Whether or not you believe the universe is a plenum, or not, and whether you believe the theories and experiments in the field of physics or not, if you hear someone state that on philosophical grounds alone, one can show a true vacuum, the absence of any and every thing, cannot exist, he or she is wrong.
At the outset let me state that a person could be of the belief of such a thing on other evidence (of the special sciences, e.g. electrical and gravitational fields seem in actuality to permeate everywhere) but if someone tried to provide a philosophical argument understand that it would fail.
Here is why:
First our premise is that space and time are purely relational, i.e. that space itself is not an independent existent. It is not a container that would still exist if all the concretes in the universe were simply to disappear. Space is a relationship between those entities and rational also between portions of entities (if they are extended in space).
The main argument against a true vacuum is that “there can be no nothing”. This goes way back to ancient Greece, Parmenides. The idea being that one grasps and thinks of things and cannot think of the sheer absence of every thing.. i.e. a complete nothing. I am paraphrasing, it is much more involved, but suffice it to say, this led some to conclude therefore that the “universe” could not have tiny “holes” in it, and that for philosophical reasons it must be tightly packed (a plenum).
Diversion 1:
When it comes to things like frequency of vibration or momentum, one can easily see that (assuming) there being a finite number of things in the universe, at any one instant in time, there are only a finite number of momenta being “occupied” or “exhibited” by that finite number of things, and there are only a finite number of frequencies at which that finite number of things could be vibrating. Moreover it is clear that more than one thing can have the same momentum, and more than one thing can vibrate at the same frequency. So among the great many things there is redundancy or degeneracy (fewer number of unique values than the actual number of particulars).
Now imagine a particular momentum or frequency which is occupied, i.e. at least one thing in the universe has that momentum or frequency, at a particular time. We would be completely nonplussed if we were to find out that at some next instant that one thing no longer had that momentum or frequency, and moreover that no other thing in the universe AT THAT INSTANT happened to have that particular momentum or frequency. In fact, given the nature of the number of possible momenta, and frequencies each being a continuum of values (and if not a continuum, an unbounded set), it is clear that at any time a great many are unoccupied/unexhibited.
Please note that reference to the particular momentum or frequency is valid, as it was relevant to discussing reality, i.e. an object possessed that particular value a moment ago, so it is completely valid to refer to that particular value now, (the one which previously was occupied) as simply not being occupied/exhibited by any entity or part thereof.
If I went up to philosopher (not the best kind) and said that “nothing has particular momentum A, although I have proof object x had that momentum a moment ago.” should I expect him to than ask me…
“Are you saying Nothing is like a Something, and that it is occupying/exhibiting a particular momentum A?”
How would I respond if he said, “To say a particular momentum has No object occupying/exhibiting it is invoking Nothing in its place, and therefor is invalid… there can be no Nothing.”
Diversion 2:
When it comes to things like relationships, one can easily see how “brother of”, “father of”, “sister of” etc. are relational. The concept’s referent is something in reality, but not something which would exist independently of the things who have those relationships. As such if all living things were to cease to exist, the term, sister would be meaningless.
If you know that in history there once was a family with 23 sisters, then the idea of 22nd sister is not hard to understand. It is a valid relational concept. Now if I note that I do not have a 22nd sister, what am I saying?
Am I saying that my 22nd sister is NOTHING, as if NOTHING were something I could call my sister? Would that “not so great” philosopher come to me and say:
“You cannot speak as though there is Sheer Nothing in your 22nd sister position. There is no Nothing.”
Non-diversion:
There is a type of philosopher who sees the above, and while knowing space is (conceptually at least) a continuum, and not an existent (i.e. relational only) will still argue, on PHILOSOPHIC grounds that there can be no “holes” in the universe. i.e. no places (whether to speak of points, positions, or volumes) where there is sheer nothing, because to do so (they would claim) would be to attempt to invoke sheer Nothing as if it were a something, but it is not.
This clearly misses the boat… and unless one could prove that all momenta MUST be occupied, or that I actually HAVE a 22nd sister (all potential relationships must be occupied), one CANNOT argue that there cannot be spaces (previously occupied relationships) which no entity occupies or extend into FROM A PHILOSOPHICAL basis.
Nothing in philosophy can say that it is invalid to say “there is a 1mm diameter spherical hole at the center of this steel ball in which there is nothing.”
[Only the special sciences could do so, and only with reference to evidence actual existents or portions thereof (fields, forces, particles, radiation etc.) are there.]