I think I get it now. There's
nothing and the
concept of nothing. That
nothing can't be a
concept and it can't be according to its definition doesn't contradict the existence of the
concept of nothing because for that to happen
nothing should be
the concept of nothing and that isn't the case just like an apple isn't the concept of an apple. That's your reasoning in a nutshell or as much of it I could decipher.
However...
Let's consider the matter of how we form concepts as according to you and as I've concurred there does exist a
concept of nothing. How do we conceive of
nothing in our minds? As the definition clearly shows,
nothing is defined negatively as not this, not that, not that either, so and so forth.
Nothing itself is not actually held in the mind like an apple is. The concept of apple evokes an image of an apple, perhaps even the way it stimulates our taste buds, and the concept of the square root of 2, at least for me, makes me think of the number 1.414... but try a similar thing with
nothing and you can't do it. There's nothing a mind can do, try as it might in every way possible, to "hold in the mind" that which is
nothing. Doesn't this mean, that
nothing isn't, as we believed, a concept? If you disagree and are of the opinion that there's a
concept of nothing then what must be acknowledged, at a minimum, is that the
concept of nothing is vastly different from the
concept of an apple.
Does this difference between
nothing and an apple matter to our discussion? When do we
define in the negative? When is it that we resort to such a tactic? This particular defining technique is usually employed when we're out of our depths which, unfortunately, happens more often than not if I'm anywhere near the ballpark. For instance I recall skimming through a Wikipedia article titled "Apophatic Theology" which, perhaps after acknowledging our near-complete ignorance of what we mean by "god", attempts to approach the divine by a method of denial, listing out as it were the qualities/properties that are
not god. If there's any underlying similarity between
nothing and god viewed thus, it must be that we
don't know what either of them are.
This brings us back to what I've been trying to say, if not in its entirety at least in part, that
nothing can't be a concept or if that doesn't go down well with you the
concept of nothing is enormously different from, say, the concept of an apple. The former is approached through negation and the latter through affirmation. One could say though that that's the nature of the beast.
Nothing is, at its heart, the negation/denial of everything there is and that's that!
What I'm getting at is, it seems, that
nothing is the mother of all negations -
not anything. So, the answer to a question that's framed thus, "Is
nothing this/that/etc.?", should be "no". Hence, the answer to the question, "Is
nothing that which can be conceived of in the mind?" should be "no". If one claims the answer is "yes" then
nothing can't be
not anything anymore for it's
something that can be conceived of in the mind.
Thus,
nothing can't be that which can be conceived of but that there's a definition of
nothing implies that we've conceived of it. That's the paradox!