Germaine Greer as Dogged Daughter : DADDY, WE HARDLY KNEW YOU <i> by Germaine Greer (Alfred A</i> .<i> Knopf: $19.95; 320 pp; 0-394-58313-2) </i>

“The Quest,” Germaine Greer titles the opening chapter of “Daddy, We Hardly Knew You,” a memoir of her search for her father’s past begun after his death in 1983, as if to lift her pursuit to mythic heights. But the premise of the heroic quest is that its object possesses unique, often mysterious, even sacred, value, capable of transforming at least the searcher and generally the wider world as well. In these terms, Greer’s is an anti-quest: “a classic example of herstory (sic), puncturing the ideology” of the hero.

Although she knew her father for more than 40 years, Greer learned almost nothing about his background, and what little information he released, she discovers, was fabricated. Reticence this absolute seems all but implausible, but apparently the “anxiety neurosis” with which Reg Greer returned from World War II effectively barred all inquiry.

“You will be wondering why I did not simply ask my mother,” Greer says. Yes, indeed, that’s exactly what I was wondering. “Suffice it to say that for Mother language is a weapon rather than a means of communication.” Two less appealing creatures than Reg and Peggy Greer, as seen through their daughter’s eyes, would be hard to imagine. But at least their singularly uncooperative natures provide her the pretext for a book.

And a book of sorts she produces: part childhood reminiscence, part travelogue, part genealogy, part history, part social commentary. Unfortunately, the lack of something meaningful at the center (Daddy, I believe) prevents these elements from coalescing. Greer is a skillful writer, and there are plenty of terrific passages here: quick insights (“Our whole lives are lived in a tangle of telling, not telling, misleading, allowing to know, concealing, eavesdropping and collusion”); painterly descriptions of landscape from Tasmania to Tuscany; a breathtaking evocation of conditions during the siege of Malta. Too often, however, the insights are facile.

This clutter becomes especially troublesome with regard to the book’s central purpose: the revelation of the “truth” about Reg Greer’s life, which his daughter confounds with the knowledge of his origins and antecedents. Now, as the popularity of Alex Haley’s “Roots” demonstrated some time ago, many people are fascinated by their lineage; at least half a dozen of my friends and relations pursue their forebears with varying degrees of preoccupation. But it seems a queer sort of obsession for a feminist to take up with scant reflection; and really this author of an early and influential feminist text, “The Female Eunuch,” has given herself over to her patrilineal search with far fewer and less sophisticated questions than readers might reasonably hope.

Instead, with prodigious expenditures of money, time and energy, she amasses and recounts quantities of genealogical detail. She is nothing if not the “doggedest of daughters,” and the descriptions of her research methods, frustrations and victories may prove instructive to other genealogists. The rest of her readers must simply slog along in her wake (wondering, perhaps, why she perseveres until they read: “I cannot go backward. I’ve spent too much of the advance.” Ah, Knopf has paid for a book, and a book they shall have).

For naught, it turns out. Because, after transforming herself into “a Greero-logist, a Greerographer, a Greeromane” and summarizing one Greer pedigree after another (perhaps so that her readers can experience the same sense of wasted time she endured), she turns out to be “not a Greer” at all but a Greeney by adoption, a Hamilton by birth. Her father’s lies and evasions masked no “prince in disguise”; he was simply ashamed to have been an illegitimate child reared by poor but honest folk whom he left without looking back.

“No matter how I try,” Greer writes, “no matter how loyal I feel, I cannot make this man a hero.” And perhaps it’s this incapacity that dooms the book. Perhaps, if you’re going to set out on a quest (itself conventionally considered a heroic undertaking), its object must be rare and precious in some way. Perhaps it--in this case he, Reg Greer--can’t be a “liar,” a “bounder” an “office masher,” snobbish and cowardly and small-minded. Perhaps the failure lies in the unworthiness of the object.

“Daddy, we hardly knew you,” Greer complains. “Why would we even want to?” the reader may sadly ask.