R. G. Swinburne; XIII*—Personal Identity, Proceedings of the Aristotelian Society, Volume 74, Issue 1, 1 June 1974, Pages 231–247, https://doi.org/10.1093/arist.

It seems evident that things sometimes get bigger by acquiring new parts. But there is an ancient argument purporting to show that this is impossible: the paradox of increase or growing argument.i Here is a sketch of the paradox. Suppose we have an object, A, and we want to make it bigger by adding a part, B. That is, we want to bring it about that A first lacks and then has B as a part. Imagine, then, that we conjoin (...) B to A in some appropriate way. Never mind what A and B are, or what this conjoining amounts to: let A be anything that can gain a part if anything can gain a part, and let B be the sort of thing that can become a part of A, and suppose we do whatever it would take to make B come to be a part of A if this is possible at all. Have we thereby made B a part of A? It seems not. We seem only to have brought it about that B is attached to A, like this. (shrink)

Philosophers often talk as if what it takes for a person to persist through time were up to us, as individuals or as a linguistic community, to decide. In most ordinary situations it might be fully determinate whether someone has survived or perished: barring some unforeseen catastrophe, it is clear enough that you will still exist ten minutes from now, for example. But there is no shortage of actual and imaginary situations where it is not so clear whether one survives. (...) Here reasonable people may disagree. There are "fission" cases where each of one's cerebral hemispheres is transplanted into a different head; Star-Trek-style "teletransportation" stories; actual cases of brain damage so severe that one can never again regain consciousness, even though one's circulation, breathing, digestion, and other "animal" functions continue; and stories where one's brain cells are gradually removed and replaced by cells from someone else, to name only a few favorites. (shrink)

We can start with some science fiction. Here on Earth, I enter the Teletransporter. When I press some button, a machine destroys my body, while recording the exact states of all my cells. The information is sent by radio to Mars, where another machine makes, out of organic materials, a perfect copy of my body. The person who wakes up on Mars seems to remember living my life up to the moment when I pressed the button, and he is in (...) every other way just like me. Of those who have thought about such cases, some believe that it would be I who would wake up on Mars. They regard Teletransportation as merely the fastest way of travelling. Others believe that, if I chose to be Teletransported, I would be making a terrible mistake. On their view, the person who wakes up would be a mere Replica of me. (shrink)