0. Am I identical to my (living) body, or to the objectively specifiable person who rejoices under the name 'BV'? Earlier I resoundingly denied this identity, in (rare) agreement with London Ed, but admitted that argument is needed. This post begins the argument. We start with the problem of first-person identity sentences.
1. 'I am I' and 'BV is BV' are logical truths. They have the logical form a = a. They are not particularly puzzling. But 'I am BV' presents a puzzle, one reminiscent of Frege's puzzle concerning informative identity statements. 'I am BV' is not true as a matter of logic, any more than it is true as a matter of logic that the morning star is the evening star. And yet it is presumably true that I am BV where 'am' expresses strict numerical identity. It is not as if 'I' and 'BV' refer to two different entities. Or at least this is not a view we ought to begin by assuming. The proper procedure is to see if we can make sense of 'I am BV' construed as an identity statement. Dualism comes later if it comes at all.
2. Here is a theory. When I say 'I am BV' I am referring to one and the same thing in two different ways, just as, when I say 'The morning star is the evening star' I am referring to one and the same thing (the planet Venus) in two different ways. Expressions have sense and they have reference. Difference of sense is compatible with sameness of reference. The difference in sense of 'morning star' and 'evening star' explains why the identity statement composed of them is informative; the sameness of reference explains the identity statement's truth.
In Frege's famous example, the common referent is the planet Venus. What is the common referent of 'I' and 'BV'? Presumably the common referent is the publicly identifiable person BV. But when BV designates himself by means of the thought or utterance of 'I, he designates BV under the aspect, or via the sense, expressed by 'I,' a semantically irreducible sense that cannot be captured by any expression not containing 'I.'
Here then we seem to have a solution to our problem. In general, one can refer to the same thing in different ways, via different modes of presentation (Darstellungsweisen, in Frege's German). So apply that to the special case of the self. What I refer to when I say 'I' is the same entity that I refer to when I say 'BV' and the same entity that Peter refers to when he says 'BV.' It is just that I refer to the same thing in different ways, a first-person way and third-person way. There is no need to suppose that 'I and 'BV' have numerically distinct referents. There is no need to deny the numerical identity of me and BV. Unfortunately, this Fregean solution is a pseudo-solution. I have two arguments. I'll give one today.
3. Consider the sentence 'I am this body here' uttered by the speaker while pointing to his body. If, in this sentence, 'I' refers to this body here (the body of the speaker), albeit via a Fregean sense distinct from that of 'this body here,' then the sense of 'I,' whatever it might be, must be the sense of a physical thing inasmuch as it must be the mode of presentation of a physical thing. Note that the 'of' in the italicized phrases is a genitivus objectivus. Somehow this 'I'-sense must determine a reference to a physical thing, this body here. But that it is the sense of a physical thing is no part of the sense of 'I.' We understand fully the sense of this term without understanding it to be the sense of a physical thing, a sense that presents or mediates reference to a physical thing. Indeed, considerations adduced by Anscombe and Castaneda show that the 'I'-sense cannot be the sense of a physical thing. For if the sense of 'I' cannot be captured by 'this body here,' then a fortiori it cannot be captured by any other expression designating a physical thing.
The analogy with the morning star/evening star case breaks down. One cannot use 'morning star' and 'evening star' with understanding unless one understands that they refer to physical things, if they refer at all. It is understood a priori that these terms designate physical things if they designate at all; the only question is whether they designate the same physical thing. But one can use the first-person singular pronoun with understanding without knowing whether or not it refers to a physical thing.
In other words, there is nothing in the sense of 'I' to exclude the possibility that it refer to a nonphysical thing, a res cogitans, for example. Descartes' use of 'ego' to refer to a thinking substance did not violate the semantic rules for the use of this term. What's more, if 'I' is a referring term and refers via a Fregean sense, then that sense cannot be the sense of a physical thing.
So that's my first argument against the Fregean approach to the problem of first-person identity sentences. The argument rests on the assumption that 'I' is a referring term. That assumption has been denied by Wittgenstein, and more rigorously, by Anscombe. That denial deserves a separate post. And in that post we ought to rehearse the reasons why 'I' cannot be replaced salva significatione by any such word or phase as 'the person who is now speaking.'