The axiomatic proposition, existence exists, in the Objectivist metaphysics and the discovery, in science, of the existence of a physical world are not synonymous.
Here is Ayn Rand's full discussion of why they are not. It's from Appendix - Axiomatic Concepts, Introduction To Objectivist Epistemology, Expanded 2nd Edition:
-- The discussion begins here --
The Physical World
Prof. K: Some philosophers treat our knowledge that existence exists as equivalent to our knowledge that there is a physical world. They hold that to know that existence exists, and is what it is independently of our perceiving it, is to know that it is different in kind from consciousness - to know that things exist which possess characteristics which no consciousness could possess - for example, spatial extension or weight. Then they claim that the propositions "existence exists" and "there is a physical world" are, if not synonymous, two perspectives on the same fact, such that if the first is an axiom, then so is the second. Is any variant of this position consistent with the Objectivist view of axioms and axiomatic concepts?
Ayn Rand: The answer is: no, emphatically. Not consistent in any way whatever. Now let me elaborate.
When you say "existence exists," you are not saying that the physical world exists, because the literal meaning of the term "physical world" involves a very sophisticated piece of scientific knowledge at which logically and chronologically you would have to arrive much later.
As to the chronological aspect, the construct that you describe here is totally impossible psychologically. You say that to grasp that something exists is to know that things exist which possess characteristics which no consciousness could possibly possess, such as extension and weight. You are talking about an enormously sophisticated level of knowledge. And you are assuming that first a man grasps that he's conscious, à la Descartes, and then he decides, "But there are certain things which have properties which consciousness doesn't have." Nothing could be further from the truth.
The simplest way to begin an answer is to point out that animals, who do perceive reality or existence, have absolutely no concept of their own consciousness. The enormous distinction between man and animals here is self-consciousness. An animal does not have the capacity to isolate critically the fact that there is something and he is conscious of it. How does that apply to man? In this crucial sense: neither does an infant. Why is it metaphysically important? Because there is no such thing as a consciousness per se, apart from that of which it is conscious. And therefore no entity could conceivably be conscious first of the fact that he is conscious and then grasp, "Oh, I'm conscious of something."
You see, this is a complete inversion of the meaning of the concepts. You can become aware of the fact that you are conscious only after the fact of performing an act of consciousness. Only after you have become conscious of something - and in fact long after - and you identify the fact that it is some function in your mind that is performing this process of awareness. Only at a relatively advanced age - after, say, months or perhaps a full year - can an infant grasp the fact that if he closes his eyes he doesn't see, if he opens them he sees. And that if he closes off his ears, then he doesn't hear. That's the beginning of his grasp of the fact that something operates inside of him that permits the process of awareness. But that is an enormously sophisticated step of self-consciousness. You cannot begin by saying, "I'm conscious" and then ask, "Of what?" It's a contradiction - in effect, a process of concept-stealing.
As to such characteristics as extension and weight, how would you grasp those ahead of grasping the existence of an outside world? Because the implication of your question is that you grasp that it is a physical world by means of observing that it has certain properties which your consciousness does not possess. But you could not have any concept of those properties ahead of grasping a physical world, nor could you say, "My consciousness doesn't possess weight or extension," ahead of grasping that there is something outside which does possess them.
But now what's the difference between saying "existence exists" and "the physical world exists"? "Existence exists" does not specify what exists. It is a formula which would cover the first sensation of an infant or the most complex knowledge of a scientist. It applies equally to both. It is only the fact of recognizing: there is something. This comes before you grasp that you are performing an act of consciousness. It's only the recognition that something exists. By the time you say that it's a world, and it's a physical world, you need to know much more. Because you can't say "physical world" before you have grasped, self-consciously, the process of awareness and have said, "Well, there are such existents as mental events, like thinking or memories or emotions, which are not physical; they are existents, but of a different kind: they are certain states or processes of my consciousness, my faculty of grasping the existence of that outside world." And the next step is: "What is that outside world made of?"
The concept "matter," which we all take for granted, is an enormously complex scientific concept. And I think it was probably one of the greatest achievements of thinkers ever to arrive at the concept "matter," and to recognize that that is what the physical world outside is composed of, and that's what we mean by the term "physical."
Now observe that a savage doesn't have a concept of "matter." He believes that reality is like his own consciousness, only it is in the power of supernatural creatures or gods or demons who manipulate it. What permits this kind of mysticism? Precisely the absence of the concept "physical world" or "matter." Now those concepts, in historical development and in the development of an individual consciousness, come very late - by which I mean they are concepts that require a long development before one can grasp them. And yet a savage grasps that existence exists. He doesn't grasp all the implications of it. Nor does he grasp the Law of Identity. But that something exists, with which he deals, even he grasps that. To the extent to which he is able to hunt or to support his life or pray to his gods, he is admitting implicitly the existence of something.
So you see the axiom "existence exists" embraces all those stages of knowledge, implicit or explicit. Whereas the concept "the physical world exists" is a very sophisticated scientific statement.
-- The discussion ends here --
Given the above, it would be wrong for any philosopher, including an Objectivist one, to say "on philosophical grounds" that there can never be a perfect vacuum where nothing physical exists.
Why? Because philosophy has nothing to say about anything in the physical world (including a "hole" in it with no matter) except this: whatever the physical world contains, they exist.
In other words, if such a "hole" were to exist, it would not contradict, in any way, the (first) axiom of existence of the Objectivist metaphysics.
