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The Cosmological Argument for the Existence of God

I
From St. Thomas Aquinas: Summa Theologia

The existence of God can be proved in five ways.

The first and most obvious way is an argument from motion. It is a self-evident truth of experience that in the world some things are in motion. Whatever is in motion must have been moved by another object, for nothing can start to move unless it has the potential to be moved towards some point, and once it starts moving this motion is actualized. Thus, motion represents the transformation from what is possible to what is actual. But nothing can progress from possibility to actuality unless it is itself acted upon by another object in a state of actuality. For example, wood has the potential to burn, but it does not actually burn unless one first sets fire to it with something that is already actually hot. It is possible for the same thing to possess both actuality and potentiality, but only when these are in different respects. For example, when something is actually hot, it cannot at the same time be potentially hot, but it can simultaneously be potentially cold. For this reason, it is impossible that an object should be at one and the same time, and in the same respect, both the mover and the moved. Objects cannot move themselves. Therefore, whatever is moved must be moved by some other thing. But this other thing must itself also be moved by yet another object, and that by another object, and so on. This leads to an impossible infinite regress of motions, and there will be no first mover, and hence no motion at all, seeing as the other motions are only possible if set in motion by the first mover — just as a staff only moves because it is first moved by the hand. Thus, one must infer the necessary existence of a first mover, who is moved by no other. It is this first mover that all agree is God.

       Second way: from “efficient causes”
       Third way: from “possibility and necessity”
       Fourth way: from “the gradation to be found in things”
       Fifth way: from “the governance of the world”,

II
Substitute “cause” for “motion”

1 Every event has a cause
2 There cannot be an infinite sequence of causes and effects
3 Therefore, there must be a first cause
4 God is this first cause
5 God exists

III
Refutations of the cosmological argument.

In each case the specific fallacy is that the conclusion contradicts one of the premises: for example, that everything has a cause contradicts the proposition that there is a God who is not a caused by anything. Of course, defenders of the argument would state that God is his own cause, but this contradicts a premise (for example, “objects cannot move themselves”).
Hume objects by stating that an infinite regress of cause and effects, or of times, is not incoherent.
Hume's objection goes to the heart of the argument. Aquinas has to labour to get us to accept that an infinite regress of causes and effects is not possible. Although the idea of time (and the succession of causes and effects) extending backwards indefinitely is a little too large for our minds to grasp, it does not follow that an infinite regress of causes and effects is impossible, simply that we have difficulty picturing it.
Bertrand Russell agrees with Hume. He argues that the universe does not necessarily have a beginning. He states, “I should say that the universe is just there, and that's all.”
Kant objects by explaining how this argument abuses the use of reason. Starting with observations about phenomena (for example, that specific effects have causes) we cannot use pure reason to draw a conclusion about an object (God) that exists independently of phenomena. Reason can only be used legitimately to form conclusions about phenomena (that is, about what we experience).
An object that moves another object in a physical sense is a physical object. A cause is an arrangement of objects at a given moment in time. Do we wish to make God into a physical object or into a “first event”?
In fact, Aquinas is thinking of causation in terms of agency. In order to move a boulder I must push it — I act upon the boulder. This raises the problem of how the will produces any kind of effect — which is the problem of freewill and determinism. However, in a physical sense, the movement of the boulder is caused by the metabolism of my body, and the notion of agency is not required to explain in a physical sense why the boulder moves. (That is why there is a problem of freewill and determinism.) The God who must be the first cause need not be endowed with any kind of intelligence or will. For example, nothing would be lost from the logic of the argument if we concluded:
3 Therefore, there must be a first cause
4 The Big Bang is this first cause
5 The Big Bang must have happened
Now we have substituted a physical event for the supreme Being, and exposed the futility of the argument and its confusion between cause as agency (a relationship between the will and the act it produces) and cause as a principle of scientific explanation of experience (the relationship between one event (a cause) and another (the effect) which follows it in time).
Hume captures this point in his Dialogues Concerning Natural Religion when he writes: “But further, why may not he material universe be the necessarily existant Being...?”
Even if we could establish by means of this argument the existence of a first cause, it would not follow that that first cause would have to be intelligent, benevolent or endowed with will, and thus it would not be possible to use the argument as a basis for any religion.

IV

F.C. Copleston is Jesuit Priest and philosophy, who inclines to defend Aquinas's argument(s) from the objections raised to it above. However, his work is expository rather than substantial — I mean, he seeks to explain what Aquinas meant, rather than to actively defend the thesis that Aquinas put forward, so if you want to understand Aquinas his work is likely to be important, but otherwise, it does not really give you any new insight into the philosophical issues. Here is a sample of what he says about Aquinas's presentation of the cosmological argument.
Aquinas is not rejecting the possibility of an infinite series as such. We have already seen that he did not think that anyone had ever succeeded in showing the impossibility of an infinite series of events stretching back into the past. Therefore he does not mean to rule out the possibility of an infinite series of causes and effects, in which a given member depended on the preceding member, say X on Y, but does not, once it exists, depend here and now on the present causal activity of the preceding member. We have to imagine, not a lineal or horizontal series, so to speak, but a vertical hierarchy, in which a lower member depends here and now on the present causal activity of the member above it. It is the latter type of series, if prolonged to infinity, which Aquinas rejects.