I recently came across the “true Scotsman fallacy” which strikes me as being highly relevant to thinking about populations from the standpoint of immanence and some of the discussions surrounding religion (where variants of this fallacy are common among believers and apologists).

From Wikipedia:

No true Scotsman is a term coined by Antony Flew in his 1975 book Thinking About Thinking – or do I sincerely want to be right?:

Imagine Hamish McDonald, a Scotsman, sitting down with his Press and Journal and seeing an article about how the “Brighton Sex Maniac Strikes Again.” Hamish is shocked and declares that “No Scotsman would do such a thing.” The next day he sits down to read his Press and Journal again and this time finds an article about an Aberdeen man whose brutal actions make the Brighton sex maniac seem almost gentlemanly. This fact shows that Hamish was wrong in his opinion but is he going to admit this? Not likely. This time he says, “No true Scotsman would do such a thing.”

Flew’s original example may be softened into the following [1]:

Argument: “No Scotsman puts sugar on his porridge.”
Reply: “But my uncle Angus likes sugar with his porridge.”
Rebuttal: “Ah yes, but no true Scotsman puts sugar on his porridge.”

This form of argument is a fallacy if the predicate (“putting sugar on porridge” or “doing such a thing [as committing a sex crime]”) is not actually contradictory for the accepted definition of the subject (“Scotsman”), or if the definition of the subject is silently adjusted after the fact to make the rebuttal work.

The interest of the fallacy, of course, is that it renders the person making the claims immune from any criticism by distinguishing between the genuine essence of a thing and all of its false actualities.