Does existence exist?

Existence exists.
Ayn Rand
Existence does not exist.
Cardinal Cajetan
Both Rand’s statement and Cajetan’s sound very odd at first blush.  What does it mean to say that existence exists?  Isn’t that like saying that stoneness is a stone or humanness is a human being, neither of which is true?  On the other hand, what does it mean to say that existence does not exist?  Isn’t that like saying that there is nothing that exists, which is also manifestly false?  Yet how could both of these statements be false?Suppose we interpreted them as the contraries “All existing things exist” and “No existing things exist.”  In that case, they could both be false if we supposed that there are at least some existing things that exist and some that do not exist.  But “Some existing things do not exist” is self-contradictory, and indeed “No existing things exist” seems no less so.  Moreover, “All existing things exist” itself seems as obviously true as a statement could be.  But it is also trivially true, a mere tautology.  And in any event, surely Cajetan did not mean to be uttering an obvious falsehood, nor Rand a trivial truth.  So, at second blush the statements might continue to seem very odd. 
Let’s try third blush.  Suppose we read “exists” in Fregean terms, as captured by the existential quantifier.  Then both statements come out as ill-formed formulae, complete gibberish.  Rand’s statement comes out as something like “There is an x such that there is an x such that…” and Cajetan’s as something like “It is not the case that there is an x such that there is an x such that…”  This would be to read Rand and Cajetan the way Anthony Kenny reads Aquinas in his book Aquinas on Being , and it is about as fair a reading of them as Kenny’s is of Aquinas -- which, as Gyula Klima pointed out, is not fair at all. 
Fourth blush is the charm.  In fact what each writer meant is perfectly intelligible when their statements are understood in context.  Rand’s remark is from her book Introduction to Objectivist Epistemology .  As Wallace Matson remarks in his essay “Rand on Concepts” in Douglas Den Uyl and Douglas Rasmussen’s anthology The Philosophic Thought of Ayn Rand , “I take her to mean by this that there are things independent of our thinking about them” (p. 23).  Rand takes this to be “axiomatic” in the sense that while it cannot be directly proved neither can it coherently be denied.  Why not?  Den Uyl and Rasmussen explore the theme in their own essay in the volume, “Ayn Rand’s Realism,” in which they note that for Rand since consciousness is always of or directed at an object, it is self-evident that something exists -- namely (as Rand states in the Foreword to the book) the object of one’s consciousness and oneself as the subject of consciousness.
Naturally one can raise questions about this.  Granted that the object of one’s consciousness exists qua object -- i.e. “intentionally” -- it doesn’t follow that it exists in mind-independent reality.  (A hallucinated tree certainly “exists,” but only qua hallucination, not qua material object.)  Granted that there is consciousness, a Lichtenberg or a Hume would still question -- not plausibly, but they would question -- whether there is an abiding self to serve as the subject of consciousness.  But even in this case Rand would arguably still have something that cannot coherently be denied, namely the existence at least of consciousness qua intentional.  More to the present point, “Existence exists,” understood merely as a claim to the effect that the existence of something or other cannot coherently be denied, is certainly intelligible.  But what does that tell us about mind-independent reality?
That brings us to Cajetan’s statement.  Jacques Maritain cites it at p. 20 of his A Preface to Metaphysics , when commenting on Cajetan’s commentary on Aquinas’s On Being and Essence .  Aquinas famously argues in that work that there is a real distinction between the essenceof a thing (what it is) and its existence (that it is).  When you perceive a tree what you perceive is being as confined, as it were, within that particular essence, the essence of that tree.  The intellect goes on to abstract the universal pattern treeness, and also to consider being as such.  But just as treeness in the abstract is different from the essence of this particular individual tree, so too is being as such, considered in the abstract or merely conceptually, different from the existence (or “act of existing”) of this particular individual tree.
Now as I read Maritain reading Cajetan, what the thesis that “Existence does not exist” comes to is simply the point that existence considered in the abstract by the intellect or conceptually is not the same thing as the actual existence of a concrete, mind-independent object.  And that is surely correct.  The point of making the point, for Maritain anyway, is (again, as I read him) to emphasize the distinction between Thomism and the Leibnizian sort of rationalism that holds that the order of mind-independent reality can be read off from the order of concepts.  This is, for the Thomist, one reason (not the only one) for insisting on the real distinction between essence and existence.  To deny the real distinction tends either to collapse essence into existence or collapse existence into essence.  Leibnizian rationalism tends in the latter direction -- collapsing existence into essence, where essences in turn collapse into concepts, which are essentially mind-dependent -- and this in turn tends in just the sort of idealist direction that was, historically, the sequel to rationalism as it gave way to Kantianism, Hegelianism, and the like. 
And as it happens, Rand, according to Den Uyl and Rasmussen (on p. 5 of the essay cited above), would, given her thesis that “Existence exists,” deny the Thomistic doctrine of the real distinction.  The idea is that to know the essence or “what-ness” of a thing is to know that it exists, and no further explanation of its existence is needed.  Hence (so the line of thought seems to go) if I know, just from consciousness of such-and-such, what such-and-such is, then ipso facto I know the existence of such-and-such.  Hence if I cannot coherently deny consciousness of such-and-such, then I cannot coherently deny that “Existence exists.”  Or, again, so the argument seems to go. 
(Note that this would also help explain Rand’s atheism: If the existence of a contingent thing is not really distinct from its essence, so that existence needn’t be added to the essence of a thing in order for the thing to be actual, then the sort of argument Aquinas gives in On Being and Essence for the existence of God -- understood as ipsum esse subsistens or subsistent being itself -- as the source of the very existence of things, is blocked.)
If this is Rand’s view then she is definitely in conflict with Cajetan and other Thomists, just as the statements from them quoted at the beginning suggests (though for reasons much more complicated than the two statements considered in isolation would suggest).  For she seems at least implicitly committed to the view that the order of mind-independent reality can be read off from the order of concepts.  How can they differ so radically given that Rand on the one hand and Cajetan and other Thomists on the other are all Aristotelians?  Den Uyl and Rasmussen give us a clue when they tell us (p. 5) that Rand’s Aristotelianism is much like that of William of Ockham, who also denied the real distinction.  And Ockham, of course, is for Thomists the man who perhaps more than any other set in motion the disintegration of the Aristotelian-Scholastic tradition.
The irony is that Rand apparently adopted a position that in fact tends toward idealism in the course of trying to defend a realist metaphysics opposedto idealism.  But then, as Pius X could have told her, we “cannot set St. Thomas aside, especially in metaphysical questions, without grave detriment.”