Attributes of the Self
I say that I think and I say that I weigh 150 lbs: I ascribe mental and physical characteristics to myself. But there is a significant asymmetry in what I mean by these attributions: when I say that I weigh 150 lbs I am saying that my body weighs 150 lbs, but when I say that I think I am saying that I think. If I weigh 150 lbs, that is only in virtue of the fact that my body does (I would wear approximately 2 lbs if I became a brain in a vat). But it is not in virtue of something else that I think—as it were, the real subject of thinking. You might wonder whether I think in virtue of my mind thinking, as I have a weight in virtue of my body having that weight, but it is surely a category mistake to say that my mind thinks: my mind is not another entity that really does the thinking—it is more like the thinking itself. The Cogito does not read: “I think with my mind, therefore my mind exists”. Nor do I say, “My mind has been thinking hard all day”, which might provoke the retort, “And what were you doing?” Thus the self is the proper subject of mental attributes: I think and see and feel and imagine and will. But the body is the proper subject of physical attributes: my body weighs 150 lbs, my body has a certain shape and size, my body contains a heart and kidneys. I can only be said to have these attributes derivatively, by dint of possessing a certain body. We can use the word “I” loosely to include the body, but strictly speaking it is the body itself that has the attributes predicated. Similarly, we sometimes use “I” even more inclusively, as when one driver says to another, “I almost crashed into you then”; but it would be quite wrong to insist that the referent of “I” here has automobile characteristics (“I have four wheels”). We can register this asymmetry by saying that I have mental attributes directly while I have physical attributes indirectly. 
I am inclined to conclude that sentences like “I weigh 150 lbs” are actually false when taken strictly and literally, though we take such falsehood in our stride, since we know how to correct for it—as in “My body weighs 150 lbs”. And that is not because I have a different weight, such as the weight of my brain; it is because I don’t have any weight. I am not identical to my body, so its weight is not automatically mine; the only sense in which I can truly be said to have weight is that I stand in a certain relation (the “having” relation) to a material body that has weight. For what weight do I have—the weight of my whole body, the weight of my brain, the weight of the part of my brain that generates my mental life? Attributing weight to selves is just a convenient but false way to talk: the referent of “I” is really weightless. But attributing mental characteristics to selves is perfectly fine and proper: the referent of “I” does think, feel, etc. Ordinary language is somewhat misleading, but the deceptive appearance is not deep—we can easily paraphrase the misleading appearance away. According to the paraphrase, it is the body that is the subject of predication; the self comes into it only via the “having” relation. So the self does not instantiate physical attributes in the immediate way that it instantiates mental attributes: I don’t have weight, shape, and size—though I do think, feel, and imagine. I perform mental acts but I don’t perform digestive acts—my body does (though I can say, “I have indigestion”).
This commonsense conclusion has a philosophically startling consequence: the self is not a physical thing. The self could only be a physical thing if it had physical attributes, but it does not—it has exclusively mental attributes (intrinsically, inherently, non-derivatively). That is why it is conceptually easy to detach the self from the body—by brain swaps, partial brain swaps, and more exotic forms of self-transfer. We recognize that the self does not have the attributes of the body: it is not a physical thing, despite its close involvement with a physical thing. To be sure, we can ascribe physical attributes to the self in the vernacular, but it is false to suggest that the self is thereby a psychophysical entity, directly possessing both mental and physical attributes—as if it were physical in logically the same way it is mental.  But to repeat, it is the body, which is numerically distinct from the self, that bears physical attributes. Nothing like this is true of mental attributes—they attach directly to the self (not to the mind). The thing that thinks is not the thing that digests—I think but I don’t digest. This is not to say that the self is an immaterial substance in the classic Cartesian sense (though we can rightly say that the self is not material); indeed, much the same argument could be given against such an idea, since there will be properties of the immaterial substance that also cannot be attributed to the self (whatever recondite properties they may be). The point is just that it is a category mistake to attribute to the self, qua the self, physical attributes. The self has a psychological nature, reflected in its psychological attributes, but it does not have a physical nature, reflected in its (sic) physical attributes. 
