I have been conflicted over abortion for a long time, and I've reached a sort of stable state in which I accept that especially in early pregnancy a fetus does not have the same rights that an infant does outside of the womb, but later in pregnancy it does. For instance, it seems clear to me that a fetus the day before birth should have equal rights to an infant born the day after, since as has been noted that difference in residency does not seem particularly significant to moral standing. And, of course, the problem with that gradualist view - the inability to assign a time in which such full rights are obtained - continues to trouble me. But, another issue that concerns me is how practices like sex-selective abortion inform the debate. If a women really has the right to choose who or what may reside within her body, and has the right to choose whether or not to carry a pregnancy to term, shouldn't it be immaterial to a third party on what basis she makes those decisions? In this case, sex-selective abortion is not morally wrong. I feel, however, uncomfortable with this, and think it could very well be wrong. But doesn't that imply I believe the fetus has the right not to be terminated because of its sex? That the fetus has some right against discrimination? If I believe a women has the right to make that choice for whatever reason she may find compelling, then certainly the sex of the fetus can't change the moral question, can it? How can I both believe the woman has a right to choose whether or not to carry a pregnancy to term, and also that sex selective abortion is discriminatory and wrong?

You have clearly done a good deal of thoughtful and critical thinking about abortion, and I suggest that you take a look at some of the philosophical literature, starting with Judith Thomson's essay "A Defense of Abortion" (widely reprinted in philosophy anthologies.) She questions some seemingly obvious premises--like your assumption that a fetus the day before birth has the same rights as a newborn--by arguing that what is at stake is not only the personhood of the fetus but also the fact that the fetus is dependent on another human being. She uses creative thought experiments to explore whether dependent beings have the right to continued dependence on this human being, especially when the dependence came about without consent (e.g. if a woman became pregnant as a result of rape). She also makes a distinction between what is clearly wrong and what is selfish/uncaring.

Even if you continue to think that sex selective abortion is discriminatory and wrong, you need not conclude that a woman has no right to choose. We think that breaking promises is usually wrong, but we still think that people have a right to decide whether or not to do so. The law should not enforce all our moral judgements, for pragmatic and other reasons.

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