Who is responsible for the marks on the canvas? The artist or happy accident?

"Intentionality has been discredited" says Matthew Slotover, editor of the art magazine Frieze. He was quoted in a jolly story in The Guardian, which described how a freelance journalist found that he had been transformed, entirely without his knowledge, into a fine artist. Illustrative photographs he had taken of motorway cafe meals across Europe were being offered to the gallery-going public as something far more sophisticated, meditations on national identity and global homogenisation - well, you know the sort of thing. The first he knew of his new profession was when he was handed a flyer by his flatmate. It seemed, on the face of it, precisely the sort of thing to discredit the pretentions of the conceptual art scene - hence the slightly snappy response from Mr Slotover.

His words will have surely caused surprise in some circles. After all, we've just finished coming to terms with the notion that intentionality is the very foundation of a certain type of art - if I were to cover a gallery floor with baked beans, stand a plaster pig in the middle and declare that the result was art, then it would be. No arguments admissable about the status of the "installation", only about its relative merit. But in another sense Mr Slotover was only re-stating an old critical chestnut - the fallacy of intentionalism, which, roughly paraphrased, states that what the artist consciously intended the work to achieve is irrelevant to any subsequent discussion of it. This idea proved very controversial, particularly with critics who wished to preserve a romantic notion of the wells of creation, but at one level it simply acknowledged a common- sense truth - that works of art have a life in their recipients' minds that could not possibly be predicted by their creator, particularly if that creator lived in circumstances very distant from our own - Homer or Shakespeare for example (about whom, in any case, no reliable evidence of original intentions exists).

A shadow has always stalked the anti-intentionalists though - even if it depends on a misconception of their argument. And that is the equally common-sense feeling that artists are only entitled to credit for things they meant to do. It may well be that the freelance's photographs take on a new density on the gallery wall, where they cease to be a simple corroboration of his functional text (or a colourful oasis in a desert of black and white print), but something in us begrudges the retrospective attribution of merit. This case is complicated by the fact that the curator of the exhibition (a friend of the picture-taker) clearly had creative intentions in picking up the photographs - authorship was thus neatly divided, with the making having been innocently undertaken by one man and the artistry calculatedly imposed by another - a perfectly respectable artistic practice in the century of ready-mades and found material. But those forms themselves are prey to a residual suspicion about false claims to intellectual property. This has even found expression in the courts - the American artist Jeff Koons found himself having to pay up after commissioning a craftsman to make a sculptural replica of a cute postcard of puppies. The added dash of post-modern irony wasn't enough, the court decided, to pre-empt the claims of the original photographer.

Such doubts can afflict works of the most unequivocal artistry - or perhaps power them. The wonderful exhibition of Howard Hodgkin's paintings, for example, (on show for just a few days more at the Hayward Gallery) achieves at least some of its effects by playing on our uncertainty about how far an artist's control can reach. The pictures offer a sort of visual oxymoron - a meticulous looseness and even for the most casually devoted viewer I suspect that will tug at a loose thread of uncertainty. It is why the pictures, for all their beauty and for all the simple pleasure they give, are never merely amenable. If you try to describe these paintmarks you find yourself using a vocabulary that is not commonly associated with control - a language of flicks, twists, splodges, swirls and even scribbles - that most disreputable of marks. The paint seems to record gestures of swift, experimental vigour and yet it is almost impossible to think of the resulting works as in any way contingent.

There is a way that this apparent paradox can be resolved. If the painter is not responsible for every mark on the canvas - in the sense that he had pre-vision of where line and speck would go - he nevertheless takes responsibility for every detail, however tiny. The painting will not be signed off, as it were, until it meets the artist's requirements, a process that, in Hodgkin's case, can take years. (This is just as true, incidentally, of painters who labour to delete the visible evidence of happy accident from their canvasses - though you sometimes need a magnifying glass to spot it.) But that explanation still doesn't deplete the rich tension of the paintings, the way in which they interrogate our unreflective assumptions about what a painter does with a brush. Would our admiration increase or decrease, for example, if we were to discover that Hodgkin had added an apparently loose bristle-mark with a single-haired brush? Would the paintings be somehow less authentically free or more creditably under command? This might be a simple question for the artist to answer - it may even involve an ethical code which he would never breach - but the fact that it is more difficult for us to decide is one of the reasons the paintings will bear so much looking.