Rebecca, I hope writing your paper went well. I agree with Magnanimity’s analysis. Be careful not to use “necessary” in the modal sense, however. Let me start by offering an illustration about how words like “possible” and “contingent” can be misconstrued. It is impossible for me to fly by flapping my arms like a bird. But, in what sense is this “impossible”? Surely, one can envisage a possible world in which I can fly by flapping my arms. What this shows, I think, is that something can be metaphysically impossible (impossible in the actual world), but not necessarily logically impossible.
The same can be said of terms like “necessity.” When Thomas says that contingent beings are ultimately caused by a necessary being, what he really means is that
dependent beings are caused by a necessary-in-the-actual-world being. I’m sure Thomas would also say that God is logically necessary, but his Five Ways don’t actually entail that. The first three of the Five Ways especially concern only God’s metaphysical necessity.
To understand, say, the First Way, just think of a universe with no First Mover as a watch without a spring. No matter how many gears there are (even infinitely-many), without a spring, none of the gears will move. By analogy, if the universe has no First Mover, then nothing would be in motion, which of course is contrary to our experience of things. I mention this example primarily because the example that Thomas himself gives (e.g. a stone being moved by a stick, which is moved by the hand) can sound incredibly esoteric to modern ears. Moreover, people often object that if the universe is eternal, no First Mover is needed, but this would be a mistake. An eternal watch would still have to have a spring. An eternal house would still have to have a foundation. The First Mover/First Cause is not necessarily something that precedes its effects
in time, but is something that
causally precedes its effects.
This may all be a moot point when it comes to your paper, I’m not sure. In any case, I hope you find these responses helpful.