The eminent philosopher Charles Hartshorne (1897-2000) in Concerning Abortion: Attempt at a Rational View writes:
What is the moral question regarding abortion? We are told that the fetus is alive and that therefore killing it is wrong. Since mosquitoes, bacteria, apes and whales are also alive, the argument is less than clear. Even plants are alive. I am not impressed by the rebuttal “But plants, mosquitoes, bacteria and whales are not human, and the fetus is.” For the issue now becomes, in what sense is the fetus human? No one denies that its origin is human, as is its possible destiny. But the same is true of every unfertilized egg in the body of a nun. Is it wrong that some such eggs are not made or allowed to become human individuals?
1. The human fetus is human in exactly the same sense that the unfertilized eggs of a celibate human female are human.
2. There is nothing wrong in preventing the development of such eggs into human beings.
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3. There is nothing wrong in preventing the development of fetuses into full-fledged human beings.
This argument is unsound due to the falsity of its initial premise. Hartshorne ignores a crucial difference between unfertilized eggs and fetuses. He ignores the potentiality of the fetus to develop, in the normal course of events, into a full-fledged human being. No egg cell by itself has this potentiality. This is a difference that Hartshorne papers over by confusing possibility and potentiality. Every potentiality is a possibility, but not conversely.
Hartshorne speaks of the "possible destiny" of a fetus and of an ovum, as if the sense of 'possible' is the same for both. Not so. There sense of 'possible' according to which each of a fertile sexually abstinent female's ova is possibly such as to develop into a human infant. But no one of these eggs has the potential so to develop.
One standardly distinguishes between logical and nomological possibility. Roughly, anything is logically possible if it is not ruled out by the laws of logic, and anything is nomologically possible if it is logically possible and not ruled out by the laws of nature. Now consider a particular ovum O of Hartshorne's nun. It is both logically and nomologically possible that O be penetrated by a sperm cell and that the resulting zygote develop into what we would unhesitatingly call a full-fledged human being. But O by itself lacks the potentiality to devolop into what we would unhesitatingly call a full-fledged human being. The same goes for a sperm cell by itself. And ditto for an arbitrary sperm-egg pair, say O and a sperm cell from Barack Obama's 'collection.'
If the above is not immediately obvious, here is a simple analogy. When I make pizza, I begin by making the dough. I use flour, water, eggs, and yeast. Having mixed those ingredients, I have a blob of stuff with the potential to rise. But surely no one will say that the flour itself, or the water or eggs or yeast by themselves, have the potential to rise. It is obviously meaningless to say, of a quantity of water, that it has a potential to rise if 'rise' is being used in the same sense as when we apply it to blobs of dough. Of course it is possible that a certain portion of flour (water, etc.) become an ingredient in a risen mass of dough. But I don't have to worry about the flour in my pantry turning into a mass of wet and moldy dough on its own.
Every potentiality is a possibility, but not every possibility is a potentiality. Sperm and egg, on their own, have no potential to develop into a human being. But a human zygote does. This is the point that Hartshorne seems to miss. Here, as elsewhere, he does not strike me as a rigorous thinker.
There is more on this topic in the category Abortion.