Will this year's Turner Prize winner stand among the all-time greats? Does it matter who the greatest artist in history is? The late, great art critic Robert Hughes, a ruthless defender of the right to make qualitative judgements, certainly thought so.But what do we even mean when we say "greatest artist"? A personal favourite? The greatest amount of technical skill? The ability to touch people across cultures and eras? One way of measuring artistic greatness without descending into top-ten lists of taste is to measure impact. While Jean-Michel Basquiat was being celebrated, raised to lofty heights as the toast of New York in the 1980s, Hughes demurred. On Basquiat's death in 1988, Hughes wrote that his rise to fame was symptomatic of a "mania for instant reputation" and compared his boosters to "right-to-lifers, adoring the foetus and rhapsodising about what a great man it might have become if only it had lived." With the clarity of hindsight we now know Hughes was right. Basquiat still has his fans, and, in 1996. His contemporary Julian Schnabel immortalised him in an eponymous biopic, but he is mostly remembered as a footnote in art history. An interesting one perhaps, a cautionary tale certainly, but a footnote nonetheless, celebrated as much for his untimely death and outsider status as for his actual work. Even better-remembered artists aren't always remembered entirely for their greatness.1995's Turner Prize winner Damien Hirst was always controversial but he certainly caught the spirit of the times: a newly confident, yet brutal and anti-aesthetic art. No doubt the 1997 Labour government was doing a fair amount of bandwagon-jumping when it prattled-on about "Cool Britannia," but there is something in the timing. Hirst and his contemporaries, including Tracey Emin, came of age just as John Major's Conservative government was coming apart at the seams. Its replacement in the Blair administration was confident yet had a hole where its heart should have been - not to mention its mind. It would be a mistake to view art through a political prism, but all culture, even the rarefied world of the visual arts, tells us something about the society that produced it. So, in once again straitened times, Hirst seems not so much revolutionary but vulgar. Some artists escape this fate. 1999's winner Steve McQueen has gone on to a successful career as a film director. The work of 1993's winner Rachel Whiteread still holds our interest and 2010's winner Susan Philipsz is an unlikely candidate for being a slave to the modish. Full disclosure: Philipsz taught at the art school I attended, but she never taught me. The lesson is simply that fashion and commerce are no guide to legacy. An unrepentant modernist, my personal favourite artists include Aleksandr Rodchenko, Russian founder of constructivism, and American abstract expressionists Mark Rothko and Barnett Newman, but none of these, I fear, has a claim to the be the greatest artist. Of twentieth century artists, none had the influence, creative longevity or artistic - and perhaps ethical - flexibility of Pablo Picasso. But then Picasso had his influences, including Cézanne. He in turn had the impressionists, they had Manet, he had the romantics... and on and on it goes. 98 years of intentionally shocking, but craft-, skill- and content-free art, where qualitative judgement is meaningless, and the laughs are wearing a bit thin. Other names spring to mind too: Velázquez, Caravaggio, Goya, Rembrandt, Holbein, perhaps even Bacon. The list is a long one. Warhol, whose work I detest, was nothing if not influential. Of course, it could be argued that Marcel Duchamp had the greatest influence on art. After all, almost the entire history of post-modernist art descends directly from his two jokes: The Bottle Rack (1914) and Fountain (1917). These "readymades" upended the art world by presenting mass produced objects and claiming them as art simply because the artist said they were. And, lo, conceptual art was born. Some would argue, myself included, that the influence was an almost entirely negative one. Actually, the joke is funny. Or rather, it was. 98 years of intentionally shocking but craft-, skill- and content-free art, where qualitative judgement is meaningless, later and the laughs are wearing a bit thin. Sticking one's neck out and declaring any artist to be the greatest ever will only be met with complaints. The truth is there have been so many great artists that without naming a strict criteria for greatness it would be impossible to name just one. But making judgements is what it's all about. Jason Walsh is Ireland correspondent of the CS Monitor and is reading for a PhD in philosophy. He is speaking at Who is the greatest artist? Balloon debate at the Battle of Ideas on Saturday 20 October Independent Voices is partnering with the Battle of Ideas festival to present a series of guest articles from festival speakers on the key questions of our time.