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...the phrase "to know" in there is telling. It requires a deep and abiding faith.

To add to your discussion of probability, universal truths, how the finite could ever know a universal, and how there could even be such a thing as universal laws of thought (logic) in a materialist universe, I add the following:

"Faith is the evidence of things unseen"

What kind of statement is that? How could faith itself be evidence of something unseen? The statement seems backwards, or even circular, doesn't it? Faith is typically characterized as belief in something in the absence of evidence, or in spite of it.

Following is an extended quote, but I think it is worth reading because it shows that faith is not belief in something in the absence of evidence, it is the precondition of reasoning itself:

"...And fourthly, many hearers need to disabuse themselves of an old canard that goes something like this: "Faith is believing what you know ain't true. Or faith takes over where reason leaves off." Faith is not something that stands over against reason, whether above reason or contrary to reason or however you wish to put it. Rather reasoning itself rest upon the presupposition of faith and collapses arbitrary without it. Now to make this point I have chosen to look not to what committed Christians have reasoned or said which you might feel is too easy and partisan on my behalf. But rather to have us consider what our hostile opponents have pointed out about a central problem in philosophy. We'll look at an issue treated by David Hume, the eighteenth century Scottish skeptic, and also by Bertrand Russell, twentieth century English philosopher. Both of these men wrote in strong opposition to religious faith and especially to Christianity. The problem we're going to look at for a few moments here is the problem of induction.
Among the expectations through which we encounter experience and encounter the world is the expectation that uniformity can be found between the diverse events, things, or experiences in the world. This expectation may in some cases be quite explicit and self-conscious but it need not be. For instance when we learned to drive a car or speak a foreign language we usually pay close attention to what is the regular function of certain parts of the car, or of the grammatical rules and ordinary word usages of the language. But we eventually come to do these things more automatically or more habitually and we no longer consciously think about the expected uniformity in our use of cars or our use of language. Our learning and reasoning tacitly assumes that the universe is such that uniformities are expected and exhibited in similar things even though they are separated by time and space - that the way things happen can be viewed as instances of general laws and what has occurred in the past is a reliable guide for predicting and thus adjusting to the future.
Now this can be described in an elaborate and abstract way, but not many of you are philosophy majors and would not want me to do that. The fact is each of us is very familiar with what I'm talking about from personal experience. We're all quite acquainted with the process of moving from particular facts in our experience to general truths which are exhibited by those particular experiences. For instance, children don't merely conclude from their pain that a particular case of flame is burning them, they usually project that fire in general, or if you will, all fire, any fire, will burn as well. From observed regularities or associations, we infer universal regularity even in the unobserved cases or yet future cases. In popular parlance we say we assume the uniformity of nature. The method of generalizing from observed cases to all cases of the same kind is called induction. The basic guiding principle here is that future cases will be like past cases - that similar things will behave similarly.
So for instance, if certain conditions and events bring about a certain effect today, the same factors will cause a similar effect later. I'll give you a down-to-earth example: Why do we expect toothpaste to spurt from the tube when we squeeze it? You might call this the toothpaste proof of God's existence, okay? We support that expectation in terms of two things: One, our past experience with toothpaste tubes, and two, the belief that nature is uniform - that the future is like the past. Without that second belief, we would not be able to learn from experience. We will not be able to use language, we will not be able to rely on memory, or advanced science. All of which involve observing similarities and projecting them into the future.
Moreover our belief about uniformity or the inductive principle is a very firmly entrenched belief. When scientists found that there were deviations in the expected orbit of Uranus they did not draw the conclusion, "Okay nature is not uniform after all, " that just impelled them to start looking for another factor as yet unknown that was influencing the orbit of Uranus. They did not give up the inductive principle, but rather hypothesized the body which by the way we now know to be the planet Neptune. And so from toothpaste to the planets we believe in reason in terms of the inductive principle. Now David Hume's question was this, and I quote: " What is the nature of that evidence which assures us of any real existence and matter-of-fact beyond the present testimony of our senses, or the records of our memory?" By what logical right, he was asking, do we claim to know that some empirical generalizations are true? What, asked Hume, are we warranted in asserting on the basis of our experiences? And he said to be very strict in his empiricism, "Only that in the past or in the cases so far observed such and such has been the case."
But Hume said we have no basis for projecting that into the future. And I quote him again: "If you insist that the inferences made by a chain of reasoning I desire you to produce that reasoning." Now of course many people make the mistake of responding to Hume saying, "Hey listen. We all assume the future will be like the past." Hume said that he understood that, there is no question that in practice we act that way, but as he said and I quote him again: "I want to learn the foundation of this inference." And then there are people who say, "Well we know it's very probable although it may not be very certain. "But that misses Hume's point as well. Hume knew very well that we don't have certainty about all matters of science. His point is that we have no logical right to affirm on the basis of our past experiences that even probability is true of the natural order. And so that the principle of induction is left without a foundation.
Bertrand Russell, the 20th century philosopher, said that we cannot justify our belief in induction on the basis of the past success we've had in believing that the inductive principle is true because that too assumes that what happened in the past is going to be like the future. Let me quote Russell here: "The inductive principle is equally incapable of being proved by an appeal to experience. Experience might conceivably confirm the inductive principle as regards to the cases that have been already examined but as regards unexamined cases it is the inductive principle alone that can justify any inference from what has been examined to what has not been examined. All arguments which on the basis of experience argue as to the future or the unexperienced parts of the past or present assume the inductive principle. Hence we can never use experience to prove the inductive principle without begging the question."
So now do we have reason for believing the inductive principle? We need to set the Christian worldview, the theistic world view side by side with the atheist world view and ask which one comports with the inductive principle and thus provides the preconditions for science, language, learning, and any intelligible human experience. And I will say it's certainly not atheism. Atheism's view of reality and historical eventuation cannot provide a cogent reason for what all of our reasoning takes for granted. It is debunked by its philosophical arbitrariness at just this point as even men like Hume and Bertrand Russell realize. Accordingly, it is most reasonable to believe in God and entirely unreasonable not believe in God, for God's existence is the precondition of all reasoning whatsoever."
Greg Bahnsen

Cordially,