Is it something over and above (to use David Pears' words) “the subject which is living this mental life” or “the subject which is having these visual impressions”? Surely some thing needs to have a mental life or have visual impressions. Or do we just intuitively presume that there needs to be a subject of a mental life or a subject of visual impressions?
Subjects in subject-predicate expressions are the subjects of predication. Can we predicate anything of the subject? We can predicate experiences or cognitive operations of the subject. For example, when I say "The rose is red", I'm predicating an attribute (or property) of the rose. However, experiences or cognitive operations aren't the same kind of predicate as “red”. These are things the subject does or carries out. The rose, on the other hand, doesn't do red, carry out red or experience red. (This is like saying “John works on the farm” rather than “John is tall”.) Do we have predicates of the latter kind which can be predicated of the subject? We can say what the subject does or what the subject experiences; though can we attribute properties to the subject? It's these kinds of criteria of identity that are missing from the subject. No; the subject has no intrinsic identity-conditions. However, if the subject has vanished, then how can it be the subject of experiences or of cognitive operations? Something must surely experience things and carry out cognitive operations.