This argument was proposed by Thomas Aquinas. It states: All things are caused and this chain of causation cannot go back forever. Thus there must have been a first cause, an eternal prime mover which itself was uncaused. What is being proposed here is not simply a first cause that started the history of the universe, but rather a transcendant first cause. For, being that the universe cannot have caused itself, the first cause must have been external.
This argument, even if it succeeds, does not establish the existence of God. The prime mover need not have been omnipotent, he may no longer exist and he might not even have been sentient - just some kind of inanimate force. The first thing to note is this reasoning says that since everything must have a cause, there existed something that didn't have a cause, contradicting itself directly. The argument attempts to escape this problem by asserting that the first cause was transcendent. But if this transcendent cause is itself exempt from the requirement of having being caused then it escapes the reasoning that required it in the first place. In other words it is somehow exempt from logic which is another way of saying it is nonsense. More about this later.
In a similar vein, one common objection is to point out that since this argument concedes the possibility of an uncaused entity, why not simply say that the universe has always existed without a primary cause. What is gained by postulating another entity?
Another fundamental difficulty is that the argument poses a problem but no real answer. The suggestion of a transcendant first cause is a non explanation. It may sound as if it answers the question but it does not. For we are left with the questions, what is this prime mover and how did he cause the universe? If one accepts the conclusion that an incomprehensible being created the universe in an unknowable way, not only has one not made any progress in understanding but one can go no further. The proposed answer simply exchanges one mystery for another in a way that stalls the whole investigation.
In Aquinas mind, the logical necessity of this argument stood on the belief that the alternative, an infinite regress of causes is simply illogical. In Aquinas time, mathematics was very rudimentary compared to our knowledge today and there was no understanding of infinite sets. In fact a clear understanding of this topic had to wait until the 19th century. The problem as Aquinas saw it was that an infinite chain of events would require an infinite time span and we could never have gotten to the present. "You can't get there from here". This claim actually commits the fallacy of begging the question. Implicit in this argument is the assumption that there is some point "there" in the past from which we must measure time. In other words it assumes some starting point which is precisely what it is attempting to prove! If one discards this idea of a starting point, then there is no logical objection to saying that the universe has always existed and that, yes time stretches back infinitely
But in fact there are alternatives to an infinite time span: An infinite chain of events need not require the passage of an infinite span of time. If the events are uniformly spaced then indeed this would require an infinite time span but if the chain of events occurred in such a manner that looking backwards, the intervals got smaller and smaller, the total time could be finite. For example the Geometric Sequence 1 +1/2 + 1/4 +1/8.... when summed out to an infinite number of terms adds up to 2!
Another possibility is that our universe arose out of some acausal universe. Without cause and effect, the concept of time makes no sense. Perhaps the Big Bang arose as a totally random event in some vastly bigger universe where things happen for no reason. If you find this suggestion preposterous, I would ask, is it any more bizzare than postulating an eternal divine prime mover who caused himself? This is not to say that any of these scenarios are what really happened. The force of Aquinas argument rests on logical necessity. That there is no logical alternative to his position. It is enough to show an alternative to undermine the proof.
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