It’s a wise child, they say, that knows its own father. Nowadays, however, wisdom is hardly required; DNA tests can do the job with scientific certainty. For the entire course of human history, men have nursed profound, troubling doubts about the fundamental question of whether or not they were fathers to their own children; women, by contrast, usually enjoyed a reasonable level of certainty about the matter.

Now, a cotton-wool swab with a bit of saliva, plus a small fee, less than £200, can settle the matter. At a stroke, the one thing that women had going for them has been taken away, the one respect in which they had the last laugh over their husbands and lovers. DNA tests are an anti-feminist appliance of science, a change in the balance of power between the sexes that we’ve hardly come to terms with. And that holds true even though many women have the economic potential to provide for their children themselves.

The subject has resurfaced lately, courtesy of a story in the Daily Mail, about a married television presenter who for years had been paying for the support of a child conceived, as he thought, as a result of his relationship with a writer. It seems that after meeting the child for the first time, he asked for a DNA test; it duly turned out that he was not, after all, the father. Poor child.

The next Bridget Jones movie may turn this under-discussed issue into a talking point. For those who didn’t follow the columns that took our heroine into the next stage of female angst — about being childless rather than single — the gist is that BJ becomes pregnant, but she is not entirely sure by whom, having been seeing the nice Colin Firth boyfriend, and the bad Hugh Grant one, in pretty short order. The matter could have been fruitfully ambiguous, with Bridget having a choice of fathers, but it was resolved in sordid contemporary fashion, one of the candidates being wrestled to the ground by Bridget’s girlfriends, so as to swab his inside cheek for a DNA sample. And so she found out the paternity of the baby and the most ancient game of humankind, Guess the Daddy, wasn’t played any more.

Now I can see that some men might rather welcome an end to the old-fashioned scenario whereby they find themselves held to account for the paternity of children born to girls with whom they just happen to have had sex. The actor Jude Law recently found himself in just this position, and unhesitatingly and ungallantly demanded a DNA test.

By contrast, the old situation, in which women presented men with a child, and the man either did the decent thing and offered support, or made a run for it, allowed women a certain leeway. The courtesan in Balzac who, on becoming pregnant, unhesitatingly sought, and got, maintenance from two of her men friends, can’t have been the only one. Uncertainty allows mothers to select for their children the father who would be best for them.

The point is that paternity was ambiguous and it was effectively up to the mother to name her child’s father, or not. (That eminently sensible Jewish custom, whereby Jewishness is passed through the mother, was based on the fact that we only really knew who our mothers are.) Many men have, of course, ended up raising children who were not genetically their own, but really, does it matter? You can feel quite as much tenderness for a child you mistakenly think to be yours as for one who is. Piers Paul Read’s interesting new novel, The Misogynist, touches on just this issue.

A.C. Grayling, the philosopher, has written with feeling on this question this week, in an article for the Evening Standard. Noting that 4 per cent of men are, all unknowing, raising children who are not genetically theirs, according to a report in the Journal of Epidemiology and Human Health, he ponders the impact a DNA paternity test can have: ‘The result can be shattering, leading to divorce, marital violence, mental health difficulties for all parties including the children.’ Well, yes. Scientific certainty has produced clarity all right, and relieved any number of men of their moral obligations, but at God knows what cost in misery, recrimination and guilt.

Our generation sets a good deal of store by certain knowledge. And DNA tests have obvious advantages when it comes to identifying less happy elements of our heredity: congenital disease, for instance. But in making paternity conditional on a test rather than the say-so of the mother, it has removed from women a powerful instrument of choice. I’m not sure that many people are much happier for it.