THE MOUNTAIN OF NAMES; A History of the Human Family. By Alex Shoumatoff. Simon and Schuster. 293 pp. $17.95.

WHAT EVERY book shows us, one might say, is an author in the act of scratching an itch. What is itching Alex Shoumatoff is the long-term trend toward the dissolution of the family. "The ties and the demands of kinship," he writes, "have been weakening, the family has been getting smaller and . . . less influential, as the individual, with a new sense of autonomy . . . has come to the foreground." Shoumatoff argues that a radically different mental order -- self-centered instead of kin-centered -- has taken over in America and Europe and in most countries that are developing along European lines. He does not categorically lament the rise of self-centeredness which he sees as having brought with it undeniable benefits. But one of its clear victims, he says, has been the warmth, sanity, and support that long-term intimate bonding (i.e., family life) brings. As one indication among the many he offers of how far the disintegration of kinship has gone, he notes that a surprising number of Americans are unable to name all four of their grandparents. (I have tested this claim with my own college-age students, and found that only 30 percent of them can do it.)

But Shoumatoff derives little satisfaction from describing the decline in the continuity and sense of belonging that traditional kinship provides. What will relieve his itch is the survival of family life. And, indeed, his book is a richly detailed history of kinship, the point of which is to encourage his readers and himself to believe that the prospects for the future of kinship are good.

To accomplish this, he draws on just about every academic field to be found in a university catalogue, from anthropology to zoology. The reader is thereby immersed in a torrent of information, much of which is fascinating. For example, over 90 percent of all birds are monogamous. The oldest known human family was a group of 13 hominids whose remains were found in 1975; it appears that they met with an accident about 21/2 million years ago in the Afar Triangle of Ethiopia. At present, American couples are having an average of only 2.2 children, which means they are barely replacing themselves. The practice of polygamy was adopted by the Mormons in 1843, when their prophet, Joseph Smith, claimed he had received word from God that having more than one wife would be all right with Him. Researchers have found a connection between a hormone-like substance called serotonin and competitive behavior. Not only do males have higher levels of serotonin than females but chairmen of academic departments and Nobel Prize winners have much higher levels than their subordinates. The greatest concentration of single people in the world is New York City which has approximately 2 million "singles." And since about 60,000 people pass through Bloomingdale's every day, most of them singles, it would appear that the store is an excellent place for one single to meet another.

ONE OF the troubles with all of this information is that it puts a severe strain on one's short-term memory, which is to say that Shoumatoff tells much more than even a leisurely reader can assimilate. Another trouble is that the line of argument being pursued here is continuously obstructed by Shoumatoff's erudition. He wants us to believe that the need for kinship is acute, that it has always been a characteristic of human life, that the conditions of modern Western life have led to a decline in the capacity for long-term intimate bonding, and that there is a rebirth of interest in family life. But an encyclopedia is not an argument, and, in any case, a reader can easily be worn down before coming to Shoumatoff's d,enouement -- a moving and well focused final chapter which takes its name from the title of the book. The Mountain of Names refers to the billion and a half names of the dead that are contained in a nuclear bomb-proof repository near Salt Lake City. Shoumatoff describes in loving detail this singular Mormon project, a living monument to the idea of kinship. "It is the closest there is," he says, "and the closest there will be, to a 'catalogue of catalogues' for the human race." Were it ever to be completed (that is, contain all the names of everyone who had ever lived), there would be close to one 110 billion names. And what would this Everest of remembrance prove? It would show what, in the end, Shoumatoff's books is mainly concerned to tell us: that we are all kin, a vast extended family who need each other more than we allow ourselves to know.