Reply #5: I don't follow your logic.

[Jim__]

1. there are an infinite number of worlds (I'm equating world with planet, but even if we accept world as universe, the argument is almost the same)- let's accept that as an assumption.
2. not every one of them is inhabited - let's accept that and say we know that there are planets in our solar system that are not inhabited, therefore this is an empirical fact.

However, how does the conclusion: Therefore, there must be a finite number of inhabited worlds follow from the premises.

How do we know that there are any uninhabited worlds outside of out solar system? If there aren't, then, there are an infinite number of inhabited worlds. Or, suppose that only 1 out of 1,000 worlds are inhabited? We still have an infinite number of inhabited worlds - note, in this case, we also have an infinite number of uninhabited worlds (just like there are an infinite number of odd integers and an infinite number of even integers).