It’s often said that the contemporary art world and the avant-garde have a similar relationship. First, the news of the shock of the new is broadcast - out of the mouths of patrons, off the pages of little magazines, out of the concrete universities, from behind the plate-glass facades of Cork Street galleries. Then, controversy reigns; the public scratches its head, wondering why so much fuss is being made over blobs of colour, a pile of bricks, a mustache drawn on the Mona Lisa; reputations are made and lost. A few decades pass; the mass catches up with what used to be the avant-garde. Collected into an ‘ism’, postcard examples blutacked to classroom walls, what was shocking is now familiar, comforting, anodyne; and so fodder for the next wave of icon smashers.

The award of the 1995 Turner Prize to Damien Hirst shows how inappropriate this model has become. Of course, superannuated art critics, tabloid hacks and blokes who’ve had him in the back of their taxis continue, in the traditional way, to be shocked by Hirst’s work and by the other worthy stuff being pumped out of British art factories. However, the world changes rapidly and radically nowadays with or without the avant-garde. The avant-garde tiger, reduced to being the culture industry’s kitten, no longer shocks. Certainly it doesn't provoke. In a world of information deluge and slip-sliding meaning, a world where pulp fictions blur into horrific realities, the avant-garde’s traditional role has gone; all it can do now is amuse, titillate, at best, surprise.

Take a good butcher's at Hirst. The thirty-year-old artist, a former builder from Leeds, turned up at Goldsmiths in the mid 1980s and, curating the seminal Freeze show of 1988, metamorphosed into the Wolf Man, the Formaldehyde Kid, the bad boy, the enfant terrible of British art, and so predictably on and on.

According to his patrons - everyone from Charles Saatchi to Dave Stewart - his installations, his pickled animals, his maggots cultivated in decomposing cows' heads, say something profound about us. They reflect, by their preoccupation with the body, with the visceral, our undefined anxieties, our intimations of mortality, rapidly gathering pace as the century nears its end.

Hirst, meanwhile, rather than sinking into poor-little-rich-artist angst, has had, successful fella, a terrific time. He slummed it in Soho-Boho style at the Groucho and the Colony Rooms. He directed the jolly video - girlies galore in naughty maid outfits - for Blur's Country House single.

The Neanderthal response to all this has been to bleat out the story about the emperor's new clothes. When his Away from the Flock, the fluffy lamb in formaldehyde, was sold for £25,000, the Sun said that this kind of art was ‘Baa-rmy!’ and went on to suggest that he was "pulling the wool over our eyes". The Guardian reported that the going price for a live Suffolk ewe was £30 and that it could be dispatched in an abattoir for £5. Brian Sewell, scourge of the avant-garde, dismissed him as a "frivolous, incoherent clown".

Fair enough. Hirst’s latest work, on show in New York next spring, part of his solo exhibition ‘No Sense of Absolute Corruption’, consists of two tanks each containing two dead, flayed cows. There’s no formaldehyde. In each tank, one cow is raised so that it appears to be mounting its partner. He wants to find out, he says, about how things rot: "By the end there'll just be a mess of putrid flesh and bones". The installation is called Couple Fucking Dead Twice.

Despite such (in)sensitivity, the intention to shock, or to fool, isn't fundamental to Hirst’s work. His recent paintings, created by spilling paint on spinning canvases, have titles like 'beautiful, vaginal, spiral, escalating, blood, space, escaping painting'; he called a ping pong ball dancing on a jet of air, 'I want to spend the rest of my life everywhere, with everyone, one to one, always, forever, now'; he called the shark in formaldehyde, 'The Physical Impossibility of Death in the Mind of Someone Living': all sentimental, romantic, tinged-with-pink titles, really.

What makes them particularly interesting is that they run counter to the tediously clever postmodernism of recent years. The titles, the pieces, exist without any ironic subtext. What you see is what you get.

This is partly explained by the fact that Hirst’s interest in the stuff of death, and life, doesn’t emerge out of, say, a spell in psychoanalysis or from some unfinished thesis on the tradition of the memento mori, but from popular culture. Growing up a good Catholic goth in Leeds in the early 1980s, where dressing in black, swapping notes about Charles Manson and dancing to the Mission were obligatory, he had the typical adolescent’s interest in death.

Although refined by the art-school mill, Hirst’s interest remains aesthetic rather than intellectual. He doesn't really want to shock. He doesn’t want to explore how far he can take the ‘event’. He isn’t another Koons, Mapplethorpe, Gilbert & George. It’s far simpler than that. This is what the body is like, Hirst states. The death-cycle of an animal is amazing. There’s nothing as startling, as unsettling, as life. All Hirst’s flesh and blood and guts and bone, that horror of the normal writ large, flows out of these feelings; and so manages to catch a kind of beauty. Hirst once said, in conversation with Will Self, "I remember getting really terrified that I could only see out of my eyes. Two little fucking holes. I got really terrified by it. I'm kind of trapped inside with these two little things."

How true is that? When you think about it, normality is extremely strange. Natural death seems far less natural than unnatural death. It’s a far more difficult concept to understand, as Rebecca West noted, than somebody dying because they've been stabbed or shot or poisoned by somebody that hates them.

Critics can intellectualize this. They can fix Hirst’s work as part of some new Brit Art movement or whatever - he describes it as their blah, blah, blah. It’s a pointless exercise because the success of the avant-garde means that in many ways it’s become irrelevant. All the critics counting all the isms count for nothing outside the art history lecture theatre.

Meanwhile, Hirst, although he’s been compared to Hockney and Warhol, compares himself to the Beatles. Which is about right: like anyone who's ever been among the greats, he's just a rock ‘n’ roll star trying to live forever. Is Hirst going to be the one to do it? Definitely. Maybe.

No Sense of Absolute Corruption will be on show at the Gagosian Gallery in New York from the end of March 1996.