Odd ones out: Franz Kafka, Grace Paley, Bernard Malamud, Philip Roth, Saul Bellow. Photographs: Corbis/Getty

"As a little bit of musk fills an entire house," wrote Osip Mandelstam, "so the least influence of Judaism overflows all of one's life."

Upon reading of the lavish new Sami Rohr prize, given to the year's best work of Jewish fiction or non-fiction, this quote was the second thing that came to mind. The first thing was the $100,000 that went with it, and the need to start writing a new Jewish novel of my own, post-haste.

But in what sense would it be Jewish? This is a perennial but weirdly slippery question among hyphenated writers, so answer-averse it's almost rhetorical, almost boring. What makes a novel Jewish? The short answer, of course, is that the maker does. Say you are the real, chosen thing, historically and genetically certifiable. Say you have the nose, the one-generation-old name, the ironic, self-deprecating temperament, the face in which can plainly be seen the entire map of Poland. (A Jew, says Sartre, is someone others take as a Jew.) According to this argument, whatever this person - let's call him, oh, RC - does, is going to be essentially Jewish, in the same way that Mandelstam's house is going to always have that "little bit of musk."

This was how a number of Jewish-American writers of my own generation started out. We'd read enough of our forebears to see that we were coming in late, and would be only back-row singers in the diaspora chorus, fashioning our cunning little fugues of internal exile, turning Kafka's lament - "What have I in common with the Jews? I have nothing in common even with myself" - into our own (anti-)national anthem.

The great ones before us had been memorialised in Irving Howe's anthology of Jewish American Stories. Singer's eros, Paley's wit, Bellow's learning, Elkin's rage, Malamud's mournfulness, Roth's ferocity, Grade's philosophical balance, Weidman's haunting world of Bartleby-like fathers, sitting in the dark ... all wrestling with their patriarchal angels, struggling (you could feel it in the nervous, visceral energies of the prose) to free themselves from, among other things, labels like Jewish-American in the first place, and anthologies too, with their gluey bindings. ("The reason one becomes a poet," writes Mandelstam's own ex-girlfriend, Marina Tsvetaeva, "is to avoid being French, Russian, etc., in order to be everything").

Every line in Howe's anthology felt alive, heterodox, and improvisational, charged with that singular, Yiddish-inflected music, at once embracing and at war with it too, as if in some Oedipal process of fusion and fission, of tearing loose and re-assemblage. Clearly for the writers of the previous generation, the second side of the hyphen, the American side, mattered. It had weight, consequence, shock value. In any case it was a Subject. But to see it that way requires an outsider's lens ("a state of useful discontent," Howe calls it, though I prefer Danilo Ki‰' phrase: "a troubling strangeness").

The Jewish writers who came after were raised inside. Most of us weren't shamed by our immigrant parents or chased in fear of our lives down the mean streets. We were suburban kids, bred with a tenacious but sentimental and also highly confused tribalism, a sense of the Chosen as a kind of embattled, under-funded, small-market baseball team, one whose fortunes, for all the media attention we generated, were forever suspended precipitously over an abyss. Only the financial and spiritual loyalty of the community would keep the franchise afloat.

We were two generations removed from a coherent communal identity. Sunday school was a joke, Hebrew school a bad joke. And let's not go into the bar mitzvahs. After a dozen years of study my own comprehension of Judaic law was a lamentable pastiche, a crazy-quilt of slogans and exhortations, easily remembered, easily ignored - Never Again! Next Year in Jerusalem! Paul Newman's Really Jewish! - accompanied by a tentative understanding that somewhere in the coiled scrolls of the Torah was a mandate that stipulated, on days of particular solemnity, the suspension of alternate-side-of-the-street parking.

So perhaps the stories we wrote would not be Jewish-American, strictly speaking, but American-Jewish instead. Or both. Or neither. After all, we may have been children of Bellow Roth Malamud Paley, but we also had a number of quirky and influential aunts and uncles from around the globe, Jorge and Italo, Tom, Flannery, the Dons, Gabe down in Colombia, jockeying for space at the family table. Besides, Bellow and Roth, we knew, hadn't grown up reading Bellow and Roth - they'd read Dostoevsky, James, Flaubert, Céline.

The Jewishness of the great Jewish-American laureates was, as Leslie Fiedler has pointed out, more than a little vestigial to begin with. This made us vestiges of vestiges. So what use were hyphens to us? ("Foo to all these categories!" says Herzog.) Our task was not to revisit the material of the previous generation, but to write the truth of our own experience, such as it was. Our own singular reactions to our own singular reality. This was what it meant to be "post-acculturated" - to steer a course between Nostalgia and Nothingness, between earnest "treatments" of the vanished world and frivolous satiric explorations of western anomie, which was rapidly performing its own vanishing act right before our eyes.

One can see the difficulties and rewards of steering such a course in any list you want to make of contemporary "Jewish" writing. The failures outnumber the successes, but then that's always the way with the novel, any novel. No one sets out to be a "Jewish writer", just as no one sets out to win $100,000 prizes: you are what you are, you do your best, you take what comes, the rest is the madness of art and all that. There's only one label that really matters, only one adjective a writer wants to precede their name, and it's of course a very simple one, and as secular as they come: great.