Can't prove the supernatural God

[SteveII]

I don't know what a theist thinks natural means. What definition of natural includes things generated out of nothing by magic?

"Could not have come from natural causes" = "Argument from ignorance"

I think it's not reasonably possible to conclude that you have eliminated all natural causes, because that assumes we know about every natural cause. And how do you eliminate there being no efficient cause? [Efficient cause is the agency involved, as opposed to the material cause which is what it was fashioned from. Of course theists often conflate the two.]

Event e with unknown efficient cause c. It could be the case that c=no cause.

Known natural causes is the set N.

c is not a member of N.

Conclusion: c is a supernatural cause. This is doubly flawed, because we haven't eliminated the possibility of c being no efficient cause.

Science learns more stuff, and extends N to N+.

Now c is a member of N+.

Conclusion was wrong.

And what makes this "supernatural" cause any different? What separates the natural causes from supernatural?

The difference between supernatural cause and a natural cause would be the properties of the efficient cause. Properties of a natural efficient cause include physical, governed by the laws of physics, repeatedly observed,  etc. Properties of a supernatural efficient cause would include non-physical, not bound by the laws of physics, powerful enough to act on the natural world. Added to that is the reasonable assumption that there is a purpose for the act. 

Can you give an example of something that has a material cause and not an efficient cause? Even better, an example that might otherwise be considered a miracle by someone at some time.

So, your position seems to be that what we call miracles have naturalistic explanations that we just don't understand yet?  

1) Isn't that an argument from ignorance? 
2) Under that reasoning, why don't we see more of these 'miracles' if it is just a matter of misunderstanding the cause? The rarity of a miracle actually supports the premise that miracles happen. 
3) If you zero in on a particular miracle example, there are often circumstances that make the 'heretofore unknown natural causes' just at the right moment and in the right context ridiculously unlikely. 
4) Whether a miracle happened or not is a probabilistic question. The more evidence and context clues the higher the probability.