Is there a defeater for this philosophical argument?

Ok, I for one would like to directly address the original question, which was whether there is “any logical or scientific refutation to [the instructor’s] argument.”

There are plenty. Let’s start with this:

If it were me, I’d challenge her definitionally right there. What the heck does “self-explaining” mean?

This assertion is just factually incorrect. You have your “scientific refutation” right here. Matter is eternal and “self-maintaining”; a bedrock law of physics is the law of conservation of energy. And matter has been shown to be simply another form of energy (that’s a simplistic explanation, I know, but probably all that she could understand). The exact same matter/energy that exists in the universe right now has existed for all time in the past and will continue to exist for all time in the future (only the forms and arrangements have changed). Can’t get much more eternal than that.

Points i and ii above are irrelevant, since they don’t speak to the conservation of matter/energy, they say only that the form and arrangement change. And point iii shows (again) the instructor’s lack of understand of physics. So what if the Big Bang cannot occur again (which assertion, by the way, is not even supported by current physics)? All that says is that the matter/energy in the universe will continue to exist, eternally. And that last part about the “theory of a change from a true vacuum…”, what the heck does that even mean? Again, it shows a profound lack of understanding of physics; there was no “true vacuum” before the big bang, there was, rather, the entire universe in one point.

So if you want to refute her argument on scientific grounds, just tell her that matter/energy is indeed eternal.

If she tries to refute that by hauling out the old saw about “So what was there before the big bang?”, you need to patiently try to explain to her that it’s a meaningless question. Since time did not exist before the big bang, that question is really asking what was before time? If time does not exist, what meaningful definition can there be for “before”? Surely, a philosopher could understand that.

And if she continues to argue, you can probably trap her. Ask her to define “eternal”. Ok, previously you defined it as something akin to “having no beginning and no end”. Ok, so now have her define “beginning” and “end”. She’ll probably define “beginning” as something like, “there exists a time before which the thing existed”. Well, since time itself did not exist before the big bang, there cannot exist “a time” before the big bang, therefore the universe had no “beginning”. Same argument holds for “end” since, if the universe ever “ends”, time will cease to exist and therefore there is no time after which the universe ceased to exist. Therefore the universe has no beginning and no end, therefore the universe is eternal. Furthermore, since the universe contains “everything” (in that nothing exists “outside” of the universe), and all the matter/energy in the universe has always existed and will continue to always exist, you can correctly state that everything is eternal. Now ask her to come up with a defeater for that one.

What is worse is that this “nothing” is maybe just a perspective rather than a solid description. Ever hear about Dirac’s thought processes during his investigation into quantum theory? In creating a relativistic wave equation for the election, and thus the quantum property “spin”, he found four solutions instead of two. This, ah, interesting page gives some detail about it: Dirac Sea. (There are better sites if you search on this term, I just happened to take a fancy to this one.) Dirac suggested that what prevented electrons from radiating away to lower and lower, and eventually negative and more negative, energy states was that those positions were already taken up by what would come to be known as positrons (but were at the time “negative energy electrons”). This led to the discovery of positrons some time later. Now, the theory has some consequences which are quite unsatisfactory, and the second link goes into that detail, but it also mentions isolated cases where the theory still works instrumentally. The conditions it does work under are… interesting to think about.

I particularly like this description from the ultra-cool antimatter drive page (:p)

As I understand it, this requires CPT symmetry to be the case. But it is an interesting description of an event, is it not?