The phrase "acknowledged a deeper" is correct and usable in written English.
It can be used when discussing a realization or understanding that goes beyond surface-level awareness, often in a reflective or analytical context.
Example: "After much contemplation, she acknowledged a deeper understanding of her emotions and their impact on her decisions."
Alternatives: "recognized a profound" or "realized a more profound".
But he acknowledged a "deep-seated antipathy toward free market competition" in some quarters, and warned of a backlash should economic conditions give way to tougher times.
But he acknowledged a deep split in the dissident community and he criticized exiled Tiananmen Square student leaders who support the trade bill as naive.
(Kirby, who died in 1994, had a profound effect on many young comics fans, including Michael Chabon, who acknowledged a "deep debt I owe in this and everything else I've ever written to the work of the late Jack Kirby, the King of Comics" in the author's note in his 2000 Pulitzer Prize-winning novel, "The Amazing Adventures of Kavalier & Clay").
In the foreword of The Structure of Scientific Revolutions, Kuhn acknowledged a deep debt to Ludwik Fleck, a bacteriologist who developed the first explicit sociology of natural science, and anticipated many contemporary views about the social construction of knowledge.
He went on to acknowledge a deeper anxiety: "John Carter" faced a test screening the following night in Portland, Oregon, before four hundred citizens and five of Disney's top executives.
Yes, the Castro government is acknowledging a deep problem.
Supporters, advisers and donors to Mr. Romney acknowledge a deep sense of concern.
Every cell in our body acknowledges a deep history, a time when organelles floated free in a world we would have found insupportable".
He has begun a small crusade to de-capitalize Internet -- and, by extension, to acknowledge a deep shift in the way that we think about the online world.
2. Death in Venice by Thomas Mann (1912, English translation 1925) In Venice, the honoured author Aschenbach acknowledges a deep longing "for nothingness".
