The liver, by the way, is so much more complex an organ than the heart, that there is little comparison. What the heart does is quite rudimentary, and it has just that one primary function. The liver has many key functions and is so complex that its organic development is not complete until the eighth or ninth month of gestation. The heart is far too simple an organ to be thought of as a defining marker for personhood. Those who rely on this flimsy marker are simply desperate for an indicator of personhood, so that "rights" can be assigned, in this case, to an embryo.
So when are we actually talking about a human life? It is a philosophical question, not easily answered. And this is why it is far easier to decide the issue in terms of legality rather than moral, religious, or other ethical considerations. Before you can assign legal rights of personhood, you must have a definable person. Was the initial single-cell fertilized egg a "human being"? Or was it merely a potential human being? Going down the path that ascribes human rights to single-cell organisms could result in the assignment of rights to all of the female's unfertilized eggs and all of the male's sperm cells.
Being alive does not define your personhood. Legally, your birth did that. And even your death will not end your personhood rights, as seen in the organ-transplant example cited below. Life is far from being the key factor in personhood. However, there is certainly no disputing the personhood of the mother. She definitely has the rights that come with it. And in the United States, her rights as a person are constitutionally guaranteed. The Due Process Clause of the 14th Amendment establishes a "right to privacy," which then involves further rights. Among those most valuable, is the right to body autonomy. Your body is yours, alone, and no government entity or other actor can segregate or "claim" any part of it, for any reason, unless you willingly permit this to occur. This is one of the reasons you have to sign a statement before many surgeries. It is why no one can utilize any of your organs for transplant after you die, unless you have fore-ordained this. Legally, it is a personal choice that matters. Pertaining to rights, regardless of whether you "believe" a fetus is equivalent to a human adult, legally a woman is not obligated to sacrifice her bodily autonomy for anyone, even her fetus, and especially her embryo. As it stands, except in Texas (for now), a woman has the unqualified right to decide whether abortion is right for her in her first trimester of pregnancy. This is what pro-choice means. Holding a pro-choice opinion does not mean you like abortions. The decision to abort is frequently highly traumatic. No one is a fan of abortion, per se.
The only way around this legal pro-choice interpretation would be to change the law. SCOTUS could do this by voiding some interpretations inherent in the Roe decision. But there is a great deal of historical precedent to overcome if they wanted to do this. [Griswold v. Connecticut, 1965; McFall v. Shimp, 1978] The problem is, they might want to do this regardless of how much precedent has guided legal decisions before and since Roe was enacted. The three SCOTUS appointments of Donald Trump were preselected based on a screening for willingness to overturn Roe. Again, the majority of Americans are against changes to Roe. But it is unknown just how radicalized the Court has become with these appointments. We might soon find out the answer to that question.
* The American College of Obstetricians and Gynecologists (September 2002). "ACOG Practice Bulletin: Clinical Management Guidelines for Obstetrician-Gynecologists: Number 38, September 2002. Perinatal care at the threshold of viability". Obstetrics and Gynecology. 100 (3): 617-24.
Luke B, Brown MB (December 2006). "The changing risk of infant mortality by gestation, plurality, and race: 1989-1991 versus 1999-2001". Pediatrics. 118 (6): 2488-97.
Tyson JE, Parikh NA, Langer J, Green C, Higgins RD (April 2008). "Intensive care for extreme prematurity--moving beyond gestational age". The New England Journal of Medicine. 358 (16): 1672-81.
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