The next topic from the Carroll-Craig debate which I wish to discuss is what Science has to say about whether or not there was a beginning. Was there a first moment of time, before which the universe did not exist? What does Modern Cosmology have to say about this question?
I think that Modern Cosmology gives a fairly clear answer: probably, but not almost certainly. But, rather than try to argue only for one particular conclusion, I will instead try to provide the evidence in both directions, on which my opinions are based.
The reason why I say probably is that, given our current best theories of the universe, there are some decent reasons to think that the universe had some type of beginning at the so-called "Big Bang". However, once you get to an early enough moment of time, we don't really understand anything anymore, so really anything might have happened. That is why the term "Big Bang Model" refers to the (very well-confirmed) theory of the expansion of the universe after the Big Bang, rather than to the Big Bang singularity itself.
Given our current best understanding of particle physics, we think we can describe fairly well the history of the universe starting at around 
seconds after the Big Bang. We're certainly on-base in the period from about 10 seconds to 20 minutes, since this is when Big Bang nucleosythesis occurred (creating the first atomic nuclei), and we can check that the current abundances of H, He, and Li atoms are in agreement with what our theory of nucleosynthesis predicts.
Inflation (which would have happened at a much earlier time) is somewhat less certain, but it makes pretty good predictions so almost everyone believes in it these days. The recent BICEP2 results indicate that the energy scale of inflation was just a couple orders of magnitude below the Planck scale seem to have been contaminated by too much dust to be reliable, although most models of inflation still place it at a ridiculously high energy scale. This is a much higher energy scale than anything else we can measure in physics, although it is comparable to the GUT scale (where most particle physicists, but not I, believe that the forces probably unify into one force). During the inflation era, the universe grew in an extremely rapid way, stretching out and diluting any information about what the universe was like before inflation.
The Planck era was approximately the first 
"seconds after" the "Big Bang". This is the era where strong quantum gravity effects become important. In other words, the quantum uncertainty in concepts of "space" and "time" become so large that our classical concepts break down. That's why I put scare-quotes around things in this paragraph—we no longer know what on earth (or in the heavens) we are talking about. This is the point when everything is pretty much up for grabs.
So, even if we can say there appears to have been a beginning based on an extrapolation of the Big Bang Model to early times, there are also reasons why we can't be completely sure, so long as we don't completely understand quantum spacetime (or the initial conditions for inflation). Certainly the universe as we know it began, but we cannot completely eliminate the possibility of a pre-Big-Bang stage.
Nevertheless, in the next few posts I will discuss the limited evidence which we do have, especially those points which were mentioned in the debate. In particular I will cover singularity theorems, the BGV theorem, the 2nd Law of Thermodynamics, the quantum eternity theorem. Oh, and the Hartle-Hawking no-boundary proposal. That too.
[Updated description of BICEP2 results]
That's a meaty course outline in the next few posts and I eagerly look forward to attend the lectures.
Few will disagree with your statement.
"I think that Modern Cosmology gives a fairly clear answer: probably, but not almost certainly."
I wonder why some in the theistic camp hang on to the Big Bang as the ultimate physical evidence of a Creator God. Why must the Biblical beginning be joined at the Big Bang hip? Scientific theories are always provisional. Notwithstanding these caveats, it is far batter to know we have evidence of the Big Bang (accepted my most physicists as the standard cosmology model). It is consistent with the literal temporal beginning mentioned in the Bible, argued by St Augustine 1,500 years before Einstein. If Big Bang were to be discredited, the Judeo-Christian-Islamic notion of a beginning of time remains intact and some other hypothesis will support it.
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Those in the theistic camp are joined at the hip with goddunnit. It doesn't matter if the universe is open, closed, flat...goddunnit. Maybe god recently created everything just the way it is, photons speeding toward us out of space, radioisotopes embedded in minerals in particular proportions, fossils layered in sedimentary rock kilometers thick...goddunnit.
The big bang is just the latest place for the god of the gaps to live.
I disagree with this characterization of the universe as having a beginning: "I think that Modern Cosmology gives a fairly clear answer: probably, but not almost certainly."
Firstly, do you really consider that to be a fairly clear answer? I looks to me to be an answer that manages to combine "yes", "maybe", and "no" all in the same sentence.
There is no such thing as modern cosmology of the big bang. We have no theories of anything that are valid at t=0. We have no clue whether anything exists outside the big bang remnant we live in. We don't know what led to or gave rise to or caused the big bang. If it somehow had no cause we don't understand that either. We don't even know what some 96% of our cosmic home is, what its properties are, or what equations would fully describe it
There is a very active cosmology of the post big bang eras. We do have great evidence that we live inside an explosion or expansion of some kind.
