He is wearing a pair of feathered wings, and nothing else. He grins cockily and knowingly, holding a couple of arrows in his hand - he's Cupid, after all. But there's nothing cute about Caravaggio's Victorious Cupid. Painted lifesize in a bright light that picks out his flesh harshly, he looks right at us while his penis and balls hang in full view at the centre of the picture. He's posed in what to educated contemporary viewers was a recognisable parody of Michelangelo's sculpted Victory. At his foot lie the discarded emblems of intellectual and public life - a globe, a book, armour - blown away by desire.
In the 20th century, the creator of this unsettling image - a man of violence and mental instability who was born in about 1565 in Caravaggio, near Milan, and died in shame and ignominy, a known murderer, in 1610 - leapt from obscurity and critical contempt to become probably the most popular of all the great Italian artists of the Renaissance and the Baroque. He is the one we feel is most our own, one of us. The name itself has become sexy, talismanic, namechecked in trendy academic books, such as Quoting Caravaggio or Caravaggio's Secrets. To be different, Peter Robb avoided the familiar name in his recent fictionalised biography and called his hero M, from the painter's birth name, Michelangelo Merisi.
Photographers imitate Michelangelo Merisi da Caravaggio's light and artists identify with his depravity. In the quiet, serious rooms of the Gemäldegalerie in Berlin, where Caravaggio's Victorious Cupid (1602) hangs, visitors are visibly embarrassed by the boy's naked display. So it's a shame that the gallery has refused to lend it to the Royal Academy's forthcoming exhibition of Baroque art, The Genius of Rome. This Cupid is the supreme embodiment of what this painter signifies today: transgressive sex. There's no doubting what the painting is about, or what the relationship was between artist and model.
Or is there? Scholars, sad to say, do doubt it. They doubt that Caravaggio was even homosexual, as is widely believed. Our only written source for this near-universal assumption, Helen Langdon points out in her spoilsport 1998 biography, is a note made by a 17th-century English visitor to Rome, Richard Symonds, after he saw the Cupid. He reported: "Twas the body and face of his owne boy or servant that laid with him." Langdon and other art historians suggest this is just tourist tittle-tattle, an unreliable bit of hearsay.
Our entire sense of Caravaggio as a modern artist is, according to historians, a fiction. We see what we want to see. It's not even true that Caravaggio was some kind of despised, marginal figure in his lifetime. On the contrary, he was the most famous artist in Rome, the founder of a new kind of sharply illuminated naturalism that influenced every one of Europe's great artists in the 17th century. Caravaggio inspired the early genre paintings of Velazquez in Spain, and the lighting effects of Dutch Golden Age painters. He was recognised as the genius of his age even when he had to flee Rome to escape a murder charge. It was after his death that the critical backlash began; his art was condemned as wild, uncontrolled, gauchely disobedient to the rules of classicism. By the 18th century his influence was downplayed and his low, realist painting was disparaged as an insignificant chapter in the history of art.
Obviously, the Victorians were not the people to reclaim this degenerate artist. It was only with an exhibition of Baroque art in Florence in 1922 that he began to come out of the shadows. As late as the 1950s Ernst Gombrich's The Story of Art treated Caravaggio as a minor figure.
The trouble with our excitement about Caravaggio is that seeing him as modern means ignoring what is so powerful in his art. Peter Robb's M tries to expose some kind of anti-Church radicalism in Caravaggio, but nothing could be further from the truth. You only have to visit some of the churches in Rome where his altarpieces hang to see what Caravaggio's naturalist art, with its use of street people as models, did. It was a weapon of the Counter-Reformation. Caravaggio found a new, more direct way of telling religious stories: he cast urchins and old men off the Roman streets as saints and angels, and he painted martyrdoms as if they were happening here and now.
In the church of Santa Maria del Popolo the founder of the Catholic Church is being executed. St Peter - a man aged and gnarled by labour, taken from an inn in some back alley to have his painting done - has already been nailed to the cross. He looks in fury at the nail holding his left hand in place. But the three younger men in the picture are subjecting him to a final ignominy. They are raising him by the legs, to crucify him upside down. It's hard, ungrateful work. You almost feel sorry for them. These are not the grotesques who crucify Christ in a painting by Bosch. They're ordinary working stiffs, doing their job.
This is who Caravaggio's painting is addressed to: the ordinary people of Rome. You too are part of the story, says Caravaggio - you too have moral choices to make. Will you do good or evil?
Yet there are problems with the view of Caravaggio as an orthodox Catholic artist. If that was the case, why were so many of his religious paintings - about half - rejected by the people who commissioned them? Modern viewers may go too far in dwelling on the sensual, near-nude angel in the foreground of The Rest on the Flight into Egypt (c 1595) - but the angel's sexy presence is an incongruously prominent feature of the painting. And how do you account for all those boys brandishing fruit or wine in a way that seems also to be an offer of sex?
You can't ignore this invitation in Boy with a Basket of Fruit (c1593-4), coming to the RA from Rome's Galleria Borghese. Soft and hedonistic, the boy's face looks at us lingeringly, provocatively, and there is no missing the message that he too is a fruit for us to pick. Art historians may argue that Baroque art was driven by patronage, and that Caravaggio's patrons were men of piety, powerful clerics - but it's hard to talk away the eroticism of a painting like this.
Perhaps Caravaggio's patrons, like him, led double lives. And perhaps the originality of his art is to acknowledge that doubleness, and to unite the two lives - to find the sacred in the profane and the profane in the sacred.
So was Caravaggio both things, the good Catholic and the sexual adventurer ? Or was he a psychopath, as he has been portrayed?
We know very little about Caravaggio, but we do know he was very violent. He had duels and participated in street fights almost constantly; he was the kind of man who would run up behind someone who had annoyed him and hit him on the head with his sword. His friends were always restraining him from doing worse and it didn't surprise anyone in Rome when he finally killed a man and fled the city.
Perhaps the insoluble contradictions of Caravaggio's art are not profound at all but the work of a heartless stylist, a monster able to make sex and religion equally seductive. Yet this cannot be so, because his paintings burn with emotion, with compassion. The street people who pose in his paintings live for ever, and he intended it that way. If he was quick to anger, his art is quick to love.
Caravaggio's lifestyle may never theless be the key to his art, the fact that it does not just veer from the holy to the unholy but explores both with unparalleled intensity. Caravaggio seems to have been addicted to danger; a friend diagnosed this as an excess of courage. It was as if he sought out instability, crisis, moments of risk. This is exactly the quality that all his paintings share - risk. His paintings are alive today because each staged tableau has a sense that it is about to break apart at any second. The men playing disciples are about to start fighting; the boy with the fruit is about to call the painter an old lech and run off; the painter is about to leap on Cupid. These paintings push painting to an edge where it is becoming life, is ending as art.
Caravaggio looks like our contemporary because his scenes are so mesmerically poised in time, dramatising moments of choice and decision in which we ourselves are implicated. Will you accept the boy's offer of fruit? Will you just stand there watching St Peter being crucified upside down, or will you do something about it? These scenes transfix us as they transfixed their original viewers. And we will always walk away from the Victorious Cupid embarrassed and confused, a little relieved to be back among the nativity scenes and landscapes by other Old Masters, which don't have us blushing and wondering where to put our eyes.
• The Genius of Rome 1592-1623 is at the Royal Academy, London W1 (020-7300 8000), from January 20 until April 16.
