For a while, I've thought that:
- Hair is not alive.
- Every part of me is alive.
- So, hair is not a part of me.
Interestingly, in L'usage de la Raison, Mersenne talks of the human as a microcosm and mentions that humans, like the universe, have non-living parts, and gives hair as an example. So Mersenne denies (2). And on further reflection, I don't think I really had much reason to accept (2). Indeed, there seem to be other clear counterexamples to (2), such as the electrons in my heart (they are parts of my heart, and parthood seems transitive, at least in this case). Maybe one could argue that while the electrons are at least a part of a living part of me, hair isn't a part of a living part of me. But that would beg the question. For if my hair is a part of me, it's also a part of my head, and my head is surely a living part of me.
So I don't see much ground for denying that hair is a part of me. It's just one of my many nonliving parts.
Of course, speaking fundamentally, there is no such thing as hair (just as there are no hearts, chairs, stones, etc.). There is only I, who am hirsute.