In an earlier post, I offered the principle that just as the laws of physics should be invariant under change of reference frame, so should the laws of morality. One consequence of that is that various inside-outside distinctions are not going to be significant of themselves. Here is an interesting little consequence of that: Any argument that abortion is permissible based on the fact that abortion takes place inside the body of the woman cannot be right, since the claim that the fetus is inside the woman's body is not invariant under coordinate transformations.
This doesn't mean that the argument is thoroughly refuted. But it does mean that the mere geometrical fact that the fetus is within the woman's body is insignificant. There may, however, be more significant related invariant facts about dependence, burden, etc. The invariance move does not, thus, settle the discussion, but moves it forward, by forcing the pro-choicer arguer to give a fuller story about the distinction in invariant terms, which terms non-coincidentally are going to be descriptively richer, thereby deepening the debate.
Of course, one doesn't need relativity theory to show the problem with the principle that one can do what one likes as long as it is within the confines of one's body. One can also proceed by counterexample. If one accidentally swallowed Whoville, one would not be permitted to follow that up with a drink of something intended to kill all the Whos.