If you describe something as indescribable, haven’t you already described it?

Great question!

Some tools—like hammers and wrenches—can be used in different ways to achieve all sorts of things. Words are tools. So I’m going to approach your question by considering three different ways of using the word “indescribable”. And these will give me three different answers to your question.

First. We sometimes use “indescribable” in a figurative, exaggerated, way. 
For example: I might say “When I saw her win, I was indescribably happy!” Perhaps I really just intended to convey something like: “I was incredibly happy!” In that case, maybe what I said was literally false since I could quite easily have described it. But we know what I mean.
It might help to compare this with someone who says, “I was literally over the moon!” Again, this is literally false, but we know what they meant. (And anyway, who said that “literally” must always be understood literally?)

Second. A more subtle case is when we use “indescribable” to indicate that we can’t be fully precise about something. 
For example: suppose I see a sunset and tell you the next morning “it was indescribably beautiful”. I’ve clearly tried to give you some description of the beauty of the sunset. So, am I contradicting myself?

Probably not. I’m probably saying that the sunset was beautiful, but that I cannot fully convey to you just how beautiful the sunset was, or in what ways it was beautiful. The sentiment here might be something like: “no one could appreciate its precise beauty unless they saw it for themselves.” This kind of phrase can convey something profound about the beauty of the sunset, but it still doesn’t allow you to understand its precise beauty, so there’s no contradiction.

This sort of use of “indescribable” (or “indescribably”) arises quite often in aesthetics, i.e. in areas where we are discussing either natural or human-made beauty. And that shouldn’t really be surprising: we shouldn’t expect that we can always translate (our reactions to) art into words!

Third. The final use of “indescribable” is the murkiest of all, but (for me) the most intriguing. This is when we want to convey that something is fully unthinkable. 
Suppose I tell you: “there is an object which is entirely indescribable”. But I don’t want you to think that I mean “indescribable” in the first sense (i.e. figuratively) or the second sense (i.e. to indicate that a certain level of precision is impossible). So I add: “it is absolutely impossible to represent this object at all: no one could possibly think about it, or refer to it, or describe it, in any way whatsoever.”

I am clearly contradicting myself, in some sense. After all: I am trying to say something about this (weird) object, whilst simultaneously insisting that it is impossible for anyone to succeed in saying anything about that object. At the very least, you certainly shouldn't believe what I’ve told you. In fact, for just the same reason, I shouldn’t believe what I said either. And this generalises: no one should believe that there is an absolutely unrepresentable object.

But that conclusion might seem very strange. Ask yourself: couldn’t there be some object which is so strange that it is absolutely unrepresentable? In plenty of ways, humans are very limited animals; we’re just hairless apes who wear shoes. So the idea that we can represent each and every object there is might seem like a bit of a cosmic-scale coincidence.

For what it’s worth, I do think that everything can be represented, and I don’t think that this is a cosmic-scale coincidence. But I’d rather leave you with this puzzle than try to answer it, since I think it’s one of the most interesting puzzles there is!