For most of us, this seems a fairly simple question because we have something to which we can refer. I can point toward my body and say, "This is my body." This is not a definition (description) but an indication. What happens, however, when we rely entirely on indication for our definitions is that we don't actually have a useful definition. Trying to determine what exactly defines your body as yours is a difficult question. (It might seem to be a useless question, too, if it weren't the case that a number of controversial ethico-medico-legal issues--abortions, amputations, and separation surgeries--are directly concerned with what is whose body. I'm not going to trace these particular problems out in this post, but if you're concerned that this is all fruitless philosophizing, I'd think again.) So I'm going to take a crack at it.
One of the positions I think I detected among the commenters on Leah's blog (see the introduction to this series for a summary) holds that what something (an organ, say) is part of your body because it is 1) attached with living tissue and 2) composed of living, organic cells. So my hand is part of me because it is attached and organic. If my hand were chopped off, it would no longer be part of me. If it were replaced with a prosthetic, that prosthetic would not be part of me because it is not organic. No matter how strenously I insisted that it was part of me, I would be mistaken.
I would suggest that there are people who would wish to add that those cells must be genetically identical (or at least genetically similar) to those that make up most of your body. I do not want to suggest that the commenters I mentioned have this requirement, but I imagine that someone does. After all, there are parasitic animals that fuse themselves onto their hosts (or live deep within their hosts) such that there is a band of continuous living tissue extending from one organism to another. Genetic markers could be a way of differentiating one body from the next.
Either way, I'm going to suggest that this is the wrong way of finding the edges of your body. Once again, I am not looking so much to prove through syllogism as provide instances in which this sort of definition seems entirely unhelpful.
1. Organ and tissue donation
I cannot systematically prove that a transplanted heart becomes part of the new owner in some metaphysical sense. What I will suggest is that we have a number of reasons for wanting to think so, primary among them practical and legal concerns. I will spend more time discussing this issue in part 3, but let's for the moment identify a few traits: the new organ was formerly part of another person (or their body, at any rate), and most likely carries a quite different genetic signature. If we say that a new heart is part of the person who received it, we must conclude that at the very least the genes do not determine what is or is not part of your body. I suppose you might want to argue that the transplanted heart isn't really part of your body, in which case my next example might prove harder to refute.
No, I don't mean the Greek mythological monster. I refer to tetregametic chimerism, in which a person has two genetic lineages. Chimerae are people (or animals) who either developed from an egg fertilized by two sperm or from two non-identical zygotes which fused into one. This means that some of their cells have one genetic code and some of their cells have another. This could result in pigmentation or hair-growth unevenness or in intersexed anatomy, but it may very well go undetected. (Which is to say, you could be a chimera and not know it.)
I hope you can see what I'm driving at. This is one body, satisfying the connected living tissue requirements, that contains multiple genetic markers. Unless you want to claim that a chimeric person has two blended bodies, genetic material cannot constitute a useful distinction.
If you really want to push it and say that at least the cells are related on the level of siblings, I'll observe that researchers have created chimerae lab rats from two non-related zygotes... and other chimerae from zygotes of different species.
3. Conjoined Twins and Parasitic Twins
(Some people may not be surprised to see this example come up. I assure you that it will appear again in this series.)
The connected living tissue requirement is a problem when there are people (genetically identical) who are connected with living tissue. Consider Violet and Daisy Hilton (right), connected at the base of the spine. At their point of connection it would be exceptionally difficult to determine which tissue was Violet's and which tissue was Daisy's. Furthermore, since they (along with most if not all conjoined twins) have connected circulatory systems, it would be impossible to say whose blood is whose. We might want to make some kind of argument based on whose "side" the blood is on, but ths is a problem (and here's the real kicker) if we're defining bodies based on connected living tissue because under this definition Violet and Daisy Hilton have one body. You could trace a path of continuous connected living tissue from the centre of Violet's brain through to Daisy's brain. Under this definition, there is no way to distinguish Daisy's body from Violet's.
I think it might be worth distinguishing the instance of conjoined twins from supernumary limbs or digits. An extra thumb or arm does constitute (I would suggest) part of your body. Additional pieces don't fall outside this category. This is interesting because parasitic twins are like supernumary organs in some respects and are like conjoined twins in others (origin, say). Parasitic twins do not have brains or consciousnesses, so do they count as separate bodies? However, we are here moving into a new way of defining body or self, and so I shall rest with the observation that it seems that connected, genetically identical, living tissue is at the very least not sufficient in defining where your body ends. I will return to this topic again in the part 3.
Finally, I will point out an interesting piece of etymology that will help segue into the next post. Organic, according to the Oxford English Dictionary On-Line, can mean a number of things. The entry most representative of common use seems to be the following:
Having organs, or an organized physical structure; of, relating to, or derivedHowever, there are other meanings, some of which are obsolete. One of these offers a second way of thinking about what does or does not constitute part of your body (the one advocated in some form or another by both dbp and Leah):
from a living organism or organisms; having the characteristics of a living
Serving as an instrument or means to an end; instrumental. Obs. (OED)