In the early 1990s, there was a famous Reebok t-shirt with the simple slogan: "Sport is an art." Nice idea, but is it true? Can sport - which, by definition, is practical (score runs, take wickets) and competitive (beat the other guy) - belong to the same sphere as painting, literature and music?

The debate is not helped by the fact that sport and the arts are usually portrayed as antagonistic opposites - athletes v aesthetes, hearties v arties, jocks v thespians. From school to adult life, it is often (wrongly) assumed that there is little overlap between artistic creators and sporting competitors. (Writers, in fact, are often just as fiercely competitive as sportsmen.)

And yet no one (well, almost no one) disputes that sport can be beautiful. Last month, I tried to describe the aesthetic pleasure of watching David Gower bat - or just seeing him stand languidly and unhurriedly at the crease. When we watch Sachin Tendulkar turn his wrists at the very last moment, flicking the blade of the bat towards the on side just as the ball arrives under his eyes, we have experienced something beautiful: not just poise and grace but also concision and completeness. Nothing can be added or taken away from that Tendulkar flick that would not diminish the shot. Within its own terms, it cannot be improved upon.

A couple of years ago I watched Arsenal play Barcelona. The game finished a draw, but it was the spectacle rather than the result that left the deepest impression on me. Judged in terms of pure beauty - the physical grace of the players, the inventiveness of their movement - the match was surely the equal of any artistic or cultural event taking place in London that evening. Only someone with his eyes closed could pretend that the match had been defined completely in terms of goals scored and points bagged.

Occasionally I still hear arts-lovers complain that all sport is dull or anti-aesthetic. They are watching the wrong stuff. Anyone who loves ballet must surely recognise Roger Federer as one of their own. Again, elegance is matched by economy: the Federer effect is created not only by what he does but by what he avoids doing. There are no false brush strokes, no unnecessary chords, no superfluous sentences. There is no straining for effect, nothing is artificially tacked on.

There is another parallel between sport and the arts. In each sphere, the greats often have golden, productive spells late in their careers - periods when the insecurities have faded, when the urgent confusions that follow from deep ambition have receded. In his essay "Late Style", the academic Edward Said described how "age confers a spirit of reconciliation and serenity on late works". Yes, the artist may have been at the peak of his powers in his middle or "High" phase. But there is something even more moving about the final creative outpouring. (If you take only one thing from this article, listen, as I am doing now, to Richard Strauss' Four Last Songs - true Late Style.)

Said was writing about the arts, but the same principle applies to sport. The discerning fan will know the feeling of having watched a great player near the end of his career play sport on a higher level - without the fear and frantic-ness of his younger, restless days. We saw Late Federer in the Wimbledon final this summer, conjuring victory despite being outplayed for most of the first two sets. Late Zidane, too, seemed to grasp the whole football pitch before he made even the simplest pass. There was greatness in the small things - especially the small things.

But being beautiful does not make something an art. Many things are beautiful that cannot be classified as art. In The Principles of Art, the English philosopher RG Collingwood (no relation) set out to define the difference between an art and a craft. A skilled worker in a furniture workshop might be highly skilled - and might derive deep satisfaction from his work - but he is not an artist. He is a craftsman. A carpenter assembles bits of wood according to a plan for a table and, usually, the more exact the plan the better the table.

In contrast, art (according to Collingwood) demands a separation of means and ends. There must be an act of alchemy, the emergence of a creative vision. A poet "converts emotions into poems". Unlike the assembly of a table, the final poem is more than - and different from - the sum of its parts.

"A great sportsmen, very occasionally, does something that transcends the activity of scoring a goal or making a shot. He taps into a deep instinct that he cannot quite understand"

Where does this leave sport? I would say sport usually has more in common with craft than art. The batsman practising in the nets over many years is honing his craft. He is searching for a technique that is reliable, consistent, resilient and robust. And if one bit breaks or becomes damaged, he hopes the rest of his game will function adequately while he makes running repairs. The job of a good craftsman is to create a finished article that can be repaired without the whole thing always needing a structural refit.

But sport is not limited to being a craft. A great sportsmen, very occasionally, does something that transcends the activity of scoring a goal or making a shot. He taps into a deep instinct that he cannot quite understand, let alone articulate. But I suspect this artistic strand can only be achieved by accident. If I was a coach, I would be worried if my star batsman said, "Today I am going to bat beautifully." Far better that he tried to bat as simply and naturally as possible - and the beauty happened along the way, as a happy but unintentional by-product.

Sport, I think, can momentarily touch the arts. But it cannot permanently belong as one.

But sports certainly fulfil some artistic roles. In the classical world, the arts had a defined religious purpose. For the Greeks, watching a play was a communal act of piety, a form of shared worship. Modern sport achieves something similar. What do we feel when we walk among the masses to a vast sports stadium? We are part of the crowd, we share a purpose and sense of hope with the thousands around us - we belong to a broader congregation. That religious language follows naturally. The art critic Robert Hughes famously wrote that train stations were the cathedrals of the industrial age. To update Hughes: sports stadiums are the cathedrals of the post-industrial age.

Above all, sport provides us with timeless stories. It reveals, in dramatic ways, essential elements of the human condition. A few years ago, speaking at a BBC debate called "Sport v the Arts", the classical scholar Edith Hall made this startling claim: "Sport has only two narratives - either you win or you lose - how boring!"

The truth could not be more different. A moment's reflection reveals that within the overarching narrative of victory or defeat (there are also draws and ties, Edith), there are countless twists and subplots - often far more interesting and affecting than the headline-grabbing result. Sometimes you have to look more carefully to see the real story.

Sport can be experienced at many different levels. Just like the arts.