sentence is from Google "I'm going whether you like it or not"

Answer

Why do people for whom English is a second language say things like "I prefer" or "I think it should be"?
And then offer suggestions that simply aren't proper English? (as your second option is) Do you realise how arrogant it sounds to suggest that you know the language better than a native speaker?