NO MATTER how often I have walked the length of Edinburgh's George Street, it has never occurred to me to think of it as "one of the greatest monumental streets in Britain", let alone the world. This, though, is how the sculptor Alexander Stoddart sees it. It is up there, he says, with Florence's Piazza della Signoria, with its replica of Michelangelo's David and other classic examples of the art of statuary, and The Mall in Washington, with its many museums and memorials, including those to Abraham Lincoln and the Vietnam veterans. Indeed, adds Stoddart, George Street is probably better than the latter "because it hasn't been contaminated by modernism".

He is not joking. Modernism to Stoddart is like monetarism to a Marxist; the mere mention of the word makes him foam metaphorically - and possibly literally - at the mouth. No-one has ever been more shocked by the new than him. Nor, in my experience, has anyone so eloquently expressed his hatred of it. Were it up to him, one can't help but think, we'd all be better off living in ancient Greece, reading The Iliad and swilling wine from pigs' bladders. To him, new is a synonym for crap. Invariably, he insists, when an old building is knocked down the one built in its place will not be an improvement. On the contrary, it's probable that it will be an eyesore. If only Edinburgh lived up to its tag of Athens of the North. Instead, we have the St James Centre.

On a blustery summer's afternoon, I met Stoddart, who was born in Edinburgh in 1959 but who now lives in Paisley where he was brought up, in the middle of St Andrew Square. A few months ago this would not have been possible, since access to the public was denied. Now, however, it has been landscaped and the Great Unwashed have been allowed in, roving over grass that the signs tell them not to disturb and discarding wads of gum on the pristine pathways. This, concedes Stoddart without wholehearted enthusiasm, is a reason to be cheerful. He is of medium height and stocky build and wearing dusty steel-capped boots, evidence of his having come directly from his studio. To friends he is called Sandy and the name suits. In his company, silence is a rare commodity. He talks with the intensity and speed of an innocent man trying to put his case to a jury with a limited attention span. When he wants you to pay special attention to what he's saying, he says things like, "now this is a very important point". Words such as "teleological", "quotidian" and "Nietzschean" gush forth as if he has been using them since Primary 1. But if this makes him sound pompous, it does him an injustice, for he is engaging, erudite company.

The idea is for us to proceed from east to west along George Street, studying the monuments as we go. Last month, Stoddart unveiled his statue of Adam Smith in the Royal Mile, the latest of several monuments he has made to significant Scottish figures, including Robert Louis Stevenson, David Hume and James Witherspoon, another Paisley Buddy, who helped draft the American Declaration of Independence. In November, his statue of the pioneering Scottish physicist, James Clerk Maxwell, the link between Newton and Einstein, will be unveiled at the east end of George Street. And later this month, Stoddart will be appearing at the opposite end of the boulevard at the Edinburgh International Book Festival where he is delivering a lecture at the behest of the Royal Society of Edinburgh.

All of which suggests that Stoddart is in with the bricks of the Establishment. Well, up to a point. While it's true there are those in high places who value what he does and ensure he's never short of commissions, there are equally influential people who view him as a reactionary anachronism mired in antiquity. His contempt for them is wondrous to behold. Take the Scottish Arts Council, for instance. "I'm very pleased to say I have been struck off by the Scottish Arts Council," he says. "No serious artist has anything to do with that crowd." His work, he adds, was once dismissed by it as "backward looking, historicist and not reflecting contemporary trends".

While this is undoubtedly accurate, it was not meant as a compliment. The SAC, he says, was advised not to have anything to do with him. What prompted this was an application for a grant from the Saltire Society, which had asked Stoddart to make a statue of Hume. "When the denizen in there that was in charge of visual arts at the time discovered that that money was going to me, he jumped out of his seat. He's gone away to Oxford now and our thoughts are very much with Oxford at this time."

