Disclaimer: I am biased towards Dr. Craig, but I will attempt to be fair-minded in my critique. Also, I am going on the basis of a two-and-a-half hour debate and Q & A section, so the chances of my getting something slightly incorrect are good.
The much-hyped debate between William Lane Craig and Lawrence Krauss did not disappoint. The topic was not the usual “Does God exist?” but rather the variant “Is there evidence for God?” This was a very charitable (and ultimately interesting) move by Craig since Krauss did not have to provide a single argument for atheism. Rather, all he had to do was dismantle the arguments of the former. The debate format was the standard opening statements, first and second rebuttals, and then a closing argument, followed by a Q&A format.
Krauss is not a philosopher (indeed, he made his dislike of philosophy known throughout the debate [though not in an uncharitable way]), but rather a scientist. As such, I found his discourses into quantum mechanics quite fascinating. However, he seemed hopelessly mired in contradiction when he repeatedly mentioned things like “the universe is not logical,” or “quantum mechanics…are not logical” in the opening speech.
The opening arguments by Craig were the same (Leibnizian Cosmological Argument, Kalam Cosmological Argument, Fine-Tuning Argument, Moral Argument, and the Resurrection Hypothesis), however his methodology differed from past debates I have seen. Instead of a brief introductory statement followed by the formal argument, Craig developed the argument conversationally yet with precision; only after explaining the argument in this way did he render it formally. I think this approach actually works better by appealing to the intuitive or reasonable nature of the arguments without causing the audience to focus on the premises themselves (that is, they can pay attention better).
I have never before seen Krauss debate, but the physicist opened up explaining he did not particularly like them. I was shocked to discover that Krauss’ entire opening statement revolved around criticizing Craig’s well-known arguments as “God-of-the-gaps.” He also mentioned that quantum mechanics demonstrates that physics does not conform to the laws of logic (thus, in my view, demonstrating a fundamental equivocal misunderstanding of the term “logic.” It does not mean, as Krauss here seems to suggest, “common sense” or “what we would expect.” This is the most charitable view as the only other sense he could mean is that it is reasonable to assume reason does not apply to physics, while also giving us a reason, which is self-contradictory.). He also suggested God cannot be the grounds of objective morality since God can’t will evil things to be good.
In the first rebuttal, as Craig does, he reiterated the frame of the debate: “My goal is to show the modest claim that God’s existence is more probable given the evidence than it would be without these claims.” He then proceeded to point out nearly every one of Krauss’ contentions as fallacious. I don’t think he necessarily needed to do that. For whatever reason, Craig came off as rushed at this time and misspoke at least twice. However, it’s worth noting that he absolutely did demolish every one of Krauss’ objections, following up with the argument from the Resurrection which was entirely untouched.
In Krauss’ rebuttal, he did mention David Hume’s argument against miracles, whereby he suggested the eyewitness testimony to miracles should only be accepted were its negation to imply a more miraculous event than to believe the testimony itself! This was as close to a genuine philosophical argument that Krauss ever got. It was well-timed and on-target, in that if his assertion was true, Craig’s “three minimal facts” argument wouldn’t even get off the ground. Krauss also went on to assert that, in contradistinction to Craig’s argument from probability, that probability was not evidence. However, this seems to misunderstand that probability just is the epistemic relevance of a hypothesis to the background knowledge and evidence! Krauss seemed very uncomfortable with any actual philosophical discourse, but visibly perked up whenever he could discuss quantum tunneling, quantum mechanics, or the vacuum, from which the universe emerged.
In Craig’s second rebuttal he again focused the debate topic. Craig does this to show both what he has argued and to show that the rebuttal was not at all relevant to the topic at hand. I wished he had discussed more cosmology and why inflationary models require an absolute beginning, but he at least mentioned these rebuttals. He completely tore apart the Humean argument against miracles by pointing out that he did not have the probability calculus back in that time. Craig seemed perfectly comfortable by this point and not at all rushed; however he had fewer points to argue against as Krauss was defaulting to “desire” as a motivator over scientific evidence.
