"[The two generals problem] said that you can't achieve consensus (both safety and liveness at the same time), they did not say you have to sacrifice safety under message-losses or asynchrony conditions. So Paxos preserves safety under all conditions and achieves liveness when conditions improve outside the impossibility realm (less message losses, some timing assumptions start to hold)." http://muratbuffalo.blogspot.com/2010/10/paxos-taught.html