Is a fetus part of a woman's body?

Andrew Coulson of The Ganteloupe wrote in to offer an answer:
When you write about abortion, it isn't clear whether you really fail to understand the abortion rights position, or you are simply feigning ignorance as a rhetorical device. If it's the former, I'd like to answer your question on the difference between a fetus and an infant.

Many supporters of abortion rights consider self-ownership to be the most elementary and inviolable right of all: We are all the owners of our own bodies. The difference between a fetus and an infant is that a fetus is a part of a pregnant woman's body whereas an infant is not. Libertarians do not want the very visible hand of government rooting around in women's uteruses, telling them what they can or can't do with any fetuses that happen to reside there. Any rights of a fetus are secondary because its existence is secondary to (and until late in the pregnancy, entirely dependent on) the woman in whose womb it is located.

The fact that abortion is a sad business is moot.

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James Taranto responds, by arguing that "self-ownership" is an archaic concept, that human as property has been long discredited, and that no mothers speak of carrying a "fetus."

Here are four other arguments. Perhaps there are more--feel free to suggest some in the comments section below.

1. If a "fetus" is a "part" of a pregnant woman's body, then they would have a common genetic code, since a "part" of a body is defined by its having the same genetic code as other "parts" in the body. (For example, the lungs and legs and livers of Person X all have the same genetic code.) An unborn baby is a genetically distinct being; therefore it is not a part of its mother's body.

2. If a "fetus" is a "part" of a pregnant woman's body, then if the woman died, the part would die as well. (For example, lungs and legs and livers don't live on when a woman dies). But an unborn baby can survive the death of a mother--see Bobbi Jo Stinnett--therefore is it not a part of its mother's body.

3. If a "fetus" is a "part" of a preganant woman's body, then the woman would have four eyes, two hearts, four lungs, etc. And yes, if the "fetus" is a boy, then the mother would also have male sexual organs.

4. Why does Caulson think that a "fetus" is "part" of a pregnant woman's body? There's only two possible reasons I can think of: (a) because the "fetus" is inside the woman; (b) because the "fetus" is dependent on the woman for survival. But both are absurd criteria: (a') being in the hospital doesn't make me part of the hospital (in that sense that I'm am no longer an individual, distinct entity); and (b') being dependant upon a life-support machine does not make me a part of the life-support machine.