"mutually acknowledge" is a correct and usable phrase in written English.
It means that two or more parties acknowledge or recognize something together. Here is an example: "The two countries signed a treaty to mutually acknowledge each other's sovereignty and establish diplomatic relations." In this sentence, "mutually acknowledge" is used to show that both countries are acknowledging each other's sovereignty, rather than just one country acknowledging the other.
On the rare occasions when non-westerners were invited to Stockholm, it was, in a mutually acknowledged term, as "strangers".
Instead, they presented a moral imperative to develop practices of stranger humanism in order to forge personal and political connections based on mutually acknowledged and always evolving differences.
He is even capable, at times, of anticipating our thoughts and memories, as if he were performing a version of a simultaneous translation on us, rendering our hidden suspicions into mutually acknowledged words.
The dogs eye the camera much the way commuters glance at one another on the train, and their gazes run a familiar gamut: offhand suspicion, manic interest, mutually acknowledged exhaustion, utter bemusement, mind-your-own-business, can-anyone-help.
Root-Takahira Agreement, (Nov. 30, 1908), accord between the United States and Japan that averted a drift toward possible war by mutually acknowledging certain international policies and spheres of influence in the Pacific.
The mom two rows behind smiled at me as we mutually acknowledged our unapologetic willingness to be manipulated.
A holder of sovereignty derives authority from some mutually acknowledged source of legitimacy — natural law, a divine mandate, hereditary law, a constitution, even international law.
The Rousseau/Kant approach helps us understand why private property is inherently a matter of social concern and the Humean approach helps us see the value of property in providing people with a fixed and mutually acknowledged basis on which the rest of social life can be built, whether or not it answers to our independent intuitions of justice.
The Motivator had some issues accurately representing his "West-Indian nose", and his self-portrait was mutually acknowledged as resembling a woman with a beard.
Though both HCP and parent expertise was mutually acknowledged within interactions, ambivalence around the concept of expertise was also evident within teaching and learning encounters.
