TO Belford Road, as Samuel Pepys might say, there to visit that imposing edifice in Edinburgh which has been called the National Gallery of Modern Art, though methinks the not-unabrasive citizenry of Glasgow, who have their very own GOMA, might dispute the "National" bit. There I wandered often through several airy rooms, empty save for the disconcertingly lifelike sculptural representations of Duane Hanson. More than once I underwent the eerie sensation that I had caught one of them breathing. I lingered long, finding much occasion for thought.

The exhibition consists of 31 of Hanson's 114 fibreglass figures, painstakingly constructed from body-moulds, nearly all of them dressed in working clothes or the leisure wear of their time, every one of them rendered in a meticulous detail which record a each sagging jowl, each fold of fat, the shadow of minute hairs on the forearm. Painted into what could pass for living flesh, they stand or sit all around you, staring bleakly past any attempt to engage them in eye contact.

This is blue-collar America transported into a gallery: a weary waitress who looks bored into being a submissive automaton, housepainters having a break they don't seem to know what to do with, a fat man wondering why he is mowing a lawn, tourists who stare vacantly upwards, baffled by what it is they are supposed to be admiring. This is how Hanson spent the most productive part of his life, those last 20 years when his cancer went into remission. After much experimentation, he seems to have decided he knew what he had to do. This is the legacy he laboured to leave.

It's a legacy which has undergone drastic critical depreciation. He has been called a one-trick pony. His work has been dismissed as shallowly mimetic. He has been accused of using the cheapest trick of all - that of pretending his people are real, of endlessly repeating glib imitations of life.

I think all of this misses the point. I think Hanson was right. I think he had found the way to make his statement and I think it is a powerful and subversive statement. The endless repetition of incorrigible and isolated individuality is the statement and each time he makes it he makes it afresh.

The nature of Hanson's achievement becomes clearer when you compare him with two other much more famous American artists. For more than a quarter of a century Norman Rockwell was the most popular painter in America. His paintings for the cover of the Saturday Evening Post were the images of America most of his countrymen wanted to believe in, renderings of wholesomely cohesive family life in the land of plenty.

Hanson's sculptures are like a morning-after supplement to Rockwell's Saturday Evening Post. He uses the same minutely accurate realism as Rockwell did, but he puts it in the service of a much darker and more honest vision. The shining-eyed inclusiveness of Rockwell's Americans becomes in Hanson the dislocated stare of the dispossessed. Hanson's people are labourers in the vineyard of the American dream who never got to taste the wine. The other American artist I think Hanson outreaches by a long way is Andy Warhol. Warhol has been feted as the artist who caught the spirit of the times. Perhaps, but he didn't seem to know what to do with it once he had caught it. He simply replicated it automatically. I think his achievement is as hollow as a Lambeg drum; it is the sound of emptiness. He doesn't inform the times with intelligence. He merely echoes them. Like some high priest of nihilism, he specialises in the mass production of meaningless icons, from soup tins to Marilyn Monroe.

Hanson does something altogether more complex and paradoxical. He creates hauntingly resonant anti-icons, individuals who represent nothing more than their own intractable individuality, the loneliness of the unique bodies in which they are trapped. He has said he preferred to sculpt heavy people, presumably because they imparted a more monumental quality to his work. They also convey the pathos of once-bright promises which have foundered in fat.

Hanson's earlier sculptures tended to be slightly melodramatic: road accidents, abortion, the victim of a gangland killing. His mature work is much more subtle. It seems to understand that the locus of failure isn't external and partial. It is internal and total. You can see it in the pauses of sad sanity in every life, everywhere.

That is what you can see in Edinburgh: people caught in moments when they have briefly awakened from the American dream and see it as a con. "We have worked the work," their expressions seem to be saying, "we have bought the tickets, and we have reached a place which is nothing like the way we thought it would be. Is this all there is?"

This exhibition had a doubly beneficial effect on me. It was like a moving confirmation in physical terms of Auden's line, "In headaches and in worry vaguely life leaks away". It demonstrated to me how successfully Hanson had realised his own stated intention to illustrate the truth of Thoreau's idea that most people lead lives of quiet desperation. And it reminded me that, in a time of spectacular charlatanism in the visual arts, substantial work still happens.

Among the unmade beds of Tracy Emin and the infantile word paintings of Fiona Banner, we can still find achievement as considerable as that of Rachel Whiteread. Everything she does expresses the seriousness of her creative intelligence. Asked to devise a statue for an empty plinth in Trafalgar Square, she put an upended transparent plinth on top of the stone one. It was a significant statement, illustrating the insubstantialness of what we are commemorating (think of the crumbling significance of a statue of Field Marshal Haig) and the insubstantialness of our ability to commemorate (think of some meaningless grand mausoleum in a crumbling graveyard). All we are really commemorating, her plinth seems to be saying, is our desire to commemorate.

Beside the thoughtfulness of purpose of a Whiteread or a Hanson, not to mention the labours of technique by which they try to realise those purposes, most modern conceptual art looks like the whimsical junk it is. This is a time when a share of the £65,000 Beck's Future 2003 prize threatens to go to a young man whose latest project is a video of him sewing pieces of wood to the soles of his feet. I think the best prize they could give him would be to take him into care.

At such a time, a visit to Hanson's world can prove a salutary experience.