I run into problems in this sentence from Vim documentation:local-options:

Each window or buffer has its own copy of this option, thus can each have their own value.

  1. Why should the modal verb "can" and the subject "have" be inverted? Is the structure othervise grammatical?
  2. Why is the pronoun "their" plural rather than singular "its" matching with the singular subject of the clause "each"?

Subject-auxiliary inversion can be used to indicate that a clause is not in the indicative mode.  The interrogative mode of simple questions is usually formed in this way:  "Can each have its own value?".

The interrogative mode isn't the only non-indicative mode.  There is also the subjunctive and the imperative.

Normally, the imperative simply drops the second-person subject.  Offhand, I can think of only one fixed form that uses inversion instead:  "Don't you dare."

Your example seems to be a subjunctive inversion.  It's more common to see this kind of inversion in conditional clauses and in negated clauses:  "Had I been permitted, I could have done something."  "Never would I do that kind of thing." 

The inversion in your sentence is grammatically correct.  It is, however, a bit unusual.  I would find it more natural to simply use the subjunctive form of the auxiliary:  "Thus, each could have its own value."

I have no explanation for this use of "their".  A singular "its" would agree with the singular antecedent "each".  There's no reason to employ gender-neutral language for genderless things like windows and buffers.  I have to consider this "their" to be an error.

I don't consider "thus" to be a conjunction, so I do consider the example to be a run-on sentence, specifically a comma splice.  Comma splices are errors in scholastic dialects, but I tend to regard them as a question of style in other contexts.

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