By the time of Krauss’ second rebuttal, he was struggling for words. He seemed to have run out of things relevant to say. He did eventually get going, but made such contradictory statements as “there is no purpose in the universe.” As Ryan Hedrich said to me during the debate, “There’s no meaning, no purpose, and yet there he is, arguing away for God only knows what reason (literally).”
In the final statements, as he always does, Craig closes by framing the debate’s point, his evidences for that point, the fact that the evidences are not shown to be implausible or contradictory, and that as long as one agrees that each individual premise is plausibly true, then one ought to believe it is plausible that God exists.
In Krauss’ final statement, he made bizarre assertions that said “contingent beings must exist” (in response to the question of why something exists rather than nothing) given an infinite number of universes; but in terms of possible worlds, this necessity demands an answer to the question of the beings themselves: contingent upon what? He also reiterated his point of view that science answers all questions as to the origins of the universe, which amounted to “there’s no explanation of the universe, except for gravity and other such natural forces.” But what about these forces themselves? At the end, Krauss framed the debate in terms of Craig’s wanting theism to be true coupled with the argument “if we can’t explain it, then God must exist” to show that Craig had not demonstrated any evidence for God’s existence.
A full 40 minutes or so of Q & A followed, in which questioners were near-universally well-behaved and thoughtfully concise rather than argumentative (even if you could tell the question was designed as an argument against either debater). An exception was a gentleman who asked Dr. Krauss about the issue of God’s cause. If everything has an explanation, what is God’s explanation? Krauss concurred that the question “who made God?” is applicable, and thus presumably either God does not exist or we should reject the Principle of Sufficient Reason (neither the questioner nor Krauss made either explicit). When Craig was able to respond he pointed out that God would find his explanation in the necessity of his own nature. At this conclusion, the questioner retorted (as he was already instructed not to do), “I was just trying to point out the circular reasoning you just used.” Quite odd.
The next question was nearly identical, but for Dr. Craig. So he mentioned God was postulated here as the metaphysically-ultimate explanation. I wish very much he had also made explicit what he hinted at in his answer, which is that to question God’s explanatory power further (beyond positing incoherence) is really just to presuppose that God is not the metaphysically-ultimate explanation after all. The lack of making this explicit allowed Dr. Krauss to make one of the better comments he had made all evening: that he postulated the multiverse as a metaphysically-ultimate explanation. Dr. Craig was not able, in the format, to respond, but doubtless he would have pointed out that the metaphysical necessity of the universe cannot possibly be true even in the event of the multiverse, because even the multiverse does not escape the laws of causality or needing an absolute beginning (though in fairness, he mentioned this much earlier).
Both debaters were very courteous, and Krauss said nothing rude at any point. One of the best points of the night was made by Craig when he remarked, speaking against the idea that physics can account for the origin of the universe from nothing, “Physics is inherently applicable to being; it is impossible for there to be physics of non-being.” To me, this was the death blow to science being an ultimate metaphysical explanation of the universe’s origin.
In summary, it was a wonderfully-done debate with charitable discourse all-around (except, perhaps, when Krauss said something about Craig being “intellectually lazy”), with Craig clearly coming out on top. While we do not know the results (or the ideological makeup) of the audience yet, I would be shocked if Craig was not declared the winner, by a landslide.
 For example, his discussion on why we cannot measure if another universe is exerting any forces upon our universe were the multiverse to exist was a particular example showcasing the level of comfort he has within his field.
 This is to stand in stark contrast to his other objections, which were entirely either self-contradictory or off-topic.
 It’s also worth noting that, in all seriousness, it did not appear Krauss understood very many of the philosophical arguments proffered, and he likely was unfamiliar with the term “Principle of Sufficient Reason” before the debate.
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