Indeed, if one could visit the workshop of one of the great monumentalists of a century ago, it might look a lot like this: plaster casts in various stages of assembly; imperious figures missing limbs or, occasionally, a head; bags of clay which until recently were a working model of physicist James Clerk Maxwell.
Stoddart is Scotland's premier neo-classical sculptor, the man who made the figures of Adam Smith and David Hume for Edinburgh's Royal Mile, Robert Burns for Kilmarnock, the beautiful Robert Louis Stevenson memorial on the capital's Corstorphine Road. He's 49, but looks boyish, with his sandy hair and dusty lab coat cut off at the elbows. He is a man of swift, enthusiastic intelligence, rarely still, and almost never silent.
Despite once being dismissed by the Scottish Arts Council as "backward-looking, historicist and not reflecting contemporary trends", Stoddart is busy. Around us are the plastercasts of past commissions: immense allegorical figures for the 6 million Millennium Arch in Atlanta, Georgia; religious commissions for a mysterious private client who has her own chapel "somewhere in North Britain"; parts of 70ft frieze for Buckingham Palace. A bust of Pope John Paul II for a Chicago seminary.
Soon they will be joined by James Clerk Maxwell, whose statue, commissioned by the Royal Society of Edinburgh, will be unveiled on Tuesday at the East End of Edinburgh's George Street. Stoddart is thrilled to be sharing a street with 19th-century sculptural greats like John Steel's Thomas Chalmers. "It's the greatest honour to be anywhere near the company of Steel."
And he is ready and waiting for the next question, the one about relevance.
"Is this relevant? Is James Clerk Maxwell relevant to us? I don't like to say: 'Yes, he is', although he is. He's relevant to our mobile phones, our navigation systems. I'm told he's the man that changed everything. But the relevance of the statue does not depend on some stupid mobile device in your pocket."
In fact, it doesn't depend on you at all. Statues, by their nature, have little truck with relevance. They refer to the past, they will last until the future. The present is transitory. The makers of monuments take the long view. "And if you ask to have your own statue made, you're a twerp."
But the very idea of elevated monuments to great individuals (usually men) provokes discomfort in the modern era. Anyone daring to make public sculpture at all has tended towards "everyman" figures, such as Kenny Hunter's Citizen Firefighter in Glasgow or the Fair Maid in Perth High Street. Most 19th-century statues have become little more than repositories for traffic cones by drunken revellers.
Stoddart is a remover of traffic cones. "It's antideferentialism, we've always had a problem with it. It's institutionalised. At one point, Glasgow City Council actually voted to adopt the cone on top of the statue of the Duke of Wellington (in Royal Exchange Square] as an official Glaswegian marketing plot, because, guess what? 'It shows we're able to laugh at oorsels'. What they're really doing is scoffing at the great.
"I try to concentrate my work in Scotland because the nation is in need of more monuments. Too many greats as yet unmarked."
Like who? Andrew Fletcher of Saltoun, who led the opposition to the dissolution of the Scottish Parliament. Archbishop Gavin Douglas of Dunkeld, the first man in Europe to translate Virgil into a vernacular language. King James IV, "our Renaissance prince". The "greatest architect of the modern age", Robert Adam. Historian Agnes Muir Mackenzie. Mary Queen of Scots. Monuments which teach us our history.
"Isn't it astonishing that there wasn't a statue of Hume until I made one? We need serious monuments which don't have the Braveheart touch. If we're to be a nation, we need that. Fletcher of Saltoun is absolutely urgent if we're to show we mean business. We don't do it with a stupid Parliament building that looks like a Barcelona-inspired cafeteria. It's a bloody outrage."
He is currently working on a figure of Willie Gallacher, the Paisley-born Communist MP. "I'm not much of a Communist myself. We belong to the other side, somewhere to the North of Genghis Khan, but he's a great man whether I like him or not. Gallacher's funeral was the biggest civic event in Paisley ever, there were 7,000 in the cortege alone. The civic monumentalist has a responsibility. There are limits, I might draw a line at Goebbels."
