If consciousness were a particular thing, process or quality, it could be fully but concisely defined, and it would be a matter of objective fact whether a given entity is or is not conscious.
Consciousness is not a thing-in-itself (or process, or quality), so, while concise, true statements can be made about it, these will only concern an aspect of it, or at best a subset of its aspects. A comprehensive account of consciousness cannot be concise, due to its multiple facets. Similarly, there is no single criterion by which an entity can be judged conscious or not.
A list of prominent theorists who take this view, and of theories that are consistent with it, should be appended here.