The Vertical Cosmological Argument has various forms and is rather conceptual, but can be described as:
1. Everything in the universe is contingent (they could “not exist”).
2. All contingent things need an ongoing cause to sustain them.
3. Therefore the universe needs an ongoing cause to sustain it.
(a more detailed description can be found here)
Common attacks from critics on this argument are 1) this untrue since it depends on the principle of sufficient reason, and 2) it’s the fallacy of composition. We won’t deal with the first here other than to say the vertical cosmological argument does not hinge on sufficient reason, but on the principle of causality, which is very different.
But the second is a bit more tricky. The fallacy of composition can be described with the following illustrations: if every tile in a floor is square, it does not follow that the whole floor is square. If all the parts to a machine are light, it does not follow that the whole machine is light. Therefore, the critics say that just because every part of the universe is contingent then it does not follow that the whole universe is contingent.
However, the fallacy of composition does not always apply. For example, the fallacy of composition would say that just because every floor tile is square, the floor does not have to be square. However, it is true that if every tile has a geometric shape, the whole floor will have a geometric shape. If every tile is brown, the whole floor is brown. If every part of the machine has weight, the whole machine will have weight. If every part of the machine has no weight (such as in a software machine), then the whole machine can have no weight. These things are not opinion; they are necessarily so, they must be true. The fallacy of composition is not a formal logical fallacy, but an informal one, and therefore only applies when it applies, which is not always, as we have just shown. Critics do not always recognize this.
Our question of course, is whether the universe and it’s parts are like the square-ness of the tiles, or like the brown-ness of the tiles. Could it be that the contingency of the universe could add up to a whole which is not contingent?
No, it cannot. The reason is that being (existing) has the nature that adding up contingent beings (things) can only give us a big pile of contingents. Adding together contingents cannot give us a necessary being. (A necessary being is one that cannot “not exist.”) While adding together lightweight parts can give us a heavy, and adding together small squares can give us a rectangle, it is not true that adding together dependent, contingent things can get anything else than a pile of contingents which need a necessary Being for their existence. Adding together all the contingents in the universe does not give us something more or something necessary; on the contrary, it merely requires a bigger cause.
Therefore the vertical cosmological argument is not disproved by the fallacy of composition, but is a sound proof that the universe is caused. We have a sure, rational, valid proof that the universe needs a cause, one that is a necessary being. This we call God.