The discontinuous distinction fallacy

Whenever someone wants to make a distinction, there is often some fool arguing that distinctions are impossible. Maybe this is one of Zeno's paradoxes, but it is probably too stupid.

So people argue that you cannot distinguish day and night, innocent and guilty, white and black.

Here is the latest example, from a NY Times op-ed:

Donald J. Trump’s scandalous proposal that the United States bar entry to all Muslims — though he later clarified his view that American citizens and a few others might be allowed in — raises two fundamental but largely unaddressed questions: Who and what is a “Muslim”?

Mr. Trump presupposes that the government could create an immigration policy that discriminates against Muslims. But implementing such a policy would be completely impossible under the current circumstances.

How would consular or immigration officials determine who is, and is not, a Muslim? This is the most obvious question, but almost no one is asking it. Instead, the debate churns on as if this problem does not exist. ...

While my father was a devout Sunni Muslim, my mother remains a devout Anglican Christian. ...

Seen in this light, the range of Muslim beliefs and behaviors is more or less indistinguishable from that of the rest of humanity. The word “Muslim,” without any further qualification, and the word “person,” are, for practical purposes, synonymous. One doesn’t actually tell you anything meaningful beyond what is already suggested by the other.

The USA does have to decide whom to let in, and often religion is a factor. If his devout Muslim father makes him a security risk, then that is a good reason to deny him a visa.

Mathematically, it is obviously possible to have a discontinuous function of a continuous parameter.

If it turns out to be truly impossible to figure out whether someone from Lebanon is likely to plant pipe bombs, then maybe we should not let anyone in from Lebanon.