I came across this description of Aquinas' third way:
Third, he argues that if there were no eternal, necessary, and immortal being, if everything had a possibility of not being, of ceasing to be, then eventually this possibility of ceasing to be would be realized for everything. In other words, if everything could die, then, given infinite time, everything would eventually die. But in that case nothing could start up again. We would have universal death, for a being that has ceased to exist cannot cause itself or anything else to begin to exist again. And if there is no God, then there must have been infinite time, the universe must have been here always, with no beginning, no first cause. But this universal death has not happened; things do exist! Therefore there must be a necessary being that cannot not be, cannot possibly cease to be. That is a description of God.
Two cases are considered here. If "all things are contingent" then all things would eventually cease to exist; but they have not, therefore this case is false. If "all things are contingent except one" then because things still exist that thing must be the first cause (god).
At least two more cases suggest themselves: "more than one (or many) things are not contingent" and "nothing is contingent."
Why are these other cases disregarded, and what conclusions could be reached by considering them?