The Thomistic cosmological argument, the classical cosmological argument, argument from contingency, argument from first cause, argument from universal causation, or more simply the cosmological argument is a general pattern of argumentation that urges an inference from certain alleged facts about the universe to the existence of an "uncaused cause," typically associated with God.  Classical formulations of the argument are incapable of identifying any particular god, though this typically doesn't faze fundies who, when they deceitfully put on their evidentialist hats, opine that their god and no other meets the description of that in the proof. Thomas Aquinas' argument from contingency is a slight modification of Plato and Aristotle's "Prime Mover" arguments.
 The Platonic/Aristotelian cosmological argument
- Every finite and contingent being has a cause.
- A causal loop cannot exist.
- A causal chain cannot be of infinite length.
- Therefore, a First Cause (or something that is not an effect) must exist.
 The Thomistic argument from contingency
Thomas Aquinas Cosmological argument.
- A contingent being exists.
- This contingent being has a cause of its existence.
- The cause of its existence is something other than itself.
- What causes this contingent being to exist must be a set that contains either only contingent beings or a set that contains at least one noncontingent (necessary) being.
- A set that contains only contingent beings cannot cause this contingent being to exist.
- Therefore, what causes this contingent being must be a set that contains at least one necessary being.
- Therefore, a necessary being exists.
 Problems with the various cosmological arguments
There are some major flaws and logical fallacies in this argument:
- It does prove enough, but instead replaces the proposed problem with a larger problem. If the universe was made by a god because nothing can exist without cause, then something must have "caused"/made that god, otherwise the argument requires special pleading to make its point. If something else were to make that god, he would not be the god of creation anymore. It has been argued, however, that God can exist without cause, because he, unlike everything else, is pure act.
- It is non-specific: Even if the universe was devised by some creative force, there is no evidence that this creative force was a religious god. There are an infinite number of causes other than a human-inspired god that could have caused the creation of the universe. The creator of the universe need not even be supernatural, or sentient or intelligent to satisfy this argument of "first cause".
- In addition to these, the argument makes the assumption that a causal chain of events cannot be infinite, that it must terminate at a point. While the nature of cause and effect is observed by experiment (within the limits of the uncertainty principle at least), whether this chain can be infinite or not is certainly not mandated by experiment and is only inductively prefered. One could even consider it an act of begging the question to assume that a causal chain is finite in order to prove a first cause.