The following is by Leonard Peikoff, acolyte of Ayn Rand:

Every argument for God and every attribute ascribed to Him rests on a false metaphysical premise. None can survive for a moment on a correct metaphysics . . . .

Existence exists, and only existence exists. Existence is a primary: it is uncreated, indestructible, eternal. So if you are to postulate something beyond existence—some supernatural realm—you must do it by openly denying reason, dispensing with definitions, proofs, arguments, and saying flatly, “To Hell with argument, I have faith.” That, of course, is a willful rejection of reason.

Objectivism advocates reason as man’s sole means of knowledge, and therefore, for the reasons I have already given, it is atheist. It denies any supernatural dimension presented as a contradiction of nature, of existence. This applies not only to God, but also to every variant of the supernatural ever advocated or to be advocated. In other words, we accept reality, and that’s all.

Most professional philosophers consider Rand and Co. not worth discussing.  Nihil philosophicum a nobis alienum putamus, however, is one of my mottoes (see here for explanation); so I will engage the Randian ideas to see if they generate any light. But I will try to avoid the polemical and tabloid style Rand and friends favor.  

In the quotation above we meet once again our old friend 'Existence exists.'  Ayn Rand & Co. use 'existence' to refer to what exists, not to something — a property perhaps — in virtue of which existents exist.  Now It cannot be denied that all existing things exist, and that only existing things exist.  This is entirely trivial, a logical truth.  Anyone who denies it embraces the following formal-logical contradiction:  There are existing things that do not exist. We should all agree, then, with the first sentence of the second paragraph. Existence exists!

So far, so good. 

But then Peikoff tells us that to postulate something supernatural such as God is "to postulate something beyond existence."  Now it may well be that there is no God or anything beyond nature.  But how would it follow that there is something beyond existence, i.e., beyond what exists, if God exists? It may well be that everything that exists is a thing of nature.   Distinguished philosophers have held that reality is exhausted by the space-time system and its contents.  But the nonexistence of God or of so-called abstract objects does not follow from the triviality that everything that exists exists.  Does it take a genius to see that the following argument is invalid?

1. Existence exists.

ergo

2. God does not exist.

One cannot derive a substantive metaphysical conclusion from a mere tautology. No doubt, whatever exists exists.  But one cannot exclude God from the company of what exists by asserting the tautology that whatever exists exists.  The above argument is a non sequitur.  Here is an example of a valid argument:

3. Nothing supernatural exists.

4. God is supernatural.

ergo

5. God does not exist.

For Peikoff to get the result he wants, the nonexistence of God, from the premise 'Existence exists,' he must conflate 'existence' with 'natural existence.' Instead of saying "only existence exists," he should have said 'only natural existence exists.' But then he would lose the self-evidence of "Existence exists and only existence exists."  And he would also be begging the question.

Conflating a trivial self-evident thesis with a nontrivial controversial thesis has all the advantages of theft over honest toil as Russell said in a different connection.  It would take a certain amount of honest philosophical toil to construct a really good argument for the nonexistence of any and all supernatural entities.  But terminological mischief is easy.  What Peikoff seems to be doing above is smuggling the nonexistence of the supernatural into the term 'existence'  Clearly, this is an intellectually disreputable move.  

It is like a bad ontological argument in reverse.  On one bad version of the ontological argument, one defines God into existence by smuggling the notion of existence into the concept of God and then announcing that since we have the concept of God, God must exist.  Peikoff is doing the opposite: he defines God and the supernatural out of existence by importing their nonexistence into the term 'existence.'  But you can no more define God out of existence than you can define him into existence.  

An Objection and a Reply

"You are missing something important.  The claim that existence exists is the claim that whatever exists, exists independently of all consciousness, including divine consciousness.  It is a substantive claim, not a mere tautology.  It is a claim about the nature of existence.  It asserts the primacy of existence over consciousness.  It is a statement of extreme metaphysical realism: to exist is to be independent of all minds and their states. This axiom implies that no existents are created or caused to exist by a mind.   But then God, as the creator of everything distinct from himself, cannot exist."

Here, then, is a Rand-inspired argument for the nonexistence of God resting on Rand's axiom of existence.

1) To exist is to exist independently of all consciousness. (The notorious axiom)

2) Things other than God exist. (Obviously true)

Therefore

3) Things other than God exist independently of all consciousness. (Follows from 1 and 2)

4) If God exists, then it is not the case that everything that exists exists independently of all consciousness. (True given the classical conception of God as creator according to which whatever exists that is not God is maintained in existence moment-by-moment by God's creative power.)

Therefore

5) God does not exist. (Follows from 3 and 4 by standard logical rules including modus tollens)

This argument stands and falls with its first premise. Why should we accept it?  It is not self-evident.  Its negation — some items that exist depend for their existence on consciousness — is not a contradiction. Indeed, the negation is true: my current headache pain exists but it would not not exist were I not conscious of it.  My felt pain depends for its existence on consciousness.

Note also that the argument can be run in reverse with no breach of logical propriety. Simply deny the conclusion and then infer the negation of the initial premise. In brief: if God exists, then Rand's existence axiom is false.  This shows that the argument is not rationally compelling. Of course, the argument run in reverse is also not rationally compelling. So we have a stand-off.

We read above that existence, i.e. existents, are uncreated, indestructible, and eternal.  Well, if there is no God, then existents are uncreated.  But how could they be indestructible?  Is the Moon indestructible? Obviously not.  Is there anything in nature that is indestructible? No. So what might Rand or rather Peikoff mean by his strange assertion?  Does he mean that, while each natural item is destructible, it is 'indestructible' that there be some natural items or other? 

And how can natural items be eternal? What is eternal is outside of time. But everything in nature in in time. Perhaps he means that everything in nature is omnitemporal, i.e., existent at every time. But the Moon did not always exist and will not always exist.

I conclude that the Randian existence axiom does not bear up well under scrutiny. Classical theism has its own problems to which I will be returning.

(Rand below looks a little like Nancy "the Ripper" Pelosi. Both leave a lot to be desired character-wise, but Rand is sharp as a tack while Pelosi is dumb as a post.)