Consciousness is not a simple property, like “blue”. It has intentionality.

Consciousness is always consciousness of something. This means that all objects of consciousness are known by means solely of its contents.

But since this is so, this divorces consciousness from certainty regarding any real existence either of subject or object.

Why? Since the status of external objects is known only via the contents of consciousness, their ontological status as truly external is undecidable. This was Descartes’ problem.

But likewise, because of this same intentionality, the subject itself is not known as such by the contents of consciousness.

This is so because the contents of consciousness are what is known, they are not what knows. Thus the ontological status of the subject as internal is likewise undecidable.

That is, the intentionality of consciousness divorces us from certainty as to the existence of the subject just as much as it divorces us from certainty as to the existence of external objects.

Since, as a result of the intentionality of consciousness, the existence of both subject and object are ontologically undecidable, there is neither a “subjective” nor an “objective” definition that could be applied to it.