''GREER, Dr Germaine; Writer and broadcaster, b29.01.1939. Educ: Star of the Sea Convent, Gardenvale, Victoria.''

Thus begins the long and impressive entry on Germaine Greer in Who's Who in Catholic Life. There she is, midway between Victoria Gillick and Basil Hume, listed among the well-known Catholics of British public life. Is this how she sees herself? It seems so. Careful scrutiny of the editor's note, which thanks ''all the entrants for their co-operation'', indicates that she not only agreed to appear in the directory but that she guaranteed the relevant details. Let's assume, then, that Dr Greer is a Catholic. What does that mean? That she believes in the Virgin Birth, Immaculate Conception, and the Infallibility of the Pope? That she believes in holy matrimony, penance, the rosary and confessional? That she eschews contraception, adultery, abortion, and even women priests?

Clearly, it doesn't mean anything of the sort. You wouldn't make such extravagant deductions about any Catholic, let alone Germaine Greer. The nature of faith is infinitely complex, as various as there are human souls. A Catholic who believes in the Virgin Birth may also favour birth control and women priests. Even if Germaine Greer did believe in some of these things, who would assume they knew what she thought without taking the trouble to ask her?

This is precisely what Dr Greer does in her arrogant new polemic. The Whole Woman, an irritable sequel to The Female Eunuch, purports to know exactly what we think, even if we're not sure ourselves. The book is based upon generalisations so blatantly untested they make one gasp and stretch one's eyes. Accuracy has always bored her. ''Women,'' she wantonly declared in the early book, ''have very little idea of how much men hate them.'' Thirty years later, she is still making these nutty, ex cathedra pronouncements.

''A few men hate women all of the time,'' she writes, ''some men hate some women all of the time, and all men hate some women some of the time.'' As a man, you may object that you've never hated anyone, let alone a woman. You may recoil at this staggering absolutism. As a woman, you can probably think of dozens of men who don't fit into any of these categories. But Dr Greer always knows better. The question is not whether men hate women, but how much. ''We do not know whether one kind of woman-hater predominates, or whether all three exist in roughly equal proportions.''

This is Greer's favourite ruse: the extreme, unfalsifiable statement. You know it's wrong, but it would be impossible to disprove. Take her claim that if virtual sex were universally available, and gestation cabinets could manufacture babies, then ''men would not regret the passing of real, noisy, hairy women''. It's a ridiculous hypothesis, but how would you amass contrary proof?

Similarly, she insists that more and more of women's time is ''wasted cleaning things that are already clean, trying to feed people who aren't hungry, and labouring to, in, from and for chain-stores.'' It's not my experience, or that of my friends, but I can't imagine Dr Greer rewriting her resonant proclamations to accommodate anyone else's experience.

It might be argued that these are just the testy asides of an impatient woman with larger targets in view. After all, Greer fulminates against female poverty, lack of childcare, the masculinisation of Britain through football, television, and the Net. Her argument that better state provision for mothers might reduce the abortion statistics is exceptionally strong. Who, moreover, could disagree that comics for adolescent girls are horrifyingly regressive, with their slobbering tips on diets, lipstick and boys.

But set those reasonable concerns against her wild hostilities and you begin to wonder whose side Greer is on. For women do seem, in her book, to be catastrophically dumb. They are ''persuaded'' to undergo the perils of IVF, abortion, and cosmetic surgery. They work for big pharmaceutical companies by buying their drugs, their make-up, their faulty birth control. Paradoxically, when those contraceptives fail, the woman is doubly to blame. ''A woman who is unable to protect her cervix from male hyperfertility is certainly not calling the shots.''

As far as sisterhood is concerned, Greer is all for diversity, even though this book is a retort to ''lifestyle'' feminism. To sit back and say nothing about that bland, have-it-all creed would have been ''inexcusable''. But is it excusable to tell young women that men hate them, to describe cervical screening as state-imposed torture, to envisage an epidemic of life-threatening hysterectomies because one in three American women, apparently, will be wombless by the time they are 60? The prohibitive cost of US healthcare alone defies that statistic.

For Greer, people are entirely defined by gender. This is what blights her diagnosis of the female condition. All women are like to her, suffering the same affliction, namely man. Her cures - among them universal childcare, segregation, the extended family, water for all, higher taxation for single-person households - may work for some but not for all. Greer's doctor-knows-best prescription is based on unfounded generalisations, poor research, and some deeply peculiar prejudices.