Perhaps this will not seem so surprising, rooted as it is in commonsense conceptions, but it has a further consequence that bites deeper, namely that it undermines materialism about mental states. Suppose we agree that selves don’t have physical attributes: then we have grounds for constructing a reductio of classic type-identity theory. For if mental attributes are identical to physical attributes, then selves will have physical attributes, since they have mental attributes and these are identical to physical attributes. For example, if pain is identical to C-fiber firing, then a self in pain will also be a self that instantiates the physical attribute of C-fiber firing. Or again, if I am thinking and thinking is identical with a physical attribute, then that attribute will be attributable to me in just the way thinking is, i.e. directly. But selves don’t have physical attributes in this direct way. Therefore type-identity theory must be false. If we call the physical attribute X, then we should be able to say that I X just as we say that I think—since Xing just is thinking. But that is either nonsense or a misleading way of saying something like this: “My brain is Xing”. Here we appeal to the “having” relation between self and body, rather as we say, “I am digesting, i.e. my gut is digesting”. But now the alleged identity is not between being in pain and C-fiber firing but between being in pain (an attribute of the self) and having a brain that contains C-fiber firing (also an attribute of the self). I have the attribute of having a brain that contains a certain physical state, and that attribute is what the identity concerns—not the attribute of C-fiber firing itself. I don’t have the latter attribute–my brain does–so that attribute cannot be identical to the attribute of having a pain, which I have. In short: mental attributes belong to selves, but physical attributes do not, so the former cannot be the latter. Mental and physical attributes are instantiated by different things—selves and bodies, respectively—and hence cannot be identical (by Leibniz’ law).
But what about a revised form of materialism that identifies mental attributes with the complex attribute of having a brain containing a certain material state? That is not the way materialism is typically formulated, but at least it is meaningful to attribute such an attribute to the self—I do have a brain that contains C-fibers. However, it is unappealing to identify a relatively simple attribute like pain with the complex relational attribute of having a brain that contains C-fiber firing: we are introducing a relation between self and brain in order to specify the nature of the simple (monadic) attribute of pain. Moreover, this relation itself is left unexplained: for what is it for a self to “possess” a brain? Is this a physical relation? It seems not to be, since no physical account has been given of the self or of the “possessing” relation. There was a pleasing simplicity to the idea that pain is just a brain state, but it turns out that this view violates the principle that selves don’t have physical attributes. And it is plain nonsense to attribute brain states to the self in the way that we attribute mental states to the self: I am the subject of thinking, but I am not the subject of whatever brain state underlies thinking—my brain is. For type-identity materialism to work we would need to identify the self with the brain, so that whatever is true of the brain is thereby true of the self; but such an identification runs into well-known problems of its own.  Perhaps we could say that materialism about mental states can work only if materialism about the self can, which is doubtful. What is true is that I have a brain with those attributes, just as I have a heart with other physical attributes: but states of that brain are not states of me any more than states of my heart are states of me.
What I have been opposing is a kind of double aspect view of the self: the reference of “I” has both a mental and a physical nature captured in the range of predications we make employing personal pronouns and names. It is quite true that I can be said to think and to weigh 150 lbs, but on closer examination these predications have very different analyses: the former is direct predication while the latter is indirect predication. I can be said to weigh 150 lbs only in the sense that I have a body with that weight, rather as I can be said to be worth X amount of money only in the sense that my possessions are worth X amount of money (I am not worth M). These physical attributes are extrinsic to me as an individual self and they can be shed without loss of identity. By contrast, my mental attributes belong to me inherently, not in virtue of some further entity associated with me, as it might be my mind. I have a mind, but it is not my mind that thinks, feels, and so on: I do these things. Thus I am connected to my mental attributes more intimately than I am connected to my (so-called) physical attributes. It is not an exaggeration to say that I have no physical attributes: I do not weigh 150 lbs, though I am close to something that does. No doubt it is this logical fact that underlies flights of imagination in which the self floats completely free of all physical embodiment, whereas no one supposes that the self can escape its psychological nature. In the imagination there can be disembodied selves, but there cannot be “disemminded” selves—there cannot exist a self without mental attributes of any kind, even in the most extravagant fiction. Thus my inner nature is to be mental, but it is not in my inner nature to be physical. Simply: I am not a physical thing. 
 What about bodily actions—aren’t they attributes of the self and yet physical? Yes I perform actions as much as I think or have sensations, but no they are not physical attributes: actions are intentional events and hence partake of the directness proper to all mental attributes.
 P.F. Strawson’s famous treatment of the self in Individuals is an instance of this type of view, except that he prefers to speak of the “person”. I don’t think this terminological decision changes the issue, and for various reasons I find the concept of a person unhelpful in these discussions.
 If I exist as a brain in a vat, is my physical nature determined by the physical attributes of my brain? But do Ihave such attributes at all—am I really gray and wrinkled and soggy? No, I merely have a brain with these attributes.
 Should it be the whole brain or just the parts that underlie mentality? What about brain bisection? How much of the brain can a person lose and survive? What if we gradually replace the cells of the brain with artificial components?
 This is not to allow that disembodiment is really possible, but the necessity for a body is not a point about the attributes a self can be said literally to instantiate. The self is not a physical thing precisely (and only) in the sense that it has no physical attributes, but only mental attributes. Yet it might still require physical embodiment in order to exist.