Pointing to a lump of raw ground beef, someone might say, "This is a potential hamburger." Or, pointing to a hunk of bronze, "This is a potential statue." Someone who says such things is not misusing the English language, but he is not using 'potential' in the strong specific way that potentialists — proponents of the Potentiality Principle — are using the word. What is the difference? What is the difference between the two examples just given, and "This acorn is a potential oak tree," and "This embryo is a potential person?"
PIP: Necessarily, if x is a potential F, and there is a y such that y realizes, whether partially or fully, x's potentiality to be an F, then x = y.
Note that PIP does not imply that there is a y that realizes x's potential. Potentialities, after all, may go unrealized similarly as dispositions may go unmanifested. A seed's potential will go unrealized if the seed is destroyed, or if the seed is not planted, or if it is improperly planted, or if it is properly planted but left unwatered, etc. What PIP states is that if anything does realize x's potentiality to be an F, then that thing is transtemporally numerically identical to x. So if there is an oak tree that realizes acorn A's potentiality to be an oak tree, then A is identical over time to that oak tree. This implies that when the acorn becomes an oak tree, it still exists, but is an oak tree rather than an acorn. The idea is that numerically one and the same individual passes through a series of developmental stages. In the case of a human being these would include zygote, embryo, fetus, infant, child, adolescent, and adult.
Not so with the hunk of bronze. It is not identical to the statue that is made out of it. Statue and hunk of bronze cannot be identical since they differ in their persistence conditions. The hunk of bronze can, while the statue cannot, survive being melted down and recast in some other form.
Consider the Pauline verse at 1 Corinthians 13:11: "When I was a child, I spake as a child, I understood as a child, I thought as a child: but when I became a man, I put away childish things." This implies that numerically one and the same man, Paul of Tarsus, was first a child and later became an adult: it is not as if there was a numerically different entity, Paul-the-child, who passed out of existence when Paul-the-adult came into existence.
So not only is potentiality (in the strong sense here in play) governed by PIP, it is also governed by what I will call the Potentiality Endurantism Principle:
PEP. Necessarily, if x is a potential F, and there is a y such that y realizes, whether partially or fully, x's potentiality to be an F, then x (= y) is wholly present at every time at which x (= y) exists.
PEP rules out a temporal parts ontology according to which a spatiotemporal particular persists in virtue of having different temporal parts at different times.
Let me conclude by throwing another principle into the mix, one that is implict above. I'll call it the Potentiality Agency Principle:
PAP. Necessarily, if x is a potential F, and x's potential is to any extent realized, then the realization of x's potential is driven, not by any agency external to x, but by x's own internal agency, with the proviso that the circumambient conditions are favorable.
The notion of (strong) potentiality that figures in the Potentiality Principle and the Potentiality Argument is governed by PIP, PEP, and PAP at the very least.