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Zygotes have fairly low success rates even naturally. If you seriously believed that life began at fertilization, you should stop having procreative sex entirely, because the risk of creating a zygote that fails to implant is too great.

Quite the knotty moral tangle you've presented here. Let's pick it apart.

(But first, a pedantic terminology point: Life as a separate, unique biological human begins at fertilization, according to science. A new human life begins when two germ cells provide the recombinant DNA and cellular machinery to generate a multicellular framework of tissues and organs which can support a sapient nervous system. The science on that is settled. The moral issues are about personhood, for which mere biological life is a prerequisite and thus (in most other circumstances) a proxy. Thus, your moral tangle can be restated more directly, "If you seriously believed that personhood began at fertilization, you should stop having procreative sex entirely, because the risk of creating a zygote who fails to implant is too great.")

Restated as a syllogism, with expansion of a few built-in assumptions:

  1. Major premise: Those who believe a fertilized egg is a person probably consequently believe his death before birth to be a tragic miscarriage.

  2. Minor premise: The risk of creating a fertilized egg which fails to implant, and thus dies before birth, is high.

  3. Conclusion: Therefore, to avoid tragic miscarriages, those who believe a fertilized egg is a person should not perform the acts which create a fertilized egg.

This is a valid syllogism. Assuming both premises are true, the conclusion must also be true.

I contend the minor premise, "The risk of creating a fertilized egg which fails to implant, and thus dies before birth, is high." Current science says that the greatest risk to the extremely young human is within the first two weeks from fertilization through implantation. A commonly cited number is that 70% of naturally fertilized eggs don't get through this filter. Yet, this article on use of a 25% survival statistic in a court case hints that you've retransmitted a meme which is fairly standard among abortion advocates:

Natural human embryo mortality has often been linked to the ethical status of human embryos. For example, in their brief article, Roberts & Lowe state that “If Nature resorts to abortion … by discarding as many as 3 in every 4 conceptions, it will be difficult for anti-abortionists to oppose abortion on moral and ethical grounds.” Ronald Green, Professor Emeritus of Religion at Dartmouth College, points out, incorrectly, that “between two-thirds and three-quarters of all fertilized eggs do not go on to implant in the womb” and asks: “In view of this high rate of embryonic loss, do we truly want to bestow much moral significance on an entity with which nature is so wasteful?” A report of the Ethics Committee of the Royal College of Obstetricians and Gynaecologists in 1983 states: “Knowing as we do that in the natural process large numbers of fertilised ova are lost before implantation, it is morally unconvincing to claim absolute inviolability for an organism with which nature itself is so prodigal”. This link has been considered by many others. Thus, McLean’s assertion, in evidence, that early embryo loss is not only of biological interest but also of political and legislative significance, was clearly correct. How specific estimates of embryo mortality inform an ethical calculus is, perhaps, not so clear. Nevertheless, for those who consider it germane, McLean’s exhortation that “It is therefore important to obtain as accurate an estimate as is possible for the occurrence of early human embryo loss”, must surely be correct too.

So, what is that accurate estimate? A second article, also originally published on F1000, puts the percentage at a coin flip with a caveat: 40-60% for normally healthy and fertile women. Opinions differ on whether F1000 is a legitimate peer-reviewed journal or merely a pay-to-publish platform, but these authors cite about 40 papers in going against popular wisdom, and reach this conclusion:

Based on this analysis, a plausible range for total embryo loss from fertilisation to birth is 40–60%. This is consistent with estimates from both older and more recent text books. Even with the wide range of mathematically possible outcomes, it is likely that estimates of 90%, 83%, 80–85%, 78%, 76% and 70% total human embryonic loss are excessive.

"Even so," one might ask, "isn't a death rate of one out of two children worth avoiding the one death?" That's morally equivalent to anti-natalism as a prevention for cancers and other causes of suffering and death. Since there's no other way to get new children, and since everyone dies anyway, preventative anti-natalism is equivalent to species extinction, whether for pre-birth or post-birth deaths.

The opposite question becomes, "isn't a life rate of one out of two children worth seeking life?" Even if the life rate were the dismal 20-30% cited by memes, the majority of humanists and Christians have long agreed that children, new people, are worth the attempt.

I would agree that a life rate of 50%, or even 20% or 10% would still be worth it, but I don't place any moral value on a fertilized egg. In addition, I agree that having fertilized eggs die incidentally is not really systematic murder, or even callous. Most Christians, I think, would agree that it's still moral to bring a child to term even if that child had only a chance of survival - if God wants to take those fertilized eggs or embryos back, let the blood be on his hands, not ours.

But the same arguments would apply for IVF. We have accepted that to get a baby, we have to accept a high failure rate for embryos - so now we're just haggling. To that end, embryo screening is a boon, not a burden. By screening out obviously unviable embryos, we are improving the chances of success, not lowering it.