I've just realized we have an irrefutable proof of the fact that large-scale government conspiracies are possible and at least one actually happened. Note that I'm not saying they are *secret* they might or might not be and that's a different topic. I'm just claiming at least one happened.

So what's the proof? Given two statements A and negative of A we know that at least one of them is true. Here are two statements for you:

* The german government (openly) conspired against jews during WWII

* All governments today conspire to tell people that the german government conspired against jews

Regardless of which one is true, it is certain that at least one of them is. Therefore there is at least one conspiracy.

Yes, they could be both false in vacuum (no killing and no claims about it happening) but we do observe governments today telling their citizens that nazi germany killed the jews, so this option is ruled out.