In the same sense that "we don't know if we are brains boiling in a vat created by a mad scientist", yes. But of course, while Hitler often made sure to not have any written orders for undertakings that may turn out to be failures, the likelihood that what happened occurred without his command, approval and knowledge range from infinitesimal to impossible.

Disagree. My understanding is that Hitler was cautious of written orders after Catholics complained about the euthanasia orders, but I could be wrong. However, it's still speculation. That's the point. I think it's highly unlikely that he had no knowledge of what was occurring, but there's no proof of any orders, which is what my statement of fact concerned. As I said before, history is a process of revision. It was unchallenged "fact" that the road to Auschwitz was straight, until the 70s.

Who are those 'some people', other than such notorious frauds as David Irving? Because I don't know any serious historian who would say anything like that. Particularly because it's not as if there was a void between Mein Kampf and 1942. Even in January 1939, Hitler said that a world war would result in "the annihilation of the Jewish race in Europe". This was then later cited by Goering that "the war has come, the annihilation of the Jewish race must be the logical consequence".

Yet even after Mein Kampf, and after January 1939, the Nazis - Hitler - did not have an ideological commitment to killing Jews. They just wanted them out of Europe, to languish and die either in a place like Madagascar or a reservation in the USSR. Mass killing was a result of radicalization spurred by the war and by an overpopulation problem, where local Nazis who had Jews dumped on them resorted to the expedient of murdering them to avoid feeding them and outbreak of disease among the tightly cramped ghettos, a practice which then spread with the objective of making Europe free of Jews rather than solving local problems (this is the structuralist explanation for the Holocaust, which I do find more persuasive).

Okay, admittedly, I did a horrible job of summarizing the functionalist vs intentionalist debate, but you got there anyway. It really seems likely to me that the Nazis stumbled and blundered their way into the holocaust. Hitler may have approved (and based on surrounding context, almost positively did), but that's just conjecture.