I've revised the earlier draft of the inductive cosmological argument. I also wish to argue that the first cause is a personal agent.
1. The universe is either caused or uncaused.
2. Complex things are unlikely to be uncaused.
3. The universe is very complex.
4. Therefore, the universe is probably caused.
(1) is true by definition. (2) can be supported by an analysis of things we know that are complex. Always, or for the most part, whenever we observe a complex entity, we discover that it is caused by the formation and unification of its diverse parts.
(3) simply points out that the universe contains many complex elements, and I don't think anyone will disagree with that. As a result, I think (4) is more likely true than its negation, which would make this a cogent inductive argument.
Now, the cause of the universe would have to be simple; and, bodies are necessarily complex, given their divisibility. Because of this, the first cause must exist beyond the universe, and is therefore immaterial, timeless, and changeless. Finally, the cause of the universe is either personal or scientific. Yet, it cannot be scientific, since scientific laws are part of the explicandum (much like in the modal cosmological argument). Hence, the first cause must be a personal agent.
This is consistent with both an eternal universe, as well as a finite universe. However, I think there are good reasons to believe that the universe is not infinitely old, which I've already touched upon in an earlier post.