The cessation of memory and the nature of the soul
The first quest you get in NieR: Automata is for the item shop vendor, who asks you to retrieve a few supplies for him because he can't go. Bum leg. He explains up front that the resistance doesn't have sufficient supplies to waste some repairing his leg, but when you return with sufficient supplies he still refuses.
His explanation is that the leg is the only 'original' part of him left, the rest of his body have long since been replaced by piece, and he doesn't want to give up the leg because he feels that it will make him a completely different person.
This is the Ship of Theseus (or Grandfather's Axe) parable; if you replace the physical structure of something piece by piece, until nothing that remains is original, is it still the same thing that it once was?
The android in the Resistance Camp doesn't seem to think so, or at least is concerned enough about the question that he refuses to fix his broken leg. There is a sense of existential terror here, not just simple sentiment, although I doubt he would cease to be between the two operations (and I doubt he believes as much himself).
This is quietly fascinating because the very concept of the YoRHa units -- 2B and 9S themselves -- is rooted in no small part to the concept of continuity of the self outside of the physical shell.
We need to establish now what 2B's real mission is-- she is not who she claims to be. She is actually 2E, an Execution unit, paired always with 9S with the orders to kill him when he discovers the secret behind the conflict between androids and machines, as 9S has done dozens of times in the past, requiring him to be killed and reset every time. We see this seeded as early as the prologue, when 9S reveals he lost all memories of the Factory mission, and is reinforced throughout the game by the save system. If you fail to save, then the 'memories' of your prior experience will reset and be re-downloaded into a new body. The actual world state will not change -- chests you opened will remain open, money collected will remain in your wallet -- but your player character will lose the experience and chips they had gained between your resurrection and finding your previous body.
The experience is, to me, the more interesting part, as it feeds back into that loss of continuity. These things that you would have learned during this ill-fated adventure won't return to the new body, but they can be re-integrated once you find the old one. And, more importantly, you as the player will likely have learned from your poorly-conceived foray into the fight that killed you.
The YoRHa units actually put very little stock in the physical body, to the point that the premise of the fast-travel system is that you upload your consciousness into a different body that's waiting at one of the other save points and just carry on. While you can theoretically go the whole game without getting killed or fast traveling, the prologue ends in the annihilation of 2B and 9S, meaning that by the time you have the ability to save the game yourself you are playing a second iteration of 2B. And... who knows how many iterations of 9S.
9S, whose memory of the mission was wiped away when his body was destroyed.
We return, in a roundabout way, to the Ship of Theseus.
The Ship of Theseus parable is about the meaning of continuity and whether exchange by degrees can preserve the nature of the thing which is being exchanged. It is concerned first and foremost with the physical reality of the thing, but your answer to the question likely depends on your interpretation of what that thing is. Because in raw, physical reality, no. The blanks of the ship, the rivets, the rope, everything has been removed and what now stands where the ship was is a completely different structure. Perhaps built identically to the original, but it is not the original.
Is that pertinent to the question, though?
Or do you put stock in the meaning of the ship? That Theseus and his men preserved it through so much time and battle, that the spirit of the vessel remains even if none of its structure does?
Let's invert this-- let's say the ship is in pristine condition, somehow unrepaired, all the original structure intact. And the crew decides to sell it.
Is it still the Ship of Theseus?
It is the same ship, in totality. It once belonged to Theseus. But ownership has changed, and so has sentiment. Can we in good faith still call it the Ship of Theseus, or is it now Once the Ship of Theseus, or the Ship of Minoa, or the Ship of Jason?
i don't think the shopkeeper had anything to worry about, losing his leg. If the Resistance androids function like the YoRHa units, replacing a bun leg would not overwrite his memories or his sense of self. Perhaps he knew this, too, and it dogged sentimentality that told him otherwise. Maybe, logically, he knew it was irrational. But the idea of losing yourself so completely... I can understand the fear.
What about 9S?
9S loses his memories cyclically, but he is so valuable that he isn't simply decommissioned-- he's reset and unleashed back into the world to gather data until the time comes when 2B must kill him again. And then he is restored, and sent out, and the cycle repeats. They could send a different S-unit. They could reprogram him to stop being so curious. This is a problem that could be fixed.
Why isn't it?
NieR: Automata tacitly implies that the soul persists. That regardless of what 9S experiences in his duties, he will always be 9S-- no matter the body, no matter the memories. This conclusion isn't really up for debate.
The question is whether it's good enough. How much of you are you, if you aren't allowed to remember? You will never get that hypothetical version of you back. Is what comes back, over and over, still you in a meaningful way? Should it still be considered you to people that watch you get replaced and dismantled and rebuilt with new parts, over and over and over again?
2B doesn't think so.
