Does "not one of them" mean “more than one of them” or “none of them”?
Not one of them thought it necessary to avoid dogmatic statements about unicorns because he had never seen one of them.
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Strictly mathematically, if you only had "not one", it could mean zero, or could mean a hundred, or any other number besides 1.
However, this idiom ("not one of them") is a stronger version of "none of them". It means "none of them", but with more emotion. Like in an exasperation, a hope that at least one of them would do something, but then realizing that not even one of them was willing to do it.
This idiom is basically a shortened form of "not even one of them".
None of them thought it necessary to avoid ...
It is a potential confusion point as strictly speaking, 'not one' could logically refer to any other digit in the base 10 system and while I can't think of an instance off hand, I am sure the term has been used - either for effect, or as a punchline/payoff - in its literal sense.