In the case of monozygotic twins, two persons result from a single fertilization event, so fertilization cannot mark personhood.
In monozygotic twinning, a single fertilization event produces a single blastula.1 Prior to about day 12, a piece of that blastula might break off and grow into a separate individual. This is a case of natural cloning, exactly analogous to a case of artificial cloning, which may soon be technologically feasible in humans. This would involve taking one of my skin cells, cloning it, and growing it into an adult—a (much younger) identical twin of me. The younger twin and I would both be persons, but only one fertilization event was involved. Furthermore, prior to the cloning event, there was only one person—I, the first twin. The second twin came to be when the cloning event occurred.

The difference between this scenario and monozygotic twinning is simply in the amount of time that elapses between the genesis of the cloned person and the cloning event. A blastula is a single organism and a single person. At this stage of development, a piece of the person can break off and begin acting as its own self-integrating, self-actualizing unit—in other words, as its own organism. When that happens, two people are present, one of whom is slightly younger than the other. Because I define a person as a human organism, my position can accommodate this situation.
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In the case of tetragametic humans, one person results from two fertilization events. While it is more difficult to present a handy analogy for this phenomenon, the logic is quite similar to that presented for twinning. At first, two organisms are present. One is subsumed by the other and, in the process, ceases to be. An imperfect analogy might be this: I need a heart, kidney, lung, and liver transplant. My friend dies in a tragic car accident and serves as organ donor. Before the car accident, there were two organisms and two persons. After the surgery, there is only one organism and one person—albeit a person whose body contains parts from another individual. The important point is that any biologist would say that two individual organisms are present prior to the tetragametic fusion and that one is present after the fusion. If that is the case, then I would see two persons present prior and one after, with the second having “died” as part of the process. This seems dissatisfying only because organisms usually cease to be through loss of integration—what we think of when we say “die.” In this case, the organism ceases to be through a process that does not involve disintegration. Regardless of whether you call it “dying” or not, to say that an organism ceases to be is not intellectually unsettling at all, and this is all I need to know in order to say how many persons are involved at each stage of the process. ↩