To return to the original question, Holocaust scholar Yehuda Bauer lists six things that he feels make the event unprecedented (he doesn't say unique because he feels that it would be possible for such a thing to happen again, but it is different from anything that came before) in human history.
First, genocides usually take place on frontiers, away from the central lands of the perpetrators, while 'the Holocaust took place in the center of what was probably the most advanced civilization of the twentieth century.'
The second and third reasons are very similar, and have to do with the universal nature of the Holocaust. Second, the Nazis targeted all those they identified as Jews among them, not just part of the group. Third, Jews were to be exterminated wherever the Germans were in control, which was eventually supposed to be the entire world. All Jews must die, everywhere in the world. 'Never before had there been a universally-conceived genocide.'
Fourth, the annihilation of the Jews was purely ideological, with no rational social or political basis. It flew in the face of reason, providing no pragmatic benefit to Germany and costing it a lot of manpower and resources.
Fifth, it was built on the Nazi brand of racism, a revolutionary concept 'to establish a new world order based on a hierarchy of races,' while previous genocides had more traditional roots and causes.
Sixth, and this one seems a bit of a stretch to me, he claims that 'the Nazis wanted to destroy the civilization from which they came, [including] liberalism, conservatism, socialism, democracy, and pacifism,' and with Athens and Rome both fallen, the Jews were 'the last remnant of the roots of European civilization.'
For what it's worth. (from the paper "On the Holocaust and Other Genocides," available from the Center for Advanced Holocaust Studies)
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