I've can't keep track of what the disagreement here is precisely anymore. Why don't we table the discussion on whether there are colors for a moment and address an easier question: Are there chairs?
Well, of course there are chairs. I'm sitting on one right now!
But providing necessary and sufficient conditions for what is and is not a chair is no easy feat. Certainly a chair is designed to be sat on. Except there are toy chairs which are not meant to be sat on. And maybe art chairs that are also not designed to be sat on, but which everyone would recognize as a chair. There are also artistic representations of chairs, that everyone might recognize as a representation of a chair. But in the case of a Picasso representation of a chair, it might be difficult to ascertain how people who might live in this represented world might sit in the chair.
Of course, representations of chairs are not chairs, so it doesn't directly address the issue of whether chairs exists, but it does address the issue of whether representations of chairs exists (they do!) and understanding this is, I believe, important to our understanding of what chairs are.
To make matters more complicated, not everything that is meant to be sat on is a chair. There are stools, sofas, benches, etc.
So how do we know what is and isn't a chair? Well most of us can tell just by looking at something whether or not it is a chair. How do we do this? There's a simple answer to this and a complex one. The simple answer is that we have complex brains and perceptual organs with sophisticated information processing abilities that allow us to classify things into chairs and non-chairs. The complex answer is a very detailed model of how this particular information processing works.
There are of course some complications. For some physical objects, we might not be able to decide whether something is a chair or not. For other objects, we might be sure that something is a chair, but we might be surprised to learn that other people completely disagree on the object's chairness. For such objects, there may be no fact of the matter on whether the object is a chair.
Now let us consider animals. Are there any animals that could be trained to identify chairs from non-chairs. E.g., we might try with dogs. E.g., we could train some dogs that it's okay for them to poop on chairs and only on chairs. We could then figure out what a dog's notion of a chair is from what it will and won't poop on.
I'm sure that we could successfully achieve this goal for chairs that sit squarely in the center of chairness. But I feel confident, that dogs would be thrown off of by more artsy chairs. And perhaps by things that are more like stools with arms than chairs, etc. Sure we might keep trying to train them using art chairs and chair-like stools, etc., but I feel pretty confident that they would ultimately not end up having the same conception of chairs that humans do. I believe that we would learn with enough effort that no real animal (other than the human animal) is ever going to be able to properly distinguish chairs from non-chairs, despite the fact that chairs exist.
Now let's suppose that some aliens visit the Earth, and they want to know all about us. In particular, they are really interested in our notion of chairs, because they are having a hard time fathoming that chairs really exist. To them, our classification seems completely arbitrary. Why is one thing a stool and not a chair, and another thing a chair, even though it's in a museum and is not something that any human could comfortably sit on at all? Maybe these aliens with enough effort will eventually be able to distinguish chairs from non-chairs almost as well as humans. Or maybe they won't because their senses and their brains just work too differently from ours to be able to do so.
If they are very clever aliens, they might reverse engineer our brains, figure out the software contained therein, and leave Earth happy knowing that they have solved the mystery of what a chair is and now convinced that they do exist. Even if they can't classify chairs from non-chairs themselves, they can now build machines to do this classification for them. Once they have done this, they return happily to their home planet and program their factories to churn out all sorts of different kinds of chairs so that they can give them to each other as cool novelty gifts during their celebrations of Zmas.
Now rerun this argument mutatis mutandis for colors, and you will readily see that colors exist too, even though it might be very problematic for other creatures to distinguish colors as we do.