Our non-Aristotelian dreams

I believe that most, maybe even more than 90% of what people tell and write about their (and other people's) dreams is not authentic. Dreams cannot often be described in our common language, common conceptual system. Why? Because our language, our semantics is "Aristotelian", based on presumption that everything is what it is, is identical with itself. A = A. A dog is a dog, a rose is a rose is a rose. A dog is not a cat, a cloud or a chair, at least not at the same time. Of course, not everything can be described and defined in such Aristotelian way. There are things that demand we use a kind of a "fuzzy" logic to describe them. There are chairs that are also to some degree, e.g. 40% tables. But even such a fuzzy thing, even a mythological chimaera, even a cloud or a wave are themselves, are identical to themselves in their definiteness or fuzziness. But in dreams things are sometimes not identical to themselves, they can be 100% A and 100% B at the same time. Oddly enough, the person dreaming doesn't usually notice any contradiction, any absurdity here. I remember having dreamed of a place that was both a room in a house with bookshelves standing at the walls, and a town square surrounded by high buildings. How to describe such a scene? How to call these shelves that are also buildings? To describe dreams we should invent a different language, use words in an unconventional way. But as a rule, dreams are not meant to be communicated extensively and exactly. Nobody can check whether the description of a dream is correct or not. Dreams belong to our private world, not to the world we share with others. And when we want or to have to share it with others, it is difficult, sometimes even impossible. But can these difficulties, these problems have a sign of our need of something really private, of our need to isolate ourselves from communication, to live in a world that does belong only to us? Can the dreams also be a means to escape from the inexorable Aristotelian logic of our everyday world where we everything has to be itself, where we too have to be ourselves, having no chance to escape from our identity that is largely imposed on us?