So the facts of life are that the things which have provoked a minority of French or Danish Muslims to violence will continue to provoke them. If you allow for those facts and if you have a solid and growing mass of five million Muslims you are bound to find among them many thousands who will be Islamic fundamentalists, who will go off to fight in Syria, Yemen, Iraq or elsewhere and who will also be prone to carry out anti-Semitic and terrorist attacks in their host nation. In practice, the state then finds itself powerless to protect its Jewish minority. All French Jewish schools and synagogues have been under armed guard for several years but this has not prevented continuing terrorist outrages. It seems very likely that Amedy Coulibaly was intending to attack a Jewish school and synagogue but ended up killing a policewoman instead before heading for the kosher deli, clearly in search of more Jews to capture or kill. Without any doubt the terrorists will succeed in making more French Jews flee.

Moreover, a number as large as five million (or Denmark's five per cent) makes the task of the local intelligence services in trying to prevent such things simply impossible. There are too many people to watch and for every terrorist there are bound to be many more sympathisers willing to contribute money, safe houses and so on. This is why the French intelligence service, just like its British counterparts, continually warns that though it may foil many Islamic terrorist plots, it cannot possibly prevent them all. Which is to say, we are bound to have more Charlie Hebdos as well as more Salman Rushdie-style fatwas. The only way to stop this would be to allow a regime of sweeping preventive detention of all suspected Muslim zealots. Most Europeans would find this incompatible with civil liberties. Some will hope that getting more Muslim religious leaders to denounce violence will make a difference, but thus far there is no evidence that this will stop the extremists.

It is no good pretending that the extremists were only a tiny minority. In the wake of the attacks the online Daily Beast reported that Parisian Muslims were prone to argue that they had all been staged: "It was a conspiracy designed by the Jews to make Muslims look bad." In some Muslim areas teachers reported that as many as 80 per cent of their students refused to observe the minute's silence decreed for the victims and some said openly that they supported the attackers. The truth is simply that to have as many as five million Muslims in your country—perhaps even just to have 2.8 million, as in Britain—means that you are bound to have at least several thousand young people liable to be tempted by jihadism. The same applies to Denmark and indeed to many other European countries.

Liberals tend to hope that their local Muslims will gradually become more integrated and more secular. This may happen in timebut it will take several more generations. Long before that process is complete there will be no Jews left in France or Denmark. The real question is how many Jews there will be left in all of Europe. After all, the Muslim population is growing everywhere and the Jewish populations of most European countries are well educated and quite prosperous. They are thus highly mobile and can easily leave for Israel, Australia or North America.

The only way that this is not going to happen is if European countries find some way of diminishing their Muslim populations. Again, it is difficult to imagine ways of doing that which will not meet strong objections from liberal opinion. Indeed, many political leaders—like Barack Obama—have been keen to denounce terrorism in general, leaving out the word "Islamic": many are so nervous of upsetting Muslim opinion that they are not even willing to call a spade a spade.