Meanwhile, Stoddart is looking skyward, to the statue of Henry Dundas, de facto ruler of Scotland from the late 1700s to the first decade of the 19th century. Before St Andrew Square was given its makeover, Dundas, perched upon a plinth so tall he seems to be nearer the clouds than the ground, was its focal point, its raison d'être. For all most people could tell, it might have been David Beckham or Billy Connolly up there. Now, observes Stoddart, unable to disguise his disgust, a series of "ellipses" ensure our eyes look down rather than up. The result is that "the entire taxonomy of this square is really a deed of frustration or defiance of the great monument in the middle. And everything is construed in terms of our use. The whole thing is a utile arrangement. Now the monument is no use to anybody. It's useless," he says, putting intolerable stress on the word's two syllables. "As such, of course, it qualifies as a work of art. That's why it's very gratifying to see the door at the top of the monument closed, so that nobody can get inside."

At which point he quotes Kant, or possibly Schopenhauer: "If an object is brought to use it has its artistic credentials traduced." In Stoddart's opinion, we live in cruel, selfish, mean-spirited, ignorant, temporal, narcissistic times. Everything is about us and the present, nothing about them and the past. Our knowledge of history is scant and our understanding of art limited. The one good thing to come out of the 9/11 catastrophe, he says, is that tourists are no longer allowed inside the Statue of Liberty. No more must it suffer "colonic infection"; it, too, has been rendered useless and restored to the status of a work of art. The same, alas, cannot be said of another of Stoddart's favourite statues, that of the Scott Monument in Princes Street, whose steps tourists climb presumably without giving a second thought to the man and his dog at its base.

St Andrew Square, concludes Stoddart wrily, is not a monumental square any more. "It's a facility." Who now would he put a statue up to here? Alex Salmond? "He's still alive." Gordon Brown? Is he still alive? Donald Dewar? He snorts, by which I gather he is not a fan of the statue of the former first minister outside the Buchanan Galleries in Glasgow. "If anyone suggested a monument to Donald Dewar today. It wouldn't happen, would it? Indecent haste. It happened in media hysteria."

As we walk, Stoddart talks, like a mountain stream in spate. Had he been in Baghdad when Saddam was overthrown would he have joined the mob who pulled his statue down? The short answer is no. The longer, more considered one, is that he would have covered it with a huge tent, dismantled it bit by bit and replaced it with a statue of Saladin, who may have done many wonderful things but who also was an early promoter of jihad. "The tearing down of statues is a very, very dangerous and infectious thing," cautions Stoddart. Nor is he any more sympathetic to those who think it hilarious to put a traffic cone on the Duke of Wellington's statue in Glasgow's Royal Exchange Square.

"When the cone goes up on Wellington, of course, there's some people who have a residual notion that Wellington was a bit of a toff - we don't like him - he was against education and he didn't like his soldiers cheering him because this - as he said - came too close to them expressing an opinion.

"Okay, for these reasons the desire to deface a statue might be there. But it's not that reason. They don't have a clue who Wellington is, basically. What they like to do is take the mickey out of a dignified form. And it's a formal aggression. Nothing to do with the concept. It's the shape of the thing and the fact that it's bigger than they are and he's the king of the castle and they, by consequence, are the dirty wee rascals.

"And that's as simple as it is. It's a perfect manifestation of the will in nature objectivised through your average drunken thug and/or the right-on councillor - of past times, I'm pleased to say - who thinks he will get on the demagoguery bandwagon by trucking with this filth."

The problem, says Stoddart, is that we do not understand what monuments are for. "It aggravates a lot of people, such a devotion to monumentalism. I have a deep understanding of it after many years of fumbling about and making false assumptions about it. It's come to the point where I think I know the whole story. In the past, I thought monuments were an expression of will. Now, I realise the great power of the monument is in the suppression of the will."

What this means is that monuments are only tangentially to do with the living. First, and foremost, they are about the dead. They are memorials to people who have done great things. Also, they are a reminder to those yet to be born of what happened in the past. Thus we need to be sure that the people to whom monuments are erected are worthy of them. They are not a matter for a short-termism or tabloid hysteria, or popular acclaim. Time, suggests Stoddart, is the great winnower. The sculptural equivalent of Pop Idol is not on his horizon.

