Lots of good points there, TYWD. Of course it's very hard to envisage islamic courts operating within a common law system.
It's quite surprising that the Archbishop, as he put it himself to a friend after the news broke, "had no idea that this would cause so much attention". The thought of imams setting up their own courts and passing judgment on the matters of muslims here in the West, and of those courts having the right to exact punishments, that's the very stuff that raises the neck hair of many ordinary people, and a prime focus of right-wing parties such as the French Front National or Berlusconi's party in Italy. And it's a fear that is shared by many muslim women. The real wish of Front National and others is to throw out the "Arabs", and the spectre of local courts that would be able to hold "Qu'ranic trials" underpins just that wish.
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Of course sharia law doesn't always mean chopping off hands and having public floggings and stonings of adulterous women, but there is no definite idea of just what counts as sharia law- trhere are several schools and ways of ruling from the Qu'ran - so a straight recognition that sharia courts are valid could be seen to invite that kind of thing. Besides, how do you define who is a muslim and should be subject to islamic law? We can't enlist all who come from an islamic country to a system of islamic courts and demand of them that they should live under what those courts decide, under their jurisdiction, can we? That would be like creating a kind of "muslim state church" though it would be free to formally leave it. The more I think about this, the more disjointed it seems, the groundwork of the remarks of Archbishop Williams.
There was a suggestion recently in Sweden, from the secretary for higher education, to provide for a public "imam college" to foster a corps of imams that would be trained within the country and recognized here - under some kind of supervision from University/Education authorities - and maybe to demand, in time, that you have to be a "certified imam" (having studied here or in some other Western country) to hold a higher office at a mosque. The proposed "imam exam" would include some acquaintance with civil and criminal law as it is practised here, and with the ideas of secularism.
That would be a way, among many, to avoid muslim groups closing in on themselves and then having the big mosques becoming centers of exile politics and hardline islamism (like the Birmingham Mosque in the UK, or some mosques in Paris). The people who set the tone at those places sre sometimes really preaching and living as if they were still in Pakistan or Egypt. Seems a useful idea to me, remains to be seen what the muslims think...