While that may be true, my scenario is a hypothetical one, one in which quantum mechanics is either impossible or unobserved.  I'm aiming to demonstrate the possibility of a supernatural explanation.

Nice try, but although I think we all know what appolose is trying to get his foot in the door for, his argument does not involve any specific entity.

For this non-issue, I would say that it is illogical to say something can be without cause.  For one, it can't create itself (as I noted above), and, for another, to say "It came into being without cause"  again implies existence before existence ("It came"?).  Also, no, quantum mechanics does not contradict this (a quantum flux is responsible for matter creation, not "nothing")

As for observing the inability to physically create matter; such an observation already has been made (possibly that's now overturned due to quantum mechanics, but this is a hypothetical situation, remember?).  In fact, it's the first law of thermodynamics (let's not confuse that with being contradicted by E=mc^2; it isn't (not that that is relevant right now)).  As I said before, once science observes something enough (in this case, the absence of a physical instigator) it assumes it's true (or says it's likely, for anyone who wants to change what we agreed science does).

"And when I read it the first few times, I thought it was the  meaning of physically as in "I am physically in Best Buy" (as opposed, perhaps, to their online store), and so those two statements would be contradictory if matter was created in the "physical" universe".

While I'm not sure if I'm understanding you here correctly, I offer this: To be created "in" does not imply to be created "by", if that answers your question.

"Only then you turn around and say that "non-physical cause" = "supernatural cause"!  ("we are left with only 1 option: a non-physical creation")  This, of course, would massively fail to support your point given the latter definition of "physical"".

I'm not sure of what you're getting at here, actually.  What definition of physical are you referring to?  My only goal here is to demonstrate that science can reach beyond the physical as an explanation, which would be, therefore, non-phsyical, which I am calling supernatural (It makes no difference if you want to haggle over the meaning of the word "supernatural"; that isn't the core point here and never was).

"Also, I ask for consistency in another area:  you claim "deduction" of the supernatural, and then (it seems) explicitly use induction to get there".

Deduction from the assumptions of science; you can make a deduction off of any two propositions, regardless of the truth value of them.

"P.S.  What about the "exports from another universe" hypothesis?  How could we eliminate that possibility, as we must for even your idea of science to contemplate the supernatural?"

We have detected no physical cause: if it were exported from another universe, and we found no trace of a physical transportation.  Then, science does what it always does; assumes that there is no means of physical transportation.  That doesn't rule out another universe, mind you, but it does mean that there was a means of non-physical transportation, so the supernatural as an explanation is present either way.

More simply, we could just pretend that, in this scenario, multiple universes have been mathematically ruled out.

appolose, what do you actually mean by 'supernatural' explanation.  I'm assuming you mean God, but perhaps you don't.

I can tell you, again, that scientific theory correctly applied will never result in the explanation that the unknown is supernatural.  It simply can't. 

What you really need to understand is that any time scientific process comes up short (which happens all the time BTW) the anwer is predefined and exclusive - 'more data required as we have no consistent theory'.

That will always be the result.  The result will never be - 'must be supernatural'.

I guess, in a sense, the way to view it is that scientific process does not allow for anything other than an 'inconclusive evidence' or 'we have a theory' result.

You're positing a scenario which (even if the supernatural existed) would result in the answer 'inconclusive evidence'.

1a.  You said the first observation was "matter cannot be created physically".  

1b.  (I don't think this could possibly be an "observation" in the way we ought to be using it here, but I'll pretend it is for 2-6.)  

2.  You said that the second observation was "matter is being created" (that ends up in the physical realm, I presume)

3.  You said that these two observations are not contradictory.  

4a.  "physically" may mean simply that it now exists in actuality.  
4b.  "physically" may refer to the idea that it complies with the laws of physics.  
4c.  I don't think another meaning makes sense, because if you were trying to say e.g. that it is not possible for a being or force of this universe to do it but it was done anyway, that is a contradiction because acting in this universe makes it "of this universe" IMO

5.  In the case of 4a, the two observations are contradictory because obviously matter has entered into physical existence

6.  In the case of 4b, the second observation would simply mean that the laws of physics are wrong and science must go back to the drawing board for an explanation.  

7.  Regarding induction/deduction:  
7a.  You said "it lays out my case for the deduction of the supernatural."  I presume this meant "... by science" in accordance with your overall stated objective in this discussion.  
7b.  You then used induction.  
7c.  Even if you are correct that using induction is in accordance with science, you are wrong to claim that you have used science to DEDUCE anything when you have in fact INDUCED something instead.  You may, however, deduce a successful induction based on that, but that would simply be saying QED (or worse, repeating yourself), now wouldn't it?  

8.  Regarding that another universe could be considered "supernatural":
8a.  Good point, but are you satisfied then that science could never ever ever ever conclude that God existed because of the possibility of other universes messing with us (lacking mathematical proof of their nonexistence)?  

9.  Regarding the idea of pretending that other universes have been mathematically ruled out:  
9a.  Didn't the original challenge involve your scenario 'being hypothetical but possible'?  If so, this means that I cannot accept pretended restrictions such as this -- you would have to actually rule out the possibility of other universes, since we don't know whether what you would pretend is possible.  

10.  1a is actually pretty important, just a reminder.   

1 a-b. Ok, we'll roll with that.

2. Yes.  That is operating under the supposition that mathematics do not allow for quantum mechanics/multiuniverses.  If you're wondering why I didn't mention that earlier, it's because I think quantum mechanics covers the idea of multiuniverses.  So, if it can't have come from anywhere, then it was created.

3.  Correct.

4,5,6.  It is C; I think it works in that when I say no being or force of this realm can do it, I'm not saying no being or force at all can do it.  As for that being/force acting in the physical, why does that make it physical?  This is how the observations are not contradictory.

7. Deduction never has anything to do with how you arrived at the premesise (spelling?); only that it follows from them.  In the case of science, I show it making two inductions, then showing the necessary consequence of those inductions (assumptions).

8. I'm not sure I understand you here quite: Science will never be sure of anything (heck, you know what I think of empiricism at all ;)  ),  Is that what you mean?

9. Possible in the sense that it uses the tools and methods of science, that is.  What our universe really is I'm not using as part of my argument against "science cannot ever, in any way, conclude supernatural".

10. Noted.