A. The Argument from Contingency. Plato, The Laws; Aristotle, Metaphysics (Book Lambda), al-Farabi, ibn Rushd, ibn Sina (Avicenna), Aquinas, Copleston, Mortimer Adler, Norman Geisler, Koons.
Contingent existents require a cause for their existence. This chain of causation must terminate in a first cause, that exists of necessity.
B. The Argument from the Principle of Suficient Reason. Leibniz, S. Clarke, R. Taylor. For every truth, there must be a sufficient reason or explanation that answers the question: why is this true? There must, therefore, be a fact that explains why something exists, rather than nothing. This fact must involve a being that exists as a matter of logical necessity, and which provides a sufficient explanation of all other facts.
C. The Kalam argument. al-Ghazzali, Maimonides, William Lane Craig. Whatever begins to exist must have a cause. The whole universe of finite things had a beginning: therefore, it must have had an infinite, eternal cause.
A. The Kalam argument. We have pretty good evidence, both from cosmology and from the second law of thermodynamics, that the physical universe (at least, the part we can observe) had a beginning in time. There are some alternative ideas -- Hawking's imaginary time/no singularity model, Linde's quantum foam -- but these are highly speculative, so far unconfirmed.
It is harder to prove that the whole Cosmos (the totality of finite things, observable or not) had a beginning in time. Kalam philosophers argue that an infinite sequence of events in time is an absurdity, but many doubt this. Aristotle, for example, believed that the cosmos is infinitely old but denied the existence of an infinite causal regress. All causal chains terminate in a finite number of steps in the first cause, but there has been an eternity of intertwined, finite chains of this kind. Aquinas thought that philosophy alone couldn't settle the age of the cosmos.
B. The Principle of Sufficient Reason. Some versions of contemporary physics seem to contradict the PSR: indeterministic models of quantum mechanics, for example.
More importantly, the PSR seems to have some very bizarre consequences. If God exists necessarily, and God had a sufficient reason for causing the universe He did, and every event in that universe had a sufficient cause, then it seems to follow that nothing could have happened differently than it did. It was impossible (in some sense) for even God to do otherwise than He has. Denies all contingency.
C. Contingency. In his famous debate with Copleston (reprinted in Russell's Why I am not a Christian), Russell raised four principal objections:
Russell's fourth objection was already answered by ibn Sina (and, perhaps independently, by Leibniz). To make the argument work, we don't need to assume that infinite regresses are impossible. Simply define the cosmos as the totality of all wholly contingent facts. Since the cosmos is a sum of wholly contingent facts, it is itself wholly contingent. All wholly contingent facts have a cause, so the cosmos must have a cause. Causes are separate from their effects, so the cause of the cosmos is separate from the cosmos. Since the cosmos, by definition, includes all wholly contingent facts, the cause of the cosmos must consist entirely of non-contingent (i.e., necessary facts). Hence, there must exist a necessary fact that is the cause of all contingent facts.
A. The notion of a necessary fact (or a necessary existence) is incoherent (Hume, Kant).
Hume: anything we can imagine existing, we can imagine not existing. Response: (1) the existence of a necessary first cause is the conclusion of the argument, not a presupposition. We don't believe that God exists necessarily because we can't imagine Him not existing: we can't imagine God at all. (2) Hume's principle is self-defeating. Hume holds that only logical or definitory truths can be necessary. Is this principle supposed to be necessary or contingent? It can't be contingent -- on what empirical evidence is it based. So it must be necessary. But, it isn't a logical truth, and it isn't true by definition.
B. The argument commits the fallacy of composition: from the fact that each part of the cosmos is caused, it fallaciously draws the conclusion that the whole cosmos is caused. Response: this is a misstatement of the argument. The argument assumes that all wholly contingent situations are caused. We can prove that the cosmos is wholly contingent, so it must have a cause.
C. The argument presupposes the ontological argument (Kant). That is, the argument assumes that God's existence is a matter of definition. Response: this objection assumes Hume's principle (A above). God's existence is proved to be necessary, not to be true by definition.
D. Couldn't the law of causality admit of exceptions? Perhaps it could, but the skeptic must at least admit that there is a defeasible law of causality: a law that creates a strong (but rebuttable) presumption in favor of the existence of a cause of any given contingent fact. The denial of such a presumption would lead directly to a very radical form of skepticism. All of our knowledge of the past (and, thus, ultimately, almost all of our knowledge of the present) depends on the presumption of causality. Moreover, our knowledge of the future, and of the probable consequences of our own actions, depends on the assumption that contingent events will not occur without a cause.
E. Contingent facts typically have contingent causes. The cosmos cannot have a contingent cause. Hence, the cosmos must be atypical in at least one of two respects: in not having a cause at all, or in having only a necessary cause. We have no reason to believe that it is atypical in the second way, and not in the first.
This is the most substantive objection. An adequate response requires an account of the nature of causal priority or asymmetry: what gives causation its direction? My proposal is that a situation A is prior to situation B just in case A is more necessary than B, i.e., every part of B necessitates some part of A, and no part of A necessitates any part of B. The cosmos contains parts that are of minimal contingency: hence the cause of these parts must beabsolutely necessary. Reaching a necessary cause from the cosmos is simply an extrapolation of our ordinary procedure of inferring a more necessary cause from each contingent situation.
F. Where did God come from?
Since God's existence is absolutely necessary, nothing can be more necessary. Hence, nothing can be causally prior to God's existence, and God's existence (unlike the existence of the Cosmos) cannot be caused.
Given the existence of a necessary first cause, how do we reach the conclusion that this first cause is God?
A. From the distinction of essence & existence (Aquinas, Gilson).
Whenever there is a distinction between essence and existence, we have contingency: the act of existence could have taken a different form (essence), or, equivalently, the essence might not have been actualized. Hence, the necessary first cause must be a being for which there is no such essence/existence distinction. God's essence is identical to His existence.
My web site. Contains my paper, "A New Look at the Cosmological Argument", and a defense of the paper, "Special Pleading, Defeasible Reasoning and the Cosmological Argument".
My lectures on both the history and the contemporary debate about the cosmological argument.