Migrants flee Syria to escape violence, rather than because they wish to inflict bloodshed on Europe.
Still, preliminary evidence from the atrocities in Paris indicating that at least one of the suicide bombers may have recently entered Europe as a refugee has fanned fears that Europe's willingness to accept hundreds of thousands of asylum-seekers provides an excellent entry point for would-be terrorists.
Poland has already withdrawn from a European Union agreement to accept 4,000 refugees, and other countries may follow suit.
EU interior ministers have ordered their officials to intensify the vetting of arrivals.
The snag is that this cannot be done, partly because many migrants arrive without travel documents, but also because there is a thriving business in fake Syrian passports, prized by migrants since they offer a better chance of obtaining asylum status.
Besides, the sheer numbers involved would overwhelm any vetting: At least 800,000 asylum-seekers landed in Europe this year, and an average of 8,000 continue to land each day.
French opposition leaders are demanding a complete closure of the country's borders to migrants.
And although German Chancellor Angela Merkel has defended her decision to provide temporary admission to all refugees, Finance Minister Wolfgang Schaeuble has likened the resulting influx to an avalanche triggered by "a slightly careless skier".
Existing EU policies to control who is coming to Europe are in tatters, and its leaders probably don't have more than a few weeks to restore order.
For if they don't do so, the entire system of free movement inside the EU will collapse because of pressure from a worried European electorate.
France is already mulling over keeping its border controls - temporarily imposed after last Friday's attacks - indefinitely.