In the partitioned area set aside for maquetes, he sprays water on a tiny clay model of his "magnum opus", a "mammoth representation and celebration of the Ossianic phenomenon" earmarked for an amphitheatre site which will be hewn out of the ground at Ben Cruachan. With a finger and thumb, he twirls a tiny spike of clay to demonstrate the height of a man. "I've been trying for this for 15 years now, and we've got a bit of headway."
We repair to the Stoddart home, a lovely 19th-century villa in Castlehead, Paisley, where he and his wife Catriona have raised their three daughters, now teenagers. Statues, busts and maquetes line every room. He takes care to explain that "the house is less opulent than it looks – the sculptures cover over the cracks. All monuments are done on a shoestring."
Sitting in the cosy kitchen with Jura the spaniel at his feet, Stoddart talks about how all this began. He went to Glasgow School of Art in 1976, a gifted draughtsman out of step with the modern era. After a "difficult first year" he started making abstract sculptures out of sheet metal "to get good crits", while finding solace in the 19th-century via the works of Schopenhauer, Wagner and GF Watts.
Then one day, after one such "good crit" he turned a corner and came face to face with the art school's plaster cast of the Apollo Belvedere. Over two millennia the statue, it seemed, had lost none of its power. He was chastened, and switched to figurative work.
After gaining a first – keeping the modernists on side by referencing Rodin – he planned to become an academic "to work with the sculpture I loved", but on a study trip to Denmark he encountered the work of Bertel Thorvaldsen, a contemporary of Canova, and was "struck dumb". He left academia to return to sculpture and spent a "difficult" six years in the studio of Ian Hamilton Finlay.
Once independent, one of his first works to propel him to public attention was the series of classical figures he made for the frontage of the Italian Centre in Glasgow. He contemplated selling his house in order to finish them.
Raise the subject of the modern and he gets combative. Modern art is "rubbish", narcissistic, snobby, devoid of skill, ignorant of taste, gripped by "nostalgia for the future". But it goes deeper than that. It's a difference of opinion about what art should do. Art, he says, has always been about "trying to alleviate the pain of existence". Modern art "collaborates with misery as opposed to trying to oppose it".
"A painting by Titian is like a Leningrad, holding out against the forces of the world. Even if they're having to eat rats in there, they still will never surrender to it. Whereas the art of Tracey Emin is a complete capitulation to the world. Cutting a shark in half and putting it in a tank of piss is just art giving up. I find it very odd when they describe art as challenging, because I always thought art was meant to calm you like a lullaby, not challenge you like some skinhead in an underpass."
Unsupported by the Arts Council, largely unrepresented in national collections, he has a strong base of private admirers who enable him to keep working. "I'm an elitist. I believe in the elite for all. We're allowed elite footballers because they're the best at sticking the ball in the net. We're allowed elite surgeons, and elite scientists. These people pursue their various careers according to the highest accomplishments and the results are superb.
"I'm trying to bring the highest elite form of art back to the people. And they are going for it.
"You calm down because at a certain point, you realise that if you had stuck with ambition to be in the contemporary art world, so many great opportunities would be cut off. It's a tiny closet and it's joyless. Everyone is wanting to get into the cupboard, I've got the run of the house."
Set in stone
James Clerk Maxwell was a mathematician and physicist who grew up in Edinburgh. His greatest achievement is considered to have been developing a unified theory of electromagnetism, which has been described as "the second great unification in physics" after the achievements of Newton. Many believe him to be the 19th-century physicist with the greatest influence on the 20th century.
On the centenary of his birth in 1931, Einstein described Maxwell's work as "most profound and the most fruitful that physics has experienced since the time of Newton". The plinth for Stoddart's figure will feature two friezes showing the "schools" of Newton and Einstein.