Atheists have no rational mechanism within their world view to account for logic...

 So much for the atheist believing himself to being rational...

This should help the Christian to have empathy on the poor Atheist in that we can understand why they are truly illogical and have essentially missed getting on the rational train altogether. 

You really do not have to listen to the entirety of the debate to pick up on and understand what Dr. Bahnsen said here in his final rebuttal.

Dr. Bahnsen laid out some convincing and logical arguments and proofs here as well as throughout the debate. The central focus on his argument though was around logic and how the atheists have no rational mechanism within their world view to account for logic. In it’s very nature logic is immaterial yet it is a very relevant universal and abstract component throughout Creation.

Dr. Bahnsen’s closing rebuttal from the Great Debate held at UC Irvine in 1985:

"Dr. Stein has demonstrated, it seems to me repeatedly, in the course of tonight's debate, the claim that was made very early on in my original statement, and that's that the Atheist world view cannot give an account of those things which are necessary for a rational discourse or science. 

When asked about Hume, and the skepticism that he generated about induction or the uniformity of nature, we don't hear an answer coming forth. I don't think there will be an answer coming forth from the atheist world view. However, Dr. Stein , who is an atheist, has said - and I think this is close to a quote - "If there were no uniformity, science would be impossible." 

Exactly, Dr. Stein! If there were no uniformity, science would be impossible. So on what basis in an atheist's universe is science possible, since in an atheist's universe there is no basis for assuming that there is going to be uniformity? 

For someone to say, "well, it's been that way in all the cases in the past that we know of and therefore very probably is going to be that way in the future" is to assume, because you're using probability, that the future is going to be like the past, that is to say, is to beg the very question that's being asked you. 

Now, of course, if you don't like the tough philosophical questions that are asked you about the nature of laws of logic, how they are justified, the nature of natural law, how it is justified, and so forth, and just dismiss it as absurd questions or non questions that no one understands and do not have meaning, seems to me is just to try to give medicine to a dead man. You see, it's to say, "I'm not going to reason about that, because I don't have an answer to it, and that's just uncomfortable." But you see, these are philosophical questions which not just Christians, by the way, but all philosophers have had to ask and face throughout the centuries.

Dr. Stein doesn't even begin to scratch the surface of giving us an answer of how an atheist world view can account for laws--laws of science, laws of logic, laws of morality. And yet he does tell us without them, science would be impossible. 

As for the transcendental argument "not being logical," I mean, you can claim that, but I have yet to see Dr. Stein show any self contradiction on any violation of the laws of logic in it, but of course, if he were, I would ask him if that law of logic is one of the things that we are necessarily to live according to? 

Are we to reason by this law, or is that just a convention? Should I say, "well, it's your convention, but it's not mine." Or is that law of logic universal, invariant and something that must be followed if we're going to arrive at truth? If it is, I'm going to ask him how it's possible to have such a thing in his universe; how he can justify it at all. But he hasn't, shown any contradiction; he has simply, again, called it illogical. 

Whether it's falsifiable or not - I mean, even asking that question, I think, shows that Dr.Stein is not really aware of the philosophical nature of the question in the debate before us.

No, transcendentals are not falsifiable--that's right--but they are very meaningful, the very sorts of things that philosophers deal with all the time. Look at Kant or Aristotle or other philosophers: you'll see they deal with the preconditions of experience. And since they are preconditions of experience, they are not falsifiable, and yet they are meaningful. 

He says that I do not have an answer to these questions either. Well, I certainly do! It's just that he doesn't like the answer. The answer is that God created the world, and this world reflects the uniformity that He imposes on it by His governing, and our thinking is to reflect the same consistency or logical coherence that is in God's thinking. 

How do we learn about those things? He revealed Himself to us. Again, these are simple answers, the sorts of things Sunday School children learn, but, you know, I've yet to find any reason not to believe them. 

For Dr. Stein to say, "well, these aren't answers" doesn't convince me at all. He says there aren't going to be answers unless I include how it took place. What is God's method, and why did he do it? Well, I don't accept those standards. I don't accept that this is a requirement for an explanation at all. And he doesn't give us a good reason except that he's not going to satisfied or it's unhelpful to him. 

He says it's a non meaningful statement to say that the laws of logic reflect the thinking of God. He wants to know things like, "can God be irrational?" Well, if you'd ask those questions in cross examination, I'd answer them. No, God cannot be irrational.

Rationality is measured by the standard of his thinking and his revelation. 

The atheist world view cannot account for the laws of logic, [and] cannot account for any universals or abstract entities, for that matter. [It] cannot account for the uniformity of nature, and therefore, [it] cannot account for the successes of science. 

Nor can the atheist's universe give us universal and absolute laws of morality. And so on three of the most important issues philosophically that men must face- logic, science, and morality- the atheist's universe is completely at odds with those things. 

Dr. Stein brought up in his second presentation so that I might rebut them. 

He wants to know about the problem of evil.

My answer to the problem of evil is this: there is no problem of evil in an atheist's universe because there is no evil in an atheist's universe. Since there is no God, there is no absolute moral standard, and nothing is wrong. The torture of little children is not wrong in an atheist's universe. It may be painful, but it is not wrong. 

It is morally wrong in a theistic universe, and therefore, there is a problem of evil of perhaps the psychological or emotional sort, but philosophically the answer to the problem of evil is you don't have an absolute standard of good by which to measure evil in an atheist's universe. You can only have that in a theistic universe, and therefore, the very posing of the problem presupposes my world view, rather than his own. God has a good reason for the evil that He plans or allows." 

See here for the transcript of the entire debate: http://www.brianauten.com/Apologetics/apol_bahnsen_stein_debate_transcript.pdf