Whew, two very interesting responses. I'm going to respond to these now. Just to warn, this will _probably_ be my last response tonight. It's getting late here, and I still have a couple hours of work to do. I will try to respond though, tomorrow hopefully. Thank you both for the responses, by the way.
Anyway.... @Mafialligator. You've pretty much already put your finger on my response to you. You say,
"Empiricism is the idea that in order to believe something is the case we must have consistent, observable evidence to back it up."
Of course, the problem is that this is not an observable rule, it's just a postulate. In fact, it was empiricism, not rationalism that Hume was critiquing when he came up with his argument against induction in the first place, and it has more or less continued in that context.
To even speak of evidence already presumes order and induction. If there's no order, evidence is meaningless. So you're just assuming this, still. It is this assumption I am taking issue with.
"Now, you could argue that this idea that the nature of the universe is knowable through observation is a faith based position and I suppose that's hard to refute,..."
Right, I would. Of course, you go on to point out that I have my faith too. Also true. Here's the crucial point, though: in my Christian world view, I can understand and make sense of why I would be able to know things, and even why I could come to faith.
On the other hand, in your atheist empiricism, there is absolutely no reason to believe that the human brain should be gifted in coming to good hypotheses about the nature of the universe, or that its faith (in induction, say) is likely to be actually true. That is, within your own worldview, your knowledge is completely inexplicable. Mine is not.
I'll be more specific. Where, in your world view, does knowledge come from? Well, undirected evolutionary processes crafted the human brain. What could go into these processes? By their nature, the past. So we agree that the past has been uniform, and we agree (arguendo) that unguided evolution crafted the human brain. And of course we can both agree that, AS LONG AS the past keeps on being uniform, it will be extremely adaptive for the human brain to believe in induction. So that's all fine.
The problem is, none of this says anything about the actual liklihood of induction being TRUE. All of this is true in any of the universes that are regular up till now, doing all the crazy things they may do later. So here you are, an atheist empiricist, with this faith commitment to induction, and it's just based on nothing. You can't account for how your having it could be tied to its truth or falsity at all, or say why it's actually likely to be true.
(None of this is confusing rationalism or empiricism either, by the way. As you more or less acknowledge, I think, on this point.)
Your world view is in this sense incoherent. You believe some things (induction, regularity of the world, the universe having a "nature" to know) that other things you believe (atheism) render unknowable and improbable: a totally blind faith. (And to dispute the burden of proof, of course -- as I read you to have acknowledged -- already requires this assumption). In other words, reason is defeated in your world view.
On the other hand, in mine -- faith based, also, by the way, I agree -- my knowledge and beliefs cohere, and reason is not defeated at all. It's a gift of God, an ability He put in my mind to reflect and know the order that He also put in the world; and then He told me all this. Thus, reason is fine in my world view, and not in yours.
"However, for practical purposes this is not a reasonable, or useful, stand to take, so I make the assumption, that the physical universe can be understood through observation, and am able therefore to not seriously consider the possibility of anything that does not have sufficient evidence to warrant believing in it. It is of course possible that this assumption is wrong, but I can still adopt a purely empirical, scientific standpoint and have this way of understanding the world remain internally consistent. "
You say it is not a useful stand to take. That, of course, already assumes it's false. If my armchair is about to turn into a 747 and take off for Monaco, contra all the laws of physics, then knowing THAT would be incredibly useful to me, because I could go hop on it and go there with it. (Assuming that the laws remained otherwise the same -- but that's one of the possibilities, obviously). Assuming induction is only useful if induction is actually true.
So in saying you can assume induction and everything will be fine for practical purposes, you're really just reaffirming your faith in induction.
A faith I happen to share, of course, but unlike you I can account for why.
Thank you again, MA, for a thoughtful post. I do appreciate actual engagement with what I'm saying.
@Warren, Mathematics is a really interesting question. First, you kind of bring up a lot of thorny side-issues about the nature of mathematics. Much of mathematics is based on deductive, not inductive reasoning. But it also works in the real world, and there are lots of debates among philosophers of mathematics as to whether it's really empirical and yet can be reduced to logic, or really ethereal and yet interacts with the empirical world.
Cutting through all that, anyway, mathematics does of course have an empirical side: 2 apples plus 2 apples equals 4 apples. And yes, I do think that it would be unreasonable to believe mathematics, either, in an atheistic world.
A key point to remember is that our brains are inside the world and have a physical history (unguided evolution, guided evolution, creation, what have you). We may feel we have a grip on ultimate truth -- 2 + 2 = 4, say -- and be unable to imagine this being false, but does our world view / cosmology explain how we could have? In the case of materialistic evolution, no. There is no reason to believe that there is some abstract set of mathematical truths, if one is a materialist. How could there be? Similarly with induction, as I outlined above, there's no reason to see how the history of our minds gave us any grip on the future or the ultimate nature of the universe; just on its behavior at the time they happened to evolve.
Of course I agree that it seems absolutely impossible to really take seriously the idea that 2 + 2 is not 4, and in fact one can't and be rational, and this is just why I'm advocating turning to God and the Bible and accepting the worldview that does not entail the absurd.
"If induction is so inherently flawed, and I am certainly moved to think so by your argument, then why does it work so well in practice? Or would you make the argument, that it only holds true within rigidly defined sets such as mathematics. "
Well, of course, I would say it works well because God _does_ exist, and upholds the world just as He promises in His Word. As long as this is true, it will work great, and people will be able to go along using it no problem even with world views that make using it absurd.
"Is it unreasonable to assume that all matter acts in the way it does simply because it must in order to be realized within our universe?"
That is of course a possibility. The problem is just that, if atheism is true, we would never have any way of knowing that. I mean, lots of things are possibilities. It's a possibility that matter acts the way it does up until Thursday because it can't be in our universe otherwise, and then it starts acting radically different, for the same reason. What would "can't" even mean, anyway? Wouldn't there just be "doesn't"?
The problem, anyway, like I say, is just that, sure, matter MIGHT just happen to be regular, but we would have no reason to know it, and no way to accord that positive probability. It might do anything at all, and we're just not privvy to the information.
"Now if, God does not exist, and the universe formed the way it did on its own, how is it unreasonable to assume that this universe has to obey certain laws in order to continue to exist?"
Same question I think, more or less -- anyway same answer. It's unreasonable because we have no way at all of knowing it to be true or even probable. What would laws mean? Just regularities in how it behaved. And sure, we could assume that the regularities existed, but that wouldn't make it probable, or mean we had any real source of knowledge like that. We could assume anything else, too.
"Now, I'm exhausted, and I have to be up for classes in 4 more hours, but if I've made even a semblance of sense rattling these things out, I'd love to hear your response."
Man, I know that feeling all too well. I hope this was responsive. Please let me know if not, or if you have further thoughts on it. As with Mafialligator, I really appreciate the thoughtful response here.
Regards.