I wasn't exactly sure where to post this question, so I decided that it's sufficiently philosophical in nature to warrant its being posted here. I may end up posting it on Mathematics SE as well.
I've been trying to model time and the space of all possible moments as something a computer scientist would consider a tree. That is, the tree has a root node, which signifies the instantiation of time, and the root node has children, all of which are possible proceeding instances. Further, each of those instances has infinitely many potential proceeding instances. This obviously yields a tree whose nodes all have infinitely many children.
Now I'm a bit worried. Here are some of the implications of such a model:
• Each node has a history.
• Sibling nodes have the same history.
• Thus, one particular history can lead to infinitely many proceeding instances.
How could it possibly be the case that the same history could lead to different states of the world? One possible conclusion is that the assumption that "there are infinitely many possible states of the world one instant from now" is naive and ultimately incorrect, in which case "there are finitely many possible states of the world one instant from now" would be correct. In THAT case, there is either one instant (which would imply that all of time is on a very particular, unchanging and predetermined course) or some finite number of instances greater than 1.
My question is the one posed in the title–is there something wrong with the assumption of infinitely many possible states of the world? If anything is unclear, make note of it and I will try to clarify.