I am sorry that my lengthy response wasn't very clear. Let me see if we can get on the same page. (Of course, it's not essential that we agree, right? Just essential that we understand the other person's arguments. I really appreciate that you're taking the time to do so with mine!)
So, there are a couple of misunderstandings here. Let's try to tackle them one by one. The first one is that I don't understand your model. At the beginning of your last message, you said, "our universe is just one out of a pool of infinity conceivable universes." Later, you said, "There would be no need for me to resort to a multiverse." So do you believe in the existence of multiple universes, or not?
My guess is not, because you said "conceivable". But since I don't know, let's explore both options.
Option 1: First, let's assume there is just one universe. Yes, it is one universe out of an infinity of conceivable universes, but none of these other universes is real. Since there is no explanation of how or why this particular universe is actualized over the other conceivable universes, any discussion of probability is useless anyway, normalizability problem or not. Do you agree? (I think so because at the end of your last message, you said, "the concept of probability is simply not meaningful in this context". Unless I misunderstand what you meant by that statement.) And if so, then you are stuck with an apparently finely-tuned universe with no explanation for it. The universe just IS, and that's the way it is. Pretty strange, right?
Option 2: Now let's assume there really is a real multiverse ensemble. In that case, there really is some physical mechanism that generates universes, so this real, physical mechanism has real probability distributions for how it generates all the constants and initial conditions. This is what I was saying last time, and if so, then again, you end up with either a very small probability of our universe being the way that it is, or a finely-tuned mechanism. Again, non-theists like the first (very small probability) because you can conceivably defeat that by N large. A finely-tuned mechanism would be problematic because then you have fine tuning at the most basic property of all of physical reality, and you can't explain that.
I really like one of the papers you pointed me to by Colyvan et al. In particular, I liked it when they said, "After all, if they [meaning the constants] could not have been different, the probability of the universe being just as we find it is 1, and no fine tuning has occurred. But what is the modality invoked here? Logical possibility? Conceptual possibility? Physical possibility? This is rarely spelled out in the usual presentations of the argument." (p. 326)
This is what I was saying, and I think you would agree. They go on to discuss the problem with using logical possibility as the modality, precisely because it runs into the normalizability problem, as you pointed out. What they are missing here is that, if there is no real mechanism that "decides" which constants to pick from, there is no point in talking about probability anyway, again, normalizability problem or not. We end up with the universe just IS.
Do you see a third option besides either these other universes are real, or they are not? Or do you see my characterization of the first option as flawed? (I think this is where more discussion will occur, but I'd like to hear what you have to say about it before I ramble about this on and on. And on and on...as I tend to do.
Another misunderstanding I think we had is related to what I just laid out as our two Options. In particular, you quoted me as saying, "everything's equally impossible or our current value is necessary." That in a nutshell is what I was saying our two options were. But I got that from the Colyvan paper: "The fine tuning argument, on its most plausible interpretation, hence not only shows that life-permitting universes are improbable, but, arguably, that they are impossible!" (p. 327) Juxtapose that statement with, "Physical possibility (construed as consistency with the laws of physics and physical constants as we find them) however, restricts the range too much for the proponent of the fine tuning argument, leaving the actual values as the only possible ones, and hence setting the probability at 1!" (p. 329, original emphases removed)
Another misunderstanding is how you then go on to characterize the normalizability problem: "each possible universe is either equally impossible, or they all have a small nonzero probability. They can't be impossible, because then the probabilities don't add up to 1, and they can't have a nonzero probability, because then the probabilities add up to infinity." The either/or statement you lead off with is not true. (Before I go on, I do think you characterized the normalizability problem accurately, but I don't think its conditions are met in reality.) Of course there are probability distributions with an infinite domain that are normalizable. We just don't know what the correct probability distribution to use is. But again, either there is a real mechanism that generates these universes, in which case there is a real distribution so it is really normalizable; or there is not, in which case it is futile to talk about any probability distribution because there is nothing to draw from.
Final misunderstanding: "If I'm right that the concept of probability is simply not meaningful in this context, then this dissolves the mystery. There would be no need for me to resort to a multiverse or necessity." Yeah, totally, you may be right that the concept of probability is not meaningful. That's what I was trying to say in my previous message (and is captured in Option 1 of this message). And, in which case, you would not need to resort to a multiverse because you have already assumed there is not one. But then you are stuck with necessity, because the universe just IS.
OK, so those are the critical parts where I either misunderstood you, or where I think you misunderstood me.
Also, let me end with this: this discussion is awesome and I hope you don't get too frustrated at how long I take to respond. You keep up the good work with cordially asking questions and rebutting Christians' arguments. I know a lot of atheists (and Christians too) that just want to have their say. Maybe that's you too, but you're hiding it really well, which means that's not you.
What I should have said in all of that was simply, I think you characterized the normalizability problem correctly but I just don't think it's relevant. Because either we're dealing with a real mechanism (which then must be normalizable by virtue of its being real) or not, in which case a discussion of probability is futile. What do you think?
PS: I just took a look back at my previous message, and I even used "Option 1" and "Option 2" in that message too. I forgot, and I guess it's just what I think so strongly that it came out twice. Shame on me, because it looks like that means I didn't actually explain anything new this time. Let me know if that's true.
PPS: What I should have said in all of that was simply, I think you characterized the normalizability problem correctly but I just don't think it's relevant. Because either we're dealing with a real mechanism (which then must be normalizable by virtue of its being real) or not, in which case a discussion of probability is futile. What do you think?
[See summary page of this discussion, with links to all the posts, here.]