Here is a simple version of the Potentiality Argument (PA):
1. All potential persons have a right to life.
2. The human fetus is a potential person.
3. The human fetus has a right to life.
Does PA 'prove too much'? It does if the proponent of PA has no principled way of preventing PA from transmogrifying into something like:
1. All potential persons have a right to life.
4. Everything is a potential person.
5. Everything has a right to life.
Probative Overkill I
One kind of probative overkill objection is easily sent packing, namely, the sort of objection that is based on the confusion of potentiality with the mere logical possibility of transformation. It is thinkable without contradiction that a pumpkin seed become a rabbit. Indeed it is thinkable without contradiction, and thus narrowly logically possible, that anything become anything. But of course a potentiality is something quite specific and has nothing to do with an empty logical possibility of transformation. After all, we know that (planted) pumpkin seeds do not become rabbits; they become pumpkins. Rabbits give birth to rabbits, not kangaroos or pumpkins. Nature is orderly.
If there are potentialities in nature, they are directed at specific outcomes. There are two points here. The first is that potentialities are directed; the second is that their directedness is to specific outcomes. They are like dispositions in this regard. Solubility is the disposition to dissolve, not the disposition to shatter or explode. Potentiality is interestingly analogous to intentionality. Necessarily, thoughts take objects. Necessarily, potentialities have outcomes. In both cases we can speak of directedness -- of thoughts to their objects and of potentialities and dispositions to their outcomes or realizations. In both cases the object/outcome enters into the individuation of the thought/potentiality. And in both cases the object/manifestation need not exist.
A potentiality can go unrealized without ceasing to be directed at an outcome. This is analogous to the situation in which one thinks of something but the thing does not exist. To say that a potentiality can go unrealized is not to say that the potentiality is not itself something real, indeed something actual. It is real analogously as a thought is real even when its object does not exist.
Anyone with an elementary grip on the notion of potentiality can see that the first kind of overkill objection fails. For it is based on a failure to see that (4) is false. If a thing has a potentiality, that is not a 'blank check' to become anything at all.
Probative Overkill II
According to a less crude objection, there is no principled way to ascribe potential personhood to a zygote without also ascribing it to spermatazoa, unfertilized ova, and pairs of sperm cells and egg cells.
Let's consider first the pair (S, O). Let S be one of my sperm cells and O an unfertilized egg cell of a nun in India. This pair exists because its members exist. But this pair is not a potential person. The very idea is incoherent. If a pair is a set or a set-theoretical construct, then it is an abstract object; but surely no abstract object has the potentiality to become a concrete individual person. But whether or not pairs are abstract objects, the notion that the pair in question is a potential person is absurd on the face of it. For a sperm cell out of all contact with an egg cell simply cannot develop into a person.
Now consider a sperm cell S. Given that there are potentialities in nature, S has the active potentiality to fertilize an egg. But as noted, potentialities are directed to specific outcomes and not others. The potentiality to fertilize an egg is not the potentiality to become a person. Surely, a sperm cell that has not fertilized an ovum does not have the potentiality to become a person.
Similarly with a an egg cell. It has the passive potentiality to be fertilized by a sperm cell. But this potentiality is not the potentiality to become a person.
It follows that the Potentiality Argument is not an argument against contraception. Contraception prevents sperm cells from 'hooking up' with egg cells, either by killing the former or by blocking their access to the ova they lust after. Thus a spermicidal jelly does not destroy potential persons.
It is worth noting that it would be the Fallacy of Division to argue that since the zygote is a potential person, each of its constituents is as well.
The Potentiality 'in Principle' Response to Probative Overkill II
"The egg cell does not have the 'ready' potential to develop into a person, but it has the 'in principle' potential because something can be done to it to give it the 'ready' potential, namely, it can be fertilized by a sperm cell. And the same goes for the sperm cell: it does not, by itself, have the 'ready' potential to develop into a person, but it has the 'in principle' potential because something can be done to it to give it the 'ready' potential, namely, it can be brought into contact with an egg cell."
"Therefore, your 'probative overkill' objection fails. If a zygote is a potential person, then so are sperm cells and unfertilized eggs. Since this is an absurd consequence, the Potentiality Argument proves too much and fails for this reason."
"The situation is really no different from that of the anencephalic fetus. It lacks the 'ready' potential to develop normally on its own into a person whose faculties are normal. But it has the 'in principle' potential for such development because something could be done to the fetus to get it to develop a normal brain."
"There is also the case of the comatose individual who will not emerge from his coma on his own, but can be made to emerge from it by special medical interventions. This individual lacks the 'ready' potentiality to emerge from the coma state, but possess an 'in principle' potentiality to do so."
"In sum, we need to distinguish between 'ready' and 'in principle' potentiality to account for cases like that of the comatose individual just mentioned. But then the distinction applies to sperm and egg cells prior to their union. Since anything with either kind of potentiality to develop into a person has a right to life, sperm and egg cells have this right as well. Herein lies the reductio ad absurdum of the Potentiality Argument."
Rejoinder to the Potentiality 'In Principle' Response
The above response eviscerates the concept of potentiality, stripping it of its usefulness. 'In principle' potentiality is intolerably latitudinarian. The idea is this:
X has the 'in principle' potentiality to develop into an F =df there is something that could be done to x to enable it to develop into an F.
But then a fetus born dead has the potentiality to develop into a normal human person because God or some other agent with superhuman powers could resuscitate it. That's possible! Or it is possible that in the future babies born without brains can be given brains, or certain pre-natal genetic interventions could be performed that would cause the fetus to develop a normal brain.
Cats cannot at present fly. But they would like to, the better to catch birds. So they have the 'in principle' potentiality to develop into airborne critters because they could be fitted out with wings.
I think this approach shows a failure to grasp the notion of potentiality. A potentiality is an intrinsic, actual, not merely possible, 'principle' in a thing that directs it toward a certain outcome. It is 'built-in.' It cannot be reduced to a possibility -- even a nomological possibility -- that the thing be modified ab extra in various ways.
So I reject 'in principle' potentialities and with them the 'probative overkill' objection to the Potentiality Argument which requires them. At the same time I issue a challenge to the partisans of 'in principle' potentialities: How do you rebut the probative overkill objection?
Or do you 'bite the bullet' and accept that human sperm and egg cells by themselves are potential persons?