The phrase "acknowledgement that without" is correct and usable in written English.
It can be used when discussing the recognition of a condition or situation that relies on the absence of something.
Example: "The acknowledgement that without proper funding, the project cannot succeed is crucial for securing support."
Alternatives: "recognition that without" or "realization that without".
Truth demands recognition and acknowledgement that justice prevailed.
An acknowledgement that people without homes need... homes!
Hardware companies show of their nice looking new products without any acknowledgement of that fact that, if you've got any regard for your investment, you're going to stick it in a case.
We might go on to have a great conversation, but it would be without any acknowledgement that I was a man and she a woman.
In another painfully honest acknowledgement that life would move on without her, Kate gave permission for pictures of her to eventually be confined to the boys' bedroom once Singe met a new partner.
After the attacks of September 11th 2001, it became clear that the forum's stated purposed of "improving the state of the world" would be difficult to achieve without some acknowledgement that religion mattered.Another effort to bring Islam and the West closer is the "Alliance of Civilisations", established in 2005 under the United Nations at the urging of Spain and Turkey.
Some detainees have been held for as long as 20 years without public acknowledgement that they are being held.
It's gotten so bad that the lazier members of the media often say things like "Well, as everyone knows it takes 60 votes to pass anything in the Senate," without any acknowledgement that (1) this is not true, it's supposed to take only a majority vote (as the Constitution specifies), and (2) this is a recent development, since the Senate has not always operated this way.
It seemed to be a self-imposed death sentence or a tacit acknowledgement that he simply could not play without banned drugs.
