The following can happen. You see yourself but without self-recognition. You see yourself, but not as yourself. Suppose you walk into a room which unbeknownst to you has a mirror covering the far wall. You are slightly alarmed to see a wild-haired man with his fly open approaching you. You are looking at yourself but you don't know it. (The lighting is bad, you've had a few drinks . . . .) You think to yourself
1. That man has his fly open!
2. I have my fly open!
Now these propositions -- assuming they are propositions -- are obviously different. For one thing, they have different behavioral consequences. I can believe the first without taking action with respect to my fly, or any fly. (I'm certainly not going to go near the other guy's fly.) But if I believe the second I will most assuredly button my fly, or pull up my zipper.
So it seems clear that (1) and (2) are different propositions. I can believe one without believing the other. But how can this be given the plain fact that 'that man' and 'I' refer to the same man? Both propositions predicate the same property of the same subject. So what makes them distinct propositions?
I know what your knee-jerk response will be. You will say that, while 'I' and 'that man' have the same referent, they differ in sense just like 'Hesperus' and 'Phosphorus.' Just as one can believe that Hesperus is F without believing that Phosphorus is F despite the identity of the two, one can believe that (1) without believing that (2) despite the fact that the subject terms are coreferential.
The trouble with this response is that it requires special 'I'-senses, and indeed a different one for each user of the first-person singular pronoun. These go together with special 'I'-propositions which are a species of indexical proposition. When I believe that I am F, I refer to myself via a special Fregean sense which has the following property: it is necessarily a mode of presentation of me alone. We can also think of this 'I'-sense as an individual concept or haecceity-concept. It is a concept such that, if it is instantiated, it is instantiated (i) by me, (ii) by nothing distinct from me, (iii) and by the same person in every possible world in which it is instantiated.
But what on earth (or on Twin Earth) could this concept be, and how could I grasp it? The concept has to 'pin me down' in every possible world in which I exist. It has to capture my very thisness, or, in Latin, my haecceitas. But a better Latin word is ipseitas, ipseity, selfhood, my being a self, this one and no other. In plain old Anglo-Saxon it is the concept of me-ness, the concept of being me.
The theory, then, is that my awareness that
3. I am that man!
consists in my awareness that the concept expressed by 'I' and the concept expressed by 'that man' are instantiated by one and the same individual. But this theory is no good because, even if my use of 'I' expresses an haecceity-concept, that is not a concept I can grasp or understand. Maybe God can grasp my haecceity, but I surely can't. Individuum ineffabile est said the Scholastics, echoing Aristotle. No finite mind can 'eff' the ineffable. The individual in his individuality, in his very haecceity and ipseity, is ineffable.
Self-reference is not routed though sense, however things may stand with respect to other-reference. When I refer to myself using the first-person singular pronoun, I do not refer to myself via a Fregean sense.
So here is the problem expressed as an aporetic pentad:
a. (1) and (2) express different Fregean propositions.
b. If two Fregean propositions are different, then they must differ in a constituent.
c. The difference can only reside in a difference in subject constituents.
d. The subject constituent of (2) is ineffable.
e. No sense (mode of presentation) or humanly-graspable concept can be ineffable.
This pentad is inconsistent: (a)-(d), taken together, entail the negation of (e). The only limb that has a chance of being false is (a). One could say that (1) and (2), though clearly different, are not different by expressing different Fregean propositions. But then what would our positive theory have to be?