What troubles me most is the passing off of the hypothesis de jour as scientific theory. Otherwise brilliant and admirable people who do so much laudable work seem to get caught up dispensing catchy sounding equivocations, and making pronouncements about what is possible, when in fact nobody knows the possibilities or probabilities or what really happened or what might really be happening differently in a universe far far away.
This works out well for theists who use mangled but sophisticated sounding first cause arguments to wow the credulous. They can quote mine this or that physicist who made some supposed theorem about things we know nothing about to supposedly demonstrate there can be no natural infinities and therefore there must have been a supernatural infinity to cause our natural finite existence.
All these vacuous but scientific sounding arguments are intended to make belief in a magic man in the sky who will bring you up to paradise for worshiping him, or lovingly torture you for eternity if you don't, all sound very reasonable and the best rational conclusion. The fact that such theists present nothing more than arm waving and fallacious logic is lost on the believers, who will buy the books, pay the admission to fund the speaking fees, send in the donations, and praise the pseudo scientists as doing the lord's own work.
I love philosophy, metaphysics, speculation, imagination, and hypothesis, providing we use our powers of self awareness to always realize when we are engaging in such. At t=0, that's all we got.
Dear Neil,
So you don't believe that the universe was created by a magical man who lives in the sky? Good! Neither do I.
I also agree with you that all our physics knowledge about
is speculative. In fact I explicitly said this in my 6th paragraph. You say that my post combines ``maybe'', ``yes'', and ``no'' all in the same sentence, but this is not too surprising since the concept ``maybe'' just means possibly yes and possibly no! Just because what happened at 
is speculative, doesn't mean we can't assess our limited current understanding to see which way the evidence points. In fact there is some evidence pointing in both directions, as I discuss in this series.
Finally, we also agree, apparently, that the existence of God is compatible with any sort of cosmology which one might care to name (closed, open, flat, etc.)---although I would qualify this with the statement that some cosmologies might provide more evidence for Theism than others. But it is quite true that the main reason I believe in Jesus has little or nothing to do with whether or not there was a Big Bang singularity. Since, as we agree, the state of early universe cosmology is quite speculative, this is a good thing!
So it seems that we agree on quite a lot. I can't agree, however, that arguing against other people's positions by rephrasing them using insulting and silly words is a productive arguing tactic. You might be amused by the fact that "goddunnit" sounds similar to a swear word, but as the blog moderator, I ask that you refrain from this type of tactic in the future. See #4 in my comments policy.
"(where most particle physicists, but not I, believe that the forces probably unify into one force)"
Now you've gone and made me curious: what are the reasons for and against such a regime of unification at high energies?
David,
The reason people believe it is that the coupling constants (i.e. strengths) of the 3 nongravitational forces vary with the distance scale in a way which suggests that they become equal at a certain high energy. See e.g. the diagrams on the left of this article.
However, this involves a fair amount of speculation since there might be any number of particles we don't know about whose masses are in between the LHC scale and the GUT scale, and if they were charged under the force they would affect the running of the coupling constant. And in fact the 3 forces don't quite meet unless you postulate that there's a new symmetry called "supersymmetry" which relates bosons and fermions, and that every particle has a supersymmetric partner at low enough energies (a lot of people thought these would be detected by the LHC but no luck yet).
And even with supersymmetry, precision measurements of the forces suggests they still don't quite meet. It's not so bad that it rules the model out, but I think it's bad enough that it should by no means be considered proven.
Also, the simplest GUT model is ruled out by the absence of detectable proton decay, but there are other models which have not been ruled out.
Oh, and I forgot to mention the important point that the representations of the various Standard Model particles under SU(3) x SU(2) x U(1)---that is their charges under the three forces---combine together in a nice way into representations of SU(5), the simplest GUT gauge group. They also combine into the slightly bigger group SO(10) (or really its "double cover" Spin(10)), if you include right-handed neutrinos. This is an important fact for GUTs which was by no means inevitable... so that should be put in the "evidence for" column.
Aron,
"Just because what happened at t=0 is speculative, doesn't mean we can't assess our limited current understanding to see which way the evidence points."
Physics is not competent to pronounce upon t=0. For one thing, that there is a t=0 is a extrapolation.
For another, physics requires a running universe, complete with spacetime, and material things already present. So, physics is not competent to pronounce upon or even to speculate on how the things came into being.