Jerwood Contemporary Painters, Jerwood Space, LondonTess Jaray, Lyon & Turnbull, London

The Jerwood's selection has some wonderful works in it, but some are, frankly, icky and others aren't paintings at all

As you stand before any of the works in the Jerwood Contemporary Painters show, ask yourself this: does it really matter that it's a painting? Is it actually concerned with paint, or is its medium just a conceptual flag of convenience? These questions seem so very old-fashioned that I'm embarrassed suggesting you ask them. But these are interesting times for painting, and terms need to be defined.

At the far end of this show, the answer to both questions is easy enough: no, and no, in that order. Tom Crawford's Product Paintings and Michael Samuels' Goodbye to Dignity exist for the sole purpose of playing with words. In what sense does a pair of shoes glued to a back-lit wooden pallet – Crawford's The life and death of an abstract painter – constitute a painting? Or, pretty as it is, Samuels' assemblage of deal side-tables? It's the Ship of Theseus paradox: if you take away canvas or paper or panel or fresco, is it still a painting? And if you then take away the feel for paint? And then the paint? Well, no, it isn't. The result may be a clever, witty, pushing-at-the-borders artwork, but it has probably been made by someone who went to an art school stronger on theory than practice.

So what are Crawford and Samuels doing in this show? At a guess, they're there as curatorial teasers. If these are the limits to which the word "painting" can be pushed, then everything within them must, by definition, be paintings. Actually, this applies to surprisingly few of the works in the Jerwood show.

Let me nail my colours to the mast. To my strict little mind, Malevich's Black Square (1915) is a painting because, whatever else it is doing, it is profoundly concerned with paint. Malevich could have asked – did ask – the radical questions raised by Black Square in other media, but, in this case, he chose not to. Black Square, bituminous, theoretical, is – to use another old-fashioned word – painterly. It is about the battle between perfection and imperfection waged by every painter since Lascaux: the difficulties and pleasures of coaxing magic out of a paste of oil and dirt, of feeling that paste under your brush. Malevich is like Goya or Manet or the young British painter, Cecily Brown: brilliant, full of ideas, but first and foremost a materialist.

But is this also true of – to pluck a picture from the wall – Johan Andersson's Kate? That Andersson's picture looks like a cover for an Abba LP is neither here nor there. After all, Renoir on a bad day was pretty icky. The difference, though, is that Renoir didn't know it. Andersson's canvas, unless I'm doing it a huge injustice, is laughing up its conceptual sleeve, playing postmodern games by being kitsch. Like the whole Bad Painting thing of the 1970s (or like Martin Maloney in our day), the idea comes first, that it happens to be expressed in paint a distant second.

To put it another way, Kate is more concerned with being clever than with being painted; unlike Black Square, it appears to believe that you can't be both at once. And I'd say that the same was true of the majority of works in this show: Andrew Griffiths' One is Close to God in the Garden and Chris Smith's Untitled, James Wright's The Retribution and Caroline Walker's The Parade among them.

Nothing new there, then, except that painting is reportedly in the middle of (yet another) comeback. Just when the medium seems about to join the blue whale, a painter wins the Turner Prize and Peter Doig gets a solo show at the Tate. So an exhibition of the work of 20 emerging artists is bound to look hot, at least in theory. In practice, this year's Jerwood Contemporary Painters is rather lukewarm, its steamiest points being its most abstract.

Out of all the artists in it, three seem genuinely interesting; and they – Varda Caivano, Nadia Hebson and Yuko Nasu – are all gesturalists or abstractionists. (Nasu's calligraphic Imaginary portrait series, BN is a wonderful picture.) You get the sense with all three of history playing backwards; that to return to real painting, painters need to re-engage with that visceral avant-garde which begins with Black Square.

For an idea of where this reconnection might lead, the artists in the Jerwood (and certainly the readers of this review) might usefully take themselves off to Tess Jaray's show in Pall Mall. Jaray has spent half a century painting geometric abstracts of steely warmth and poise. She is now 70, and her work isn't merely as fresh and crisp as it was in the Sixties, it is startlingly new; maybe even avant-garde. Could this be where art is headed? I hope so.

Jerwood Contemporary Painters: Jerwood Space, London SE1 (020 7654 0171) to 18 May; Tess Jaray: Lyon & Turnbull, London SW1 (020 7930 9115) to 1 May