In reply to john arran:
> It's been a while since I've come across such a charming way of thinking about something so fundamental, so thank you for that.
> Strikes me that this is a mathematical perspective rather than that of a physical scientist.
A lot of the key themes did come from maths books - Douglas Hofstadters probably being the main inspiration. But he never really spelled out that accepting these ideas leads to a conclusion that we don't really die so 'neatly'. (the last paragraph, when considered also works with this idea).
> Also reminds me of something else: If you were to replace the head of Trigger's broom and reuse the old one on a different broom. And then replace the handle of Trigger's broom and reuse the old one on the same other broom. Which one would then be Trigger's broom?
Imagine entering a "teletransporter," a machine that puts you to sleep, then destroys you, breaking you down into atoms, copying the information and relaying it to Mars at the speed of light. On Mars, another machine re-creates you (from local stores of carbon, hydrogen, and so on), each atom in exactly the same relative position. Is the person on Mars the same person as the person who entered the teletransporter on Earth? Certainly, when waking up on Mars, you would feel like being you, you would remember entering the teletransporter in order to travel to Mars, you would even feel the cut on your upper lip from shaving this morning.
Okay think about that for a moment (maybe read it a few times), get that clear in your head before reading the rest.
Then the teleporter is upgraded. The teletransporter on Earth is modified to not destroy the person who enters it, but instead it can simply make a replica at a time, all of whom would claim to remember entering the teletransporter on Earth in the first place. Is the you who wakes up on Mars - you? Is this somehow a different scenario to the first case or not?
Our language is ambiguous (which is great, because it allows puns, double meanings, impreciseness, paradoxes) - which I think means it's not suited to meaningfully answering such a binary question so easily. The intuitive notion of identity (what is what) breaks down at extremes.