An Intro to the Philosophy of Religion, Ch. 5 Part 2 (Cosmological arguments)

Cosmological Arguments
Dependence version 1:

5.27 Every being* is either dependent or self-explaining.
5.28 Not every being can be dependent.
5.29 Therefore, at least one self-explaining being exists (a being which in turn explains the existence of the dependent beings).

*Both objects and events count as "beings" here. A dependent being is one that refers to another being for its existence.

Infinite Regress and the Principle of Sufficient Reason
The infinite regress objection (IRO) aims at premise 5.28.  While a finite chain of dependent beings could require a self-explaining being, an infinite chain of dependent beings wouldn't require such a being.  One reply to IRO leverages Big Bang cosmology to show that current theories support a finite universe.  Another reply to IRO invokes the Principle of Sufficient Reason:

PSR There must be a sufficient cause, reason, or explanation for the existence of every thing and for every positive fact

Thus, even given an infinite chain of dependent beings: some remaining facts lack explanation.  For starters, the fact that there is something rather than nothing.  Also, the fact that there exists a certain infinite collection of things.  Defenders of IRO have replied that these facts are indeed explained by an infinite regress.  An example is given in which someone has fifteen dollars--ten dollars in one pocket that he got from the ATM and five dollars in the other pocket that he received from someone in repayment of a loan.  Now, what if we asked this fellow to explain why he has fifteen dollars, why does he have some money rather than none at all?  The idea is that once this person explains where his five and ten dollars came from (individually), there isn't any further explanation required (for the fifteen dollars).  I recall Plantinga providing a slightly different example in God, Freedom and Evil.  A mother has three sons that are sent off to war and they all die during the call of duty.  There are individual explanations for why each son died, but there may not be an joint explanation for why all three of them died.

Do these examples show that the infinite regress objection satisfies PSR?  Not if one accepts the external explanations principle: "A set of dependent beings is explained 'with no explanatory remainder' when each member of the set has an explanation and at least one member of the set is explained by appeal to something outside the set of dependent beings to be explained."  In the case of the fifteen dollars, there was an appeal to something outside the set (the ATM and the loan re-payer).  In the infinite regress objection, this isn't true, and thus the objection fails to satisfy the PSR.

A serious objection to PSR, raised by Leibniz himself, is that the grand totality of all other facts (the SUPERFACT) requires an explanation.  But what exactly would count as an explanation for something like a SUPERFACT?  Whatever the explanation, it couldn't be a necessary truth; else, the SUPERFACT would obtain in all possible worlds and thus only the actual world would be possible.  What if the SUPERFACT's explanation is not necessary?  Rea and Murray only leave us with the vague notion that "only very special propositions are true in just one world...truths that are true in only one world are hard to think of."  They conclude that we should reject PSR.

Dependence version 2:
We might try to replace PSR with a weaker principle, such as there can be no independent contingent thing.  Thus the new argument can be construed as follows:

5.30 Every being is either dependent or necessary.
5.28 Not every being can be dependent.
5.29 Therefore: at least one necessary being exists (a being which dependent beings at least partially depend for their existence).

This version is still susceptible to the IRO.  Finally, Rea and Murray consider it "no easy task" to argue that the universe as a whole is itself a contingent thing.

The kalam version
William Lane Craig's recent work on this version of the argument has attracted attention from philosophers, cosmologists, and physicists.

5.31 Whatever begins to exist has a cause of its coming into existence
5.32 The universe began to exist
5.33 Therefore: the universe has a cause for its coming to exist.

 The first premise seems obvious, but in fact has fostered lively debate.  The second premise is justified both on a priori and a posteriori grounds.  As to the latter, the best cosmological theories (the Big Bang) all posit a universe that began to exist.  As to the former, some philosophers have argued that an actually infinite series of past moments is impossible.

This argument describes the cause-to-universe relationship in an interesting way, because it posits that the cause exists simultaneously with the effect and not prior to the effect as we would normally expect.  This is important because some object to this argument on the grounds that a timeless cause is incoherent.[1]   The best illustration of this (not in the book but from Craig himself in a lecture I heard one) is that of a bowling ball and a pincushion.  The bowling ball causes the pincushion to be indented in a certain fashion.  Now, imagine that the bowling ball and the pin cushion have forever been in this position.  It would not be the case that one event was causing a succeeding event.  Likewise, "Craig argues that God's causing the universe to come to be could be simultaneous with its coming to be."  He also concludes that this timeless cause needs to have some kind of personal agency, namely the ability to bring about effects "at will."  So, Craig thinks this argument gets us to a timeless quasi-personal being that caused the universe to come into existence.  There are numerous objections to this argument that delve deeply into theories of time, causal explanation, infinity, and more.

[1] Quentin Smith has devoted much attention to this topic.  Check out his article on Infidels, "The Uncaused Beginning of the Universe" (1988).