Appeal to authority

[Belacqua]

Most of metaphysics, as traditionally done, starts with faulty assumptions about how things 'must be' and proceeds to derive rather useless conclusions.

Well, this is true of some metaphysicians, and not true of others. Aristotle's metaphysics starts with the observations that things change. I don't think that's a faulty assumption. 

The most important moves away from Aristotelian metaphysics were brought about by Galileo and Newton, who are also not guilty of the charge you make. So I'd want to be careful with saying "most of metaphysics." Maybe it's true that most of anything is worthless (Sturgeon's Law) but that doesn't mean the whole field should be dismissed. 

Important metaphysicians have generally based their thinking on the best science of the time (Kant, Nietzsche) and important physicists have acknowledged their debt to philosophy (Einstein's comments on Schopenhauer, Heisenberg's book Physics and Philosophy, et.al.) 

So, here's the question: what can justify a belief? At the very least, there is a requirement that when two differing views are offered, there is some way to resolve the disagreement. 

Yes, this is an important question. 

"Some way to resolve the disagreement" may be tricky, however. I wouldn't want to say that only those questions are important which may be resolved by limited fragile human beings. Philosophy proceeds by dialectic -- people arguing with each other -- and many of its questions may never be resolvable. This doesn't mean they are worthless. 

In the science, a disagreement is resolved by finding some observational test where the two views predict different results and then going and doing the test. At least one of the viewpoints will be shown to be incorrect (assuming correct experimental design, etc).

What is the dispute resolution procedure for philosophy or theology? How do two differing theological views get mediated? By which gives the best argument? According to whom?

One way to address the question of how we have confidence in metaphysical positions would be to look at your own metaphysical beliefs and asking why you hold them so firmly. 

Based on what you've said, I think I can make a basic summary of your metaphysical position. Please correct me if I'm wrong:

1) Empirical observation tells us about the real world. 

2) Beliefs (things we hold to be true) about the real world are given increased confidence if they are intersubjectively repeatable. 

3) The real world is knowable at least in part through empirical observation intersubjectively repeated, except for math, which is largely not based on empirical observation, yet is in some way true and important for understanding the real world (in combination with observation). 

I'm certainly not saying these are bad metaphysical principles -- only that in themselves they are not provable through empirical observation. It leaves open some questions which I don't know about your metaphysical beliefs:

4) Is there anything about the real world which is not, even in principle, observable by humans? That is, is there any other subject, like math, which may be said to be true but is not empirically-based? 

5) The things which are outside science's purview: are they important to think about? Must we give up on them forever? Since Newton, science has progressed by accepting that certain things will be accepted without explanation. For example, Newton told us how gravity behaves, but gave no theory for what it is, and we still lack anything along those lines. Does this mean that such questions are forever unanswerable by humans? 

So, again, if I have these wrong please correct me. They are metaphysical issues on which I think you are very firm in your convictions. So you see that in principle it is possible to hold very firmly to a set of metaphysics without being stupid about it.