This implies a solution to the “weak” Ship of Theseus problem: yes, it’s the same ship.
I think this also implies a solution to the “strong” Ship of Theseus problem: “a new ship is created from the old parts” – but I’m less confident both that it implies this, and that it’s the right conclusion to make. Consider also: mitosis. Which one is “the bacterium”™? But it doesn’t quite make sense (to my fuzzy intuition) to say “the bacterium doesn’t exist any more”.
I think any such algorithm should be able to cope with both “the flower doesn’t exist any more” and “the flower is now two flowers”. I don’t understand this one well enough to make suggestions.
This is a good point. For all three of these (new ship from old parts, mitosis, and two flowers) the algorithm’s answer would be that there are multiple admissible notions of what-the-relevant-object-is, i.e. multiple locally-minimal boundaries consistent with the initial conditions. And indeed, human intuition also recognizes that there are multiple reasonable notions of what-the-object-is. Different object-notions would be relevant to different queries (i.e. different sets of variables considered “far away”).
E.g. in the strong ship of Theseus problem, low-level internal structure of the materials carries over from old to new ship, but their exact connections might not (i.e. nails might be in different places or boards in different order or even just new pitch on the hull). One ship-notion considers anything depending on those connections to be “nearby” (so that information can be safely thrown away), while the other ship-notion considers at least some things depending on those connections to be “far away” (so that information cannot be safely thrown away). On the other hand, if the ship is perfectly reconstructed down to a molecular level, then all of the information is carried over from old to new, and then the algorithm would unambiguously say it’s the same ship.
This implies a solution to the “weak” Ship of Theseus problem: yes, it’s the same ship.
I think this also implies a solution to the “strong” Ship of Theseus problem: “a new ship is created from the old parts” – but I’m less confident both that it implies this, and that it’s the right conclusion to make. Consider also: mitosis. Which one is “the bacterium”™? But it doesn’t quite make sense (to my fuzzy intuition) to say “the bacterium doesn’t