Why a "Vertical" Causal Series Requires a First Cause

Consider a series of events, with each one causing the next. The Big Bang, the expansion of the universe, the motion of matter, the solar system, and so on. Each event leads to the next. This is a "horizontal" causal series, and short of attempts to prove that an infinity is impossible, there is nothing about this series that logically demands a first event. Perhaps the string of events stretch back into the past for an infinite amount of time. The key point here is that this series involves in fieri causes.

Now consider a series of dependency causes. In other words, a series of in esse causes. An existent thing, such as a lake, is here and now dependent upon warm air, which is in turn here and now dependent upon the heat from the Sun, which is dependent upon the nuclear reactions in the Sun, which are dependent upon gravity pulling the Sun in on itself, which is dependent upon mass, and so on. Unlike a chain of events, a series of dependency causes is "vertical", going "down" to the most fundamental thing. And unlike a horizontal chain of causes, a vertical chain requires a first cause. "First" in this sense simple means something that is not dependent upon anything further. The "bottom level" in the present, not the first event in the past.

To see why this is so, think about living after the Zombie Apocalypse. Banded together with other survivors, one day you are monitoring for radio transmissions when you hear something. "Hello?....*static* *garbled*... Hello? If you can hear me, we have surviv...h....*garbled*...."

Excited, you think, "Where is that coming from?!" You tell your friends that you are receiving a radio transmission from another group of survivors and that you should go try to find the source of this transmission. Maybe you can pool your resources and begin to rebuild society! After a long journey, you discover the source of the transmission: it is a radio tower acting as a repeater. It receives a radio wave, amplifies it, and then re-transmits it.

Damn. A bust. But wait! The repeater is also a receiver, so you really have not discovered the source of the radio waves. You need to keep going. That transmission must be coming from somewhere! Eventually, let's say, you find the survivors and everyone lives happily ever after. The point is, you were receiving a radio transmission, and this entailed that someone was transmitting. No matter how many repeater towers were between you and the survivors, someone or some thing  (maybe just a recording) was transmitting. To make it into a formal argument:

1. If there is no transmitter of X, then there is no X to be received
2. But something is receiving X
3. Therefore, there is a transmitter of X

So the chain of dependency causes involve each member "receiving" existence from the next member of the chain. The lake receives its current, sustaining, in esse existence from the warm air, which receives its existence from the Sun's nuclear reactions, which receives its existence from gravity, and so on. And this can only bottom out in a transmitter of existence: something that can actualize without needing to be actualized by anything further.

For further reading, see this paper.