Years ago I read with interest Berger and Luckmann's classic The Social Construction of Reality. As near as I could tell, Berger was a sociologist who may have been (and still is?) a Christian. He taught at a variety of schools, including Evangelische Akademie in Germany, the University of North Carolina, Hartford Theological Seminary, the New School for Social Research, Rutgers University, and Boston College, and later in his career became the director of the Institute on Culture, Religion and World Affairs (formerly the Institute for the Study of Economic Culture).
About the only thing I remember about the book is that not infrequently Berger employed the term "bracketing," particularly when the subject of religion cropped up. As near as I could tell, Berger (and Luckmann's) bracketing was an attempt to put aside (or put on hold) their Christian religious beliefs while expatiating on and developing their thesis on the sociological acquisition of the knowledge of reality.
At the time I read Berger's book (the 1980s), I simply chalked up Berger's bracketing to, at best, an attempt to retain objectivity in a discipline that wasn't then (and probably still is not) brim full of committed Christians who did not believe in hermetically sealing off their Christian presuppositions from their so-called secular intellectual pursuits; and at worst, a slight compromise to keep the peace in a predominantly anti-supernatural, anti-god milieu (not to mention, but I will, his need to make a living). Hey, sociologists have families and need to eat, too! Besides, didn’t Jesus say we’re to be as harmless and doves but as wise as serpents? After all, why get our unbelieving peers on the defensive before they’ve had a chance to ask us of the hope within us (1 Pet 3:15)?
As to whether or not Berger's tendency to bracket any and all truth claims associated with religion was the better part of wisdom and perhaps even God's will for him as a Christian in agnostic academia, I'll leave to others to speculate. The fact remains, he bracketed any Truth claims in that particular book. Whether the bracketing continued in Berger's other books (e.g., The Noise of Solemn Assemblies; The Sacred Canopy: Elements of a Sociological Theory of Religion; and a Rumor of Angels: Modern Society and the Rediscovery of the Supernatural) I do not know. Perhaps someone more familiar with Berger's thoughts on religion and the supernatural would care to venture an informed opinion and share it with fans of SE/BH.
The purpose of my lengthy introduction is to suggest that people engage in bracketing all the time, and not just academics, exegetes, and hermeneutists. Is bracketing successful, at least partially? Yes, to some extent.
Some Christians even need to learn how to do so, since both deliberately and sometimes perhaps unwittingly they attempt to shoehorn theology into conversations, discussions, dialogs, and debates where it may not belong but rather sticks out like a pregnant pole-vaulter.
Yes, we Christians are to be ready to give an answer to those who ask us of the hope that is within us, but notice that Peter's admonition says we are to give an answer, and an answer implies a question (1 Peter 3:15)!
Sociologists, scientists, mathematicians, doctors, lawyers, politicians, and blue-collar workers, ad infinitum, all carry certain presuppositions and assumptions with them everywhere they go. The notion that anyone at any time can be 100 percent objective is risible. We are all subjects, are we not? How can subjects separate themselves from themselves? Impossible. To bracket oneself is a contradiction in terms. There are things human beings (and God) simply cannot do. We cannot, for example, engage in things that are characterized by mutual exclusivity. Neither God nor any of us can make a square circle or cause two plus two to equal three.
On the other hand, we have been given the ability by our Creator to be able to look at ourselves at one remove in what is called a self-reflexive mode. Perhaps apropos your question (or perhaps not!), I thought of “Doubting Thomas.”
Thomas wanted to believe what Jesus said, but he had difficulty bracketing his doubts and simply believing, unless he could be persuaded to do so by empirical proof. When Jesus said to him and the other disciples,
". . . I go to prepare a place for you, [and] if I go and prepare a place for you, I will come again and receive you to Myself . . .. And you know the way where I am going” (Jn 14:3-5),
in response to these words, Thomas said in effect,
Lord, I don’t even know your destination, let alone how you’re getting there!
And then Jesus said to him,
”I am the way, the truth, and the life . . .” (14:6).
In conclusion, in one sense, bracketing is clearly impossible, since we cannot separate ourselves from ourselves. On the other hand, we are able to step back and question some of our assumptions when we are wrestling with an inner- and/or outer conflict. King David is known for saying,
”Why are you in despair, O my soul? And why have you become disturbed within me? Hope in God, for I shall again praise Him For the help of His presence” (Ps 42:5,11).
We can bracket such things as assumptions, negative (stinkin’) thinkin’, but we succeed only in fooling ourselves if we think our brackets are hermetically sealed. Yeah, we can play devil’s advocate with others and with ourselves, but when all is said and done, we cannot simply divest ourselves of the roots of our being, which Kenneth Burke calls true piety. The only way to do so at a fundamental level is by being persuaded otherwise.