I've just seen someone comment: We send our children to fight in a war we know not what we are fighting for. I am not English expert (it's not even my first language) but the structure just seems wrong but I have no idea if it is or why it is or isn't wrong. Need an expert's opinion.
"Know not" (along with other verb+not constructions) has been a feature of English for quite a long time. Look at Hamlet's lament (c. 1600) to his companions Rosencrantz and Guildenstern:
I have of late—but wherefore I know not—lost all my mirth ...
Subject to the usual caveats regarding Google NGrams (basically, that they are often misused, are riddled with inaccuracies, and are almost always open to interpretation and dispute), here is a fairly unsurprising graph of know not vs do not know.
It appears that "know not" began to be eclipsed by "I do not know" by the middle of the 19th century. Use of the former has been diminishing, but has it disappeared completely?
I think not.
Yes. The same verb+not form as "know not." Think of how many times you've heard someone say that. It has an archaic and somewhat stilted feel, but is it grammatically copacetic? Certainly. As @Sven notes in a comment, it is frequently employed "for literary or oratory emphasis" (as it was in President John F. Kennedy's inauguration speech).
You’ll also hear the construction in proverbs like “waste not, want not.”
Apparently in old English there was no 'do' support to form the negative verb as in the now more common form 'don't know'.
I suppose the intention of that use is to make the sentence sound somewhat dated.
Compare also with the quote from some English versions of the Bible
... they know not of what they speak ...
At my civil marriage ceremony in England in 1997 I was asked to say: "I do solemnly declare that I know not of any lawful impediment why I [name] may not be joined in matrimony to [name]." Those exact words were compulsory, maybe they still are.
The introduction of civil marriages in the UK dates back to the 1830s. That is the point at which those very words were incorporated as essential words to be used in the ceremony. They were grammatically correct then as they are now, but I do not suppose anyone would use them nowadays.