When natural languages first had need to refer to concepts as such, this need was so limited and so vaguely understood that the very same term would refer both to a concept and to that to which the concept pointed. A horse is a mammal. and A horse is on my lawn. seem superficially to be statements of the same sort. Some people, sensing a difference, declare that the first statement is essential, while the second is accidental, but this way of speaking and of writing seems to treat a horse as referring in both cases to the same thing, and embroils us in conflicts over which attributes are essential, which are accidental, and by what methods we all ought to agree on a resolution. The primary difference between the two statements is that in A horse is a mammal. the term a horse typically refers to a concept, whereäs in A horse is on my lawn. the term a horse usually refers to something to which the concept corresponds, which we may call an instantiation of the concept.

I say usually because in theory someone might use a horse only for creatures who were, amongst other things, found on her lawn; but we understand that this practice is not usual, and can find the difference between concept and instantiation by considering usual practice. At the same time, we can see that struggles about essential and accidental attributes are largely rooted in different people simply using related but different concepts.

Even people who are careful to indicate a distinction between some Y and the concept of Y when Y is not itself a concept may fail to do so when it is. But the concept of the concept of X is not the concept of X unless we can find some X which is no more or less than the idea of itself.

From this point, we should see that, to believe that instantiations depend upon their concepts, we must accept an infinite regress. The alternative is not to accept that concepts depend upon that which instantiates them — some concepts are not instantiated — but to understand that concepts must be constructed by employing some thing or things that are not concepts.

In any case, always marking the distinction between concept and instantiation can become a very great burden as we begin to ponder ideas as such, part of which burden would fall upon a reader dealing with compounding of expressions such as the concept of; but, one way or another, we should remember what we are contemplating or discussing.

The confusion in using the same term for concept and instantiation is most acute in existence statements.

The subject in Unicorns do not exist. is the concept of unicorns, not any instantiation of that concept. Grammatically we treat nothing as a something and grammatically we treat non-existence as a property of nothing-as-something. But, underlying this practice, statements about non-existence are really statements that some concepts have no instantiations; if claims about non-existence refer to properties of somethings, then these somethings are concepts. Unicorns do not exist. is not really about unicorns; it is about the idea of unicorns. We can only speak or write of the idea of unicorns.

And, when we speak or write of existence, we are speaking and writing of concepts. The claim Horses exist. is really about the concept, that it is instantiated. Coherent existential claims are no more or less than claims that concepts are instantiated.

That statements of form X exists. unpack to form The concept of X is instantiated. should lead one to recognize that a proper reading of The concept of X exists. unpacks to The concept of the concept of X is instantiated. We don't generally need a concept before we use something that would instantiate it — otherwise the infinite regress of concepts would be needed — but anything that we use is at least potentially an instantiation of multiple concepts. Some might be tempted to conclude that, thus, X exists. needn't refer to the concept of X, and can be unpacked as X is potentially an instantiation of some concept. It may seem doubtful that anyone has ever previously intended such a thing with an existential claim, and certainly existential claims are not usually claims about the ability to find or to construct an idea of a thing said to exist. However, to be potentially an instantiation of some concept is no more or less than to possess properties, so this notion would treat existence as something like a generalization of the concept of property. Still, the formula cannot be adapted to X does not exist. as unpacking it to X is not potentially an instantiation of some concept. is always incoherent when not false, whereäs declarations such as Unicorns do not exist. may be coherent and true. And we are incoherent if by a horse we mean the same thing in A horse has no properties. as in A horse is on the lawn.

I don't propose that we try to reshape our speech and writing nor our work-a-day thinking to distinguish overtly-and-always concept from instantiation. I don't even propose to do so in all philosophic discourse. But, when discussion of existence seems troubling or profound or both, then we may need to bring that distinction to bear.

Some people, encountering a discussion such as the foregoing, will not much attend to it, because they feel certain that they clearly see a truth that contradicts it. I'm going to address propositions of two sorts, mistaken for such truth.

One sort, in which X is something like what is meant by a horse in A horse is on the lawn. says X V because it exists. where the variable V takes the value of a verb. For example, A hot stove burns you because it exists. The first thing to note is that specific values of V that supposedly prove existence aren't universally applicable; we don't say A horse burns you because it exists. Generally, existence is intended to be seen as a necessary but not sufficient condition for X to V. But, when we add conditions to achieve sufficiency, we find that the added conditions (eg, being at a temperature at or above 118°F) are by themselves sufficient, without a mysterious complementary property of existence possessed by X; the notion of such a property results from thoughtlessly confusing a way in which a concept of X may be said to have properties with the way in which X has properties. What we call the horn of a unicorn is itself a concept of a horn.

Though I have encountered at least one would-be follower of Ayn Rand who mistook the tack of because it exists for hers, she made a different mistake. She declared the concept of existence to be irreducible but axiomatic, and that we were to see that it were found and proven in-so-far as a self-contradiction would result from denying Existence exists. However, because we can show that a self-contradiction indeed obtains while interpretting existence and its coördinate terms as in the prior discussion, her attempt to prove the existence of some other concept (profound or otherwise) is a failure.

If we unpack Existence exists. as we can, it is The concept of being an instantiated concept is instantiated. The source of self-contradiction in denial of this proposition is that the concept of a concept being instantiated must have been instantiated for the proposition to be formed, though this proposition could not hold before formation of the concept of existence. And its subjects are not of the sort that Rand and her followers imagined or imagine.

For whatever it's worth, if we grab for potential instantiation then the unpacking is to The concept of potential instantiation is potentially instantiated. that is, more simply put, to A concept can be formed of being the subject of a concept. Again, self-contradiction ensues if we attempt to deny the claim, but in neither expression is the subject for which Rand reached.