Imagine sitting down to dinner with guests from the Zionist Federation, Jews For Justice For Palestinians, Independent Jewish Voices and the Board of Deputies. Sounds like a recipe for disaster, right? Yet over the last couple of years this is precisely what my wife Deborah and I have been doing - organising dinners in our home in which Jewish leaders and opinion formers from all sides of the Israel debate come together, with surprisingly convivial results.

Organising these dinners stemmed from our concern as to how debates over Israel are conducted in the Jewish community. Israel is no longer the point of consensus it once was and debates are often accompanied by bitterness and anger. There is good reason to think that divisions over Israel have the potential to divide the Jews as never before.

It is vital that we find a way of learning to live with these divisions. Whether or not we would like to, it is impossible to go back to a time when criticism of Israel occurred in private, if at all. One way of maintaining Jewish relations across the divide is to promote civility in debates.

What is civility? In the United States, the Jewish Council for Public Affairs has recently promoted a statement on civility that argued: "We will discover civility in the guarding of our tongues and the rejection of false witness. We will find it wherever we show care for the dignity of every human being, even those with whom we may strongly disagree. We will find it by listening carefully when others speak, seeking to understand what is being said and trying to learn from it".

Like all ideals, that of civility is hard to live up to. Yet it remains vital to work towards a more civil Jewish community if we are to prevent the Jewish people from dissolving into series of mutually antagonistic clans, sniping at each other on newspapers' letters pages.

I have been working for the last two years under the banner of the New Jewish Thought project to start a process of civil, intra-Jewish dialogue on Israel. The project has been confidential and many of its details must remain so, but I want to publicise it now with the aim of widening the discussion on civility.

To date, we have organised 10 dinners with nearly 60 participants in order to discuss how we talk about Israel. Every dinner is carefully organised to include a cross-section of views and we have welcomed public Jewish figures as diverse as Melanie Phillips, Jonathan Freedland, Brian Klug and Anthony Julius, as well as communal leaders such as Jeremy Newmark of the Jewish Leadership Council, Mark Gardener from the Community Security Trust and Vivian Wineman of the Board of Deputies. Pro-Israel campaigners such as Jonathan Hoffman of the Zionist Federation have attended, along with Jewish pro-Palestinian campaigners such as Richard Kuper from Jews for Justice for Palestinians, and rabbis from across the communal spectrum, including Julia Neuberger.

If the mix of people sounds rather combustible, the atmosphere has for the most part been constructive, convivial and even warm. Home hospitality predisposes most people to moderate their tone and encourages us all to let our guard down. The custom of sharing food together dates back to antiquity as a means of creating peace and recognising one another's common humanity. In Judaism, too, the dinner table can serve as a sacred space. Proceedings at the dinners are confidential as this privacy encourages candid conversation.

Although I organise and co-host the dinners, I never claim to be a disinterested facilitator. I have published articles outlining my own views on Israel and I do not hide them. While I have a deep love for the country, have visited and worked there, I am also strongly critical of the political path it is following.

But I am also someone who has been deeply involved in the Jewish community and does not want to see it torn apart. So I try my best to both participate in and facilitate the conversation.

Perhaps because I am the co-host and guests are predisposed to be nice to me, the dinners usually work out well. There have only been two occasions when anything close to a row broke out and these were the result of the difficult histories between participants whom we had unwisely invited to the same dinner.

The project has not yet brought harmony to the Jewish community. Differences remain wide as ever. However, the dinners have revealed many shared concerns between those with apparently polarised opinions. Some pro-Israel campaigners have talked of their private anxieties at the direction Israel is taking; some pro-Palestinian campaigners have shared their fears about antisemitism.

The dinners have revealed that my concern about civility, while it is not universal, is shared by people on all sides. There have been a number of occasions when productive connections have been made by people who before the dinner had only met on bad-tempered public platforms and in comment threads.

This project is, hopefully, the start of something. If Jewish leaders and opinion formers have the opportunity to reflect on how we talk about Israel, civility is likely to move up the communal agenda, at least a little. If nothing else, the project has proved that people who have attacked each other in public may be able to develop a more civil relationship in private.