Did they assume reincarnation? Reincarnation can be very challenging in Buddhism because the Buddha taught there is no permanent self and this has led to the question of what reincarnates. I think it's possible strip Buddhism of it's popular religious concepts and the core of what is left is natural though not the same as contemporary science sees the natural order. I think the issue is consciousness.
I actually did a presentation on this a few years ago. The talk was on Nagajuna's 'sunyata' (emptiness) and how everything is interdependant, nothing has inherent existence.
The 'anatman' (no self) is an issue within this philosophy and it tackles the question of what is transient from incarnation to incarnation.
The answer is 'consciousness' because Buddhists don't believe that there is a 'soul' to move on. What there is can be described as one long continual existence and each incarnation is a stage within that one existence. It is described as a river that changes constantly but is ultimately still the same river. If I throw a stone into the river, then that river has changed, but it is still the same river.
Needless to say, I only took one Buddhist philosophy unit!
Brian.