Leonard Peikoff, Objectivism: The Philosophy of Ayn Rand, Meridian 1993, p. 31:
"Supernatural," etymologically, means that which is above or beyond nature. "Nature," in turn denotes existence viewed friom a certain perspective. Nature is existence regarded as a system of interconnected entities governed by law; it is the universe of entities acting and interacting in accordance with their identities. What then is a "super-nature"? It would have to be a form of existence beyond existence; a thing beyond entities; a something beyond identity.
The idea of the "supernatural" is an assault on everything man knows about reality. It is a contradiction of every essential of a rational metaphysics. It represents a rejection of the basic axioms of philosophy . . . .
Is this a good argument? That alone is the question.
It is clear that that there cannot exist anything beyond existence: There exists an x such that x does not exist is a formal-logical or narrowly-logical contradiction. So far so good. And let us cheerfully acquiesce in Peikoff's definition of 'supernatural' as that which is beyond nature. We also grant that the concept of existence is "the widest of all concepts," one that "subsumes everything." (p. 5) We can even grant that nature is existing things regarded as a system of causally interacting entities governed by natural laws.
All of this granted, it still does not follow that a supernatural entity is an entity beyond entities or an existent beyond existents. For if the concept of existence "subsumes everything" as we just quoted Peikoff as saying, then it subsumes any supernatural entities there might be, whether God or unexemplified universals, or Fregean propositions, or mathematical sets, or Cartesian thinking substances, or states of consciousness if they are naturalistically irreducible, or . . . . All of these categories are categories of the supernatural given Peikoff's use of the term. Now these categeories might be empty, but one cannot show them to be empty by intoning the formal-logical truth that nothing exists beyond existence.
I submit that anyone who carefully reads the above passage and thinks about it objectively will be able to see that Peikoff's argument is a blatant non sequitur. He is making one or the other of the following mistakes. He is either attempting to answer a substantive philosophical question by terminological fiat, or he is equivocating on 'existence.' I will explain each of these in turn.
A. It is illegitimate to attempt to answer a philosophical question by rigging one's terminology in such a way that the answer 'falls out' of the terminology. One cannot legislate the supernatural out of existence by using 'existence' in such a way that only natural items exist. Equally, one cannot legislate the supernatural into existence by a similar move. For example, one cannot define God into existence by saying that God is by definition an existent being since a nonexistent God is not God, and God is God (A is A!).
B. If Peikoff is not making the first mistake, then he is equivocating on 'existence.' That is, he using it in two different senses. He is using it both as the "widest of all concepts" to cover everything that exists, but also in a narrow sense to cover only natural existents.
It is trivially true that there is nothing natural beyond nature, and nothing existent beyond existence. But these trivialities do not supply anyone with a good reason to reject the supernatural. It is because of such shoddy reasoning as I have just exposed that most philosophers have a hard time taking Objectivism seriously. Objectivists should take this in a constructive way: if you want your ideas to gain wider acceptance, come up with better arguments for them.
(Don't complain that I've 'taken Peikoff's argument out of context.' It stands on its own, and if it is bad, no amount of further context will improve it. If I quoted Descartes' Meditation V ontological argument and showed why it is unconvincing would you complain that I had taken it out of context?)