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The phrase 'cannot admit this' is correct and usable in written English.
You could use it when you want to express that you are not willing or not able to accept something as being true or right. For example: "I cannot admit this mistake was mine - it must have been someone else's fault."
Exact(3)
Moreover, she cannot admit this motivation while at the same time remaining a patriot.
But we cannot admit this because we are committed to the belief that what we do is the only possible recipe for "victory".
Cameron, like Barack Obama, cannot admit this, of course, as they jointly pull the plug.
Similar(57)
To this day, Myers cannot admit that he and Steve Parrish have occasional contact and that they are both working toward a common goal: F.D.A. regulation.
It would seem appropriate to end with this quote from Bertrand Russell: "I cannot admit any method of arriving at truth except that of science" (Russel 1997).
But they cannot admit it.
FTs cannot admit 49% private patients.
Some cannot admit to themselves what they have lost.
"This transit and the toleration of these proceedings by the Grand Ducal Government constitute a flagrant breach of neutrality, and cannot admit of a doubt.
In particular, this shows for almost everywhere 1/2<λ<1, the L2 space of the λ-Bernoulli convolutions cannot admit a Fourier frame.
But, as Universities UK are themselves the first to admit, this cannot happen without new legislation.
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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