ANDREW GREELEY and Michael Novak are veteran controversialists who delight in public battle. Since the teaching authority of the Catholic Church is under serious challenge on many fronts today, it is natural that both have waded in with books challenging and exhorting their fellow Catholics. Each wants to tug the church in his own particular direction. Each is conservative on some issues while being innovative on others. It makes for stimulating reading if inconsistent policy prescriptions.

Greeley, priest, sociologist, public opinion analyst, newspaper columnist, and more recently best-selling novelist, has written his latest book in collaboration with his sister. It is considerably more modest than its portentous title would suggest. Rather than a grand plan to "save" the whole Catholic Church, it offers some sensible ideas and insights on how the Catholic Church in the United States could be improved.

Essentially, Greeley and Durkin want the pope and the majority of American bishops to get better in touch with those many lay Catholics and younger priests who have not left the church but who quietly dissent from one or more of its teachings. They describe them as "do-it-yourself Catholics" who reject the church's ban on birth control and reject papal infallibility yet remain Catholic in their basic convictions "about life and death and about the nature of God and God's love."

"As long as you define yourself as Catholic, no one is going to throw you out of the Church or refuse the sacraments to you, regardless of what you do in your bedroom or what reservations you have on doctrinal matters. Make your peace with God, in other words, and don't worry about the Pope or the bishops," they report is the attitude of many American Catholics.

Why would anyone remain a Catholic who disagreed with major tenets of church teaching? The authors quote approvingly the comment of the writer John R. Powers: "It's almost as hard to stop being a Catholic as it is to stop being a black."

Greeley and Durkin stress several major themes. They urge the importance of art for religion, contrasting the indifference and hostility of many American priests and bishops toward art with the attitudes of the popes who were great patrons of art. They argue that the eternal truths of religion have to be retold in modern terms in stories in which sinners and sin are present but in which good persists and can triumph over evil. (This is, in part, a response to those who have criticized Father Greeley's novels as sensationlist.) Readers of his earlier works will be familiar with Father Greeley's warm memories of the Chicago inner city and suburban parishes he has known. They will be ready for his argument in this book that what happens in the local parish is likely to be far more important to the future of the church in the United States than anything that happens in Rome.

The authors emphasize that the Catholic sensibility and tradition have always been sacramental and analogical. In contrast to the Protestant view of the "radical otherness" of God and His separation from this world except for the crucifixion and the resurrection, Catholics see God everywhere in the events and things of the world. Catholics see many metaphors and analogies for God in the natural universe and in everyday human life.

In this context, the authors make a plea for the restoration or reinvigoration of many Catholic practices that have fallen into disfavor since Vatican Council II. "If you concede the appropriateness of an analogical approach to God . . . then angels and saints and holy souls and processions and rituals and stained glass windows and statues and holy cards and medals and blessings are also legitimate."

If that argument will strike some Catholic readers as retrogressive, others will be impressed by the force and boldness with which the authors argue that "sexual passion is sacramental." It is, they write, one of the important ways that God shows Himself to us and reveals the enormous passion of His love for us. The authors condemn the anti-sexual, anti-women attitudes that recur often in church policy and writings. They call for the ordination of women to the priesthood. They write about the cult of the Blessed Virgin Mary, and they have much that is wise and beautiful to say about marriage itself. This is not a book for readers who are theologically sophisticated, but as a popular work for the general readers for whom it was written, it succeeds.

MICHAEL NOVAK is almost as fluent and prolific a book-writer as Father Greeley. He has written better books than this one. It reads at times like the research notes for and the arguments left over from his previous book, The Spirit of Democratic Capitalism. In that work, he declared his discovery that capitalism and democracy were interdependent and that mankind could best advance toward prosperity and freedom by adopting the economics of Adam Smith. Several critics argued that Novak made too facile a connection between capitalism and democracy. They pointed out that capitalism has flourished in many times and places such as early 19th-century England and late 20th-century Singapore where democracy did not exist.

Novak's enthusiasm is undimmed. In this book, he offers a romantic vision of the entrepreneur who is described as "abstaining from consumption and from miserly hoarding in order to invest in creative ventures . . . . Individuals drink different draughts of this restless creativity, this capitalist spirit, whose aim is not to live sumptuously or even comfortably, as was the spirit of pre-capitalist persons of wealth, but to create ever new wealth in a sustained and systematic way."

Novak as a young professor in the '60s was a guru to campus radicals. He was a mainstream Democrat in the '70s. He has now converted to neoconservatism and become a scholar at the American Enterprise Institute. He co-chairs with former Treasury secretary William Simon a committee of Catholic laymen organized to do battle with American Catholic bishops over their forthcoming pastoral letter on the economy. Novak is worried that the bishops will not be sympathetic enough to the virtues of free enterprise and the free market. By studying the history of Catholic thought on social and economic issues, Novak constructs an intellectual rationale for his committee. He argues that Catholic thought as laid down by successive popes "has slowly but steadily come to embrace the basic institutions of the liberal society."

"It is time for that process to become more self- conscious, self-confident, and boldly imaginative. I do not believe that Catholic social thought should serve the liberal society. On the contrary, I hold that the liberal society, among known and workable present and future societies, best serves Catholic social thought: best uplifts the poor, institutionalizes the dignity of the human person, makes possible the growth and manifold activities of human associations of every sort, and conspires to establish a more voluntary and open and communitarian form of life than any society of the past, present, or foreseeable future."

I am tempted to agree with that statement but I would heavily qualify it by nothing that my experience, like that of Novak's, is based on living in societies where Anglo-American cultural values prevail. I am not absolutely confident that I know what best uplifts an Iranian Muslim or institutionalizes the dignity of a Guatemalan Indian or would establish a more voluntary and open society for a Brazilian villager. If Novak has any doubts, they do not slow him down as he water-skis across global ideological seas.

"In praising liberal institutions, one must also note their many and persistent failings," Novak continues. But nowhere does he do so. This book is a celebration of the capitalist status quo.

What finally undermines this book is the impression it conveys that in writing so much about economics, Novak is living beyond his intellectual means. Theologists have to live dangerously in an intellectual sense since they engage various kinds of social phenomena. But in writing such earlier works as Choosing Our King or The Rise of the Unmeltable Ethnics, Novak found it easier to assimilate theories of politics and the history and sociology of ethnics than he does the economics of development.

In their book, Greeley and Durkin write: "Few (Catholics) take seriously any more the Church as teacher -- on either moral or social action matters." They try hard, however, to move the church's position on women's rights. Similarly, Novak labors to bring the pope and the bishops into line with Adam Smith. These books suggest that not only do ideas matter but also that what Rome says still counts in the war of ideas.