Yes, and it is not a set becuse a set is an exiting thing (abstract or not).
According to ZF "all members of {} are sets" (Or by jsfisher's words: "Every member of {} is a set, without exception" ( http://www.internationalskeptics.com/forums/showpost.php?p=6713481&postcount=13621 )) .
In other words, ZF does not follow its own determination.
All members of {} are <insert anything here>. That's all there is to it. It's vacuous truth: http://en.wikipedia.org/wiki/Vacuous_truth
ETA: That's not ZF by the way, it's actually even more basic than ZF. It's logic.
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. Hence, he cannot understand logic, and he certainly cannot get <insert anything here> about mathematics.