Our walk along George Street takes us past the site where his statue of James Clerk Maxwell will be placed. Few, one imagines, would dispute that Maxwell is deserving of such an honour, yet it is nearly 130 years since he died. In Stoddart's book, this is no bad thing. Apart from anything else it shows the regard with which Maxwell is still held and how well his reputation has weathered, abroad as well as at home. As is typical of Stoddart's work, this statue will be classical in design. Much to the derision of his critics, he looks back in awe at the work of sculptors in the ancient world. His sculptures, like theirs, are dignified, respectful. Irony is not part of his armoury. He comes to celebrate, not to mock. Drapery, he says, is used to hide man's untidy bits and pieces and "sartorial trivia". It is also ageless. Not for him the likes of Dewar, depicted in a rumpled suit, hands in his pockets, specs slightly askew. For what kind of a message is that to send out to future generations?

Nor does Stoddart have any time for conceptualism. At Glasgow School of Art, which he attended from 1976 to 1980, he must have stood out like The Three Graces in a garden centre. He was neither a nouveau Glasgow Boy nor part of the Britart pack. Saatchi has never shown any interest in his work and nor have any of the Scottish national galleries. His contempt for the banality of conceptualism is refreshingly, bracingly, withering. Drooling over Francis Chantrey's statue of George IV, at the intersection between George Street, Hanover Street and Dundas Street, he says: "This kind of thing to achieve - I know from personal experience - is really tricky. And it's absolutely beyond the pygmy conceptual capacities of your average contemporary art tutor, who can't tell the time on an orthodox clock these days." As for Damien Hirst's shark preserved in formaldehyde, mere words are inadequate to describe what he feels about it. Suffice it to say, a local fishmonger could do far better.

But what of the likes of Ian Hamilton Finlay, who at least acknowledged a classical influence? Stoddart concedes that he was "interesting as a sort of spanner in certain modernist works", but that's about as far as his enthusiasm goes. Finlay, he says, was "a poetaster" who never wrote a poem that matched Walter Scott's Marmion. "As for a philosopher - as some people say he was - I also know philosophers, and I've never read Finlay as a philosopher writing more than a paragraph. I've asked Roger Scruton about him and he's a real philosopher. I keep company with philosophers, and none of them rate Finlay as a philosopher."

His unstinting praise is reserved for men such as the aforementioned Chantrey, the Scottish Victorian sculptor Sir John Steell and Alexander Handyside Ritchie, whose statues and friezes make George Street such an embellishment to Edinburgh. Ritchie's work can be seen above the Dome bar on the north side of George Street. At the George Street-Frederick Street intersection is Chantrey's bronze of William Pitt the Younger and, a block further west, where George Street meets Castle Street, is Steell's statue of Thomas Chalmers who, in 1843, led the Disruption, when 470 ministers left the Church of Scotland and joined the Free Church. In his hand, Chalmers holds the Bible open at Proverbs 29, v. 18, which Stoddart almost has off pat: "Where there is no vision the people perish. But he who liveth by the law happy is he." John Knox, whose sculpture in Glasgow's Necropolis is one of Stoddart's favourites, could not read the words with more feeling.

On four occasions in the fairly recent decades, observes Stoddart, it has been suggested that the statues be removed from George Street, in order to free the flow of traffic. Not that he is against cars. Pedestrianised streets, he says, suck the lifeblood out of cities. If he had his way, he half-jokes, we'd go back to horses and carts and heaps of steaming dung. As things are, however, we must be vigilant in protecting what we already have. Among those who've advocated getting rid of the statues was Ricky Demarco, the arts impresario. That was in the 1970s, says Stoddart, when Demarco was a young, iconoclastic man. He thinks differently now, apparently.

Far from statues being removed, Stoddart would like to see their number increased. He has his eye on a vacant site opposite Charlotte Square, home to Sir John Steell's Albert Memorial and the Book Festival. His personal preference would be for one of Hugh MacDiarmid, whose politics may have been seriously skewed but who was "a great poetic epicist". But he is willing to consider all other serious alternatives. How about JK Rowling? "You have to obviously by-pass all the stupid suggestions."

Alexander Stoddart discusses the place of statues in the modern city at the Edinburgh International Book Festival at 4.30pm on August 25