Agnosticism IS the most dishonest position

[Objectivist]

They define the concept "tree" and "rock" not each and every tree and rock.  Again, the role of a concept in cognition is to condense a huge number of units into one.  A unit is one of a group of similar things.  similar things vary only in their specific measurements.  The concept tree subsumes all trees that exist now, have existed, or will ever exist. We don't define each individual tree just as we don't define every unit of the concept "man".  We don't have a definition of Sally or Rob or John because these are not abstractions.  concretes have descriptions, abstractions have definitions.  If we defined every concrete we come upon that would defeat the purpose of definitions, which is the final step in concept formation.  Think of a concept as a file folder, a word as the label on the file folder and a definition as a shorthand description of what's in the folder, enough to let you know what's in there and to differentiate the contents of one folder from another.  Unit economy is the name of the game in cognition.

Right. We form concepts based on our experience. We have direct experience of a number of different things, and abstract these into an abstract concept in the mind. 

As the man said in the 13th century: there is nothing in the mind that wasn't first in the senses. (I'm not completely sure this is true, but we can go with it for now.) And as the same guy was careful to point out, the kind of thing we can sense depends on the kind of bodies we have, and the kind of animals we are. We obviously can't sense some things that other animals can sense, and there's no way we can even comment on what aliens might sense.

 Yes, exactly right.  We form concepts based on perceptions and because the senses work in a causal fashion, the form in which we perceive is dictated by the nature of our senses, their identity.  Yes, other types of organisms sense things based on the nature of their senses.  insects sense ultraviolet light.  Bat's "see" in the dark by means of sonar.  The form in which we perceive things is different but the objects that we sense are the same. 
 

So concepts are abstractions derived from concrete examples.

 Exactly.  And what is an abstraction?  It is the result of a process of measurement omission.  This is crucial to understanding concepts and it's one of Ayn Rand's great achievments in philosophy.  

And since we can't sense many things, it's almost certain that there are things in the universe we can't conceive of. The apophatic theologians are at pains to remind us that, in their opinion, some things about God are this way. Can't be sensed, and can't be conceived of.

But by what means are they aware of this god?  That's the crucial question?  The notion that there are some things about God that can not be sensed, implies that there are some that can.  By what means?

Therefore, in their view, although natural theology demonstrates the existence of God, there is still much about him that can't be conceived of by people. But the fact that we can't conceive of it doesn't mean it's not there.

But it doesn't.  You can't infer a god's existence by looking at nature.  The concept of inference rests on the primacy of existence principle.  The notion of gods assumes the primacy of consciousness principle.  Therefore any attempt to infer gods existence is not only invalid but unsound since the claim that a god exists is self-contradictory.  Inference from nature can only get you to something that is natural.  That's my view anyway. 

In addition, human beings have the ability to form new concepts by recombining elements of previous concepts. You can conceive of an imaginary animal, for example, though you've never seen it, by combining portions of different animals. I have experienced things that were unique, or at least seemed so to me, so I have a concept of uniqueness, and now I can imagine things that don't really exist that are unique -- that is, not members of existing groups.

Here is where I think you go off of the rails.  I see the disconnect between us.  you are using the term conceive here in a much more colloquial way than I am.  I am using the term in a very precise and technical meaning since this is a philosophical discussion. We don't form new concepts by taking parts of other concepts and recombining them.  That's not the way that concepts work.  We don't take parts of other concepts and rearrange them.  We form new concepts by integrating other concepts as wholes into higher-level abstractions.  What you are describing here is imagination which works completely differently.  Concepts are mental integrations of two or more similar things that we perceive organized by isolation of essential characteristics with their specific measurements omitted or abstracted away and united under a single definition.  Imagination is the rearrangement of perceptions into new combinations that don't exist in nature.  It is not a process of abstraction.  Imagination is the creation of an object, albeit a mental object whereas conception is a process of identifying an object.  Imagination is subjective and concepts are objective, at least valid ones are.  If you use the term "conceive" as a package deal the way you are doing it can only lead one to confusion.  This can be avoided by consciously integrating our thinking with the primacy of existence.  Failure to adhere to this principle will only result in the blurring of the lines between the real and the imaginary.  

Well, that's all I have time for now.  I have to go chase after those little green tickets.