Asking laypeople to choose cutoff dates based on pictures doesn't make sense.
It measures empathy, but people can have empathy for non-sentience objects. If I carve a cute baby face into a rock, people will empathize with it. Yet, their empathy for a rock is a bad reason to restrict my rights forcing me to spend time and effort polishing the rock, sheltering it from the elements, and broadly catering to its well-being as a full time job.
Zygotes and fetuses prior to the third trimester are scientifically incapable of being sentient. They are as self aware as rocks. The physical structure of the brain simply doesn't support anything beyond the basic brainwaves of a self regulating nervous system.
Similarly, children born completely without forebrains (complete anencephaly) are just missing the the tops of their heads. They have a brain stem for controlling heart beat/metabolism/etc, and their brain wave activity is still stronger and more developed than unborn fetuses. Yet, such children are still objectively non-sentient.
It's highly probably that fetuses aren't sentient for the third trimester, but the beginning of the third trimester was deemed the last cutoff where we can be still 100% sure, instead of 99.9% sure. That is why that cutoff is used. To absolutely guarantee not a single abortion is murder by any coherent definition.
It can't be murder if there is no mind occupying the flesh. Just like smashing a rock isn't murder, or killing cheek cells while brushing my teeth isn't murder, legal abortions are guaranteed to not be murder.
...That's why an amputated arm isn't put on life support. Without "someone" occupying the body, it is just medical waste or organ donor material. I've only seen two ways people reject this reality:
  1. Invoking blind religious beliefs. (Ex. A soul magically popping into existence when two molecules touch.) I hope I don't need to specify why religious beliefs should not restrict others' freedoms.
  2. Starting from different axioms. (Ex. Not valuing "sentience / agency / consciousness" as what makes human life valuable)
    Think carefully about what your axioms imply. (Ex. Someone who thinks having "human DNA" makes us deserving of life would already be roped into outlawing toothbrushes, per my earlier example.)
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I'd go with 2, "Distinct whole human organism" to be specific. It gets around the idea of rocks and skin cells having a right to life, but it accounts for the obvious wrongness of killing someone in a reversible coma or twisting the limbs off a five month-old unborn baby.
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I love this paper as a piece of legal reasoning. I can't see many judges going this far though.
I learned things I didn't know from this article.
A good article from last July by a pro-choicer that disses Roe on grounds other than just its extremism:
"With the Supreme Court having, in effect, written abortion law covering the first two trimesters of pregnancy, offering an opinion about abortion is costless. Pro-lifers can say that abortion ought to be outlawed even in cases of rape and incest, knowing full well that they’ll never have to look a rape victim in the face and explain why she had to carry her attacker’s baby to term. Pro-choice advocates, meanwhile, don’t have to directly advocate allowing second-trimester abortions; the Supreme Court removed that burden. No wonder abortion politics are so polarized and poisonous."
Actually, the article provides reasons to "let Roe go" that even a pro-choicer of the infanticide persuasion might hold.