'Not having finished" or 'Having not finished'?

[2006]

Obviously, some of us don't agree.

 

[konungursvia]

Clearly.

 

[chester_100]

Another way of trying to express what I meant by the assertion it`s ridiculous to describe as a state of achievement anything which is in fact a non-action. To stretch it a bit:

Having not completed her homework, she decided it was not unpleasant attaining the heights of incompletion; later that day, she went on to leave unfinished a short story, and by nightfall, she had not finished an entire novel. She would go on to win the Nobel Prize in Inaction, for during her forties and fifties she managed not to translate the complete works of Balzac into the complete works of Dickens. In her old age, she revealed her secret: `Not completing things is an art; we must begin by not starting, and then, every day, we must remember to devote several seconds to not continuing. Before you know it, you`ve got your non-work ready to leave unpublished.`

Do you see what I mean....

It`s `Not having completed,` not `having not completed.`

That certainly solves the logical problem.
How about syntax?
All of the constituents in the first one are in perfect syntactic order. As you say, the second one is sort of awkward.