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The phrase "acknowledge that not" is correct and usable in written English.
You can use it when you want to express recognition of a situation or fact that is being negated or not accepted.
Example: "I must acknowledge that not everyone agrees with this decision."
Alternatives: "recognize that not" or "admit that not."
Exact(60)
4. Acknowledge that not everyone cares about what you have to say at any given moment.
But I acknowledge that not everyone is a Kantian.
They acknowledge that not every call they make is perfect.
It is important to acknowledge that not everything is getting worse.
Most advocates of an armed humanitarianism acknowledge that not all crises can be addressed.
We need to acknowledge that not all students can succeed in these advanced courses.
Mr. Feldman is quick to acknowledge that not everyone lives like this.
It's important we acknowledge that not all people come out as lesbian, gay, bi or trans.
Professionals must first acknowledge that not every legal task must be performed by a licensed lawyer.
Many farmers, including Mr. Ten Eyck, acknowledge that not all regulations are bad.
By the second edition of "Etiquette" (1927), she had to acknowledge that not everyone had servants.
More suggestions(16)
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acknowledge that no
emphasize that not
been recognized that not
recognition that not
recognizes that not
affirm that not
acknowledging that not
recognise that not
acknowledgement that not
agree that not
recognize that not
recognizing that not
has recognized that not
recognized that not
Write better and faster with AI suggestions while staying true to your unique style.
Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com