Take a look back in Ingres

I think I had better start by laying my cards on the table: I know Alison Watt, I like her paintings and I can't pretend that I don't care about the success of the exhibition that opens tomorrow at the Scottish National Gallery of Modern Art, not least because she is represented by the Ingleby Gallery, in which I have an obvious interest. So now that that's out of the way, I am not, in this instance, an impartial critic, though that doesn't make me a completely disingenuous one.

I think I had better start by laying my cards on the table: I know Alison Watt, I like her paintings and I can't pretend that I don't care about the success of the exhibition that opens tomorrow at the Scottish National Gallery of Modern Art, not least because she is represented by the Ingleby Gallery, in which I have an obvious interest. So now that that's out of the way, I am not, in this instance, an impartial critic, though that doesn't make me a completely disingenuous one.

In fact, the reasons that I got involved with Watt professionally are precisely the same as those which prompt me to recommend her exhibition. She is a considerable painter and, in the context of the art of our time, a very unusual one. She first made her name in the heady atmosphere of Glasgow School of Art in the 1980s, among the group of young figurative painters whose work caught the mood of the time and who found a very public sort of success very early in their careers. In retrospect she dealt with this better than most, working away despite the spotlight shining on her every move and so building a reputation as one of her generation's more enduring talents.

Her paintings, until very recently, were predominantly - almost exclusively - of people, often naked and arranged in intentionally stilted tableaux in bleached surroundings, like fragments of some kind of story that never quite got fully told. In the mid 1990s, she began an examination of the female nude as seen through the work of the French painter Jean Auguste Dominique Ingres, balancing the undressed figures from his most famous pictures against panels of painted fabric. In these newest paintings the figure has gone completely, leaving just the fields of fabric.

On the face of it this reads like a recipe for a rather dull exhibition: 10 large paintings, all oil on canvas, all between 5ft and 7ft in each dimension; depicting swathes of textile, some patterned, some plain, draped and folded, nipped and tucked. It sounds a bit boring, yet the effect of these pictures is compelling and very odd. They need to be seen to be believed, and seen in the flesh rather than in illustrations. At the Gallery of Modern Art they have been hung very sparely across three rooms: each paintings has its own wall, its own space, and each becomes like a world into the viewer is invited to dive. It's a very seductive experience.

As one would expect from an artist with Watt's pedigree, they are very nicely painted but not quite with the high finish that appears from a distance or in reproduction. In fact, close up, they look quite different with a contradictory physical presence. On the one hand, they are so finely wrought (such is her meticulous approach that paintings crawl out of her studio at a rate of roughly four a year and this entire show took three years to make), and yet the quality of the paint itself is loose and chalky: the brushstrokes almost messy and surprisingly urgent.

Watt's ostensible subject here is fabric, but that is not really what these paintings are about. There is a sense of absence in them, or rather an almost ghostly presence which gives them a haunted quality, evoking not just the human form, but, bizarrely, a whole range of possible emotions: seductive one minute, quiet and almost soothing, tense and tightly coiled the next.

So what is it that makes these apparently simple paintings work in such a complicated way? To be honest, I'm not completely sure. I have been looking at them, on and off, for the last six months and I still haven't quite got the measure of them, but they seem to operate in the same way as the best sort of abstract art. The four newest "white" paintings ( Sabine, Rosebud, Riviÿre and Shift) do it most strongly. Stripped of the more decorative associations of the patterned pictures, they contain some seemingly specific implications - linen, sheets, bed, sex - but it is the less obvious associations that give them such weird strength. They are helped by their physical size so that the individual marks - the swoops and folds of the fabric - are somehow secondary to the engulfing power of the whole.

In a sense it is what you bring to these paintings that dictates what you will take away, in much the same way as it does with the work of artists such as Robert Ryman, Yves Klein, or Mark Rothko. These references might seem misplaced in relation to an artist whose work has such a clear link with Classicism and whose acknowledged influence is a 19th-century Frenchman, but the best of these new paintings seem to have much more in common with these 20th-century masters than with her earlier hero.

Watt has enthused about the critic Robert Rosenblum's description of Ingres' work as "a fusion of visual truths and abstract fantasies", and this seems like a very apt description for the way in which her own paintings work their strange magic.

Many of her titles still refer directly to Ingres' paintings, especially his portraits of a certain sort of fashionable lady, the Mesdames Riviÿre, De Tournon and, of course, Moitessier, and, certainly, her understanding and enthusiasm for his work provided a way in to making these new paintings.

But Ingres is really just the conceptual starting point, a ghost at the banquet. The most apposite title of all belongs to the most recent painting and which she has extended to the exhibition as a whole - Shift - with its connotations both of fabric and skin and above all of transition. These pictures do mark a shift in Watt's work, but they also show a very clear continuity and present a resolution. For all of their classical connotations, these pictures belong to the art history of the early 21st century and with them Watt stands out as that rare thing: an artist who is capable of bringing something completely new to the old traditions.

Shift by Alison Watt: Scottish National Gallery of Modern Art, Belford Road, Edinburgh EH4 (18 Nov to 8 Jan). The exhibition is sponsored by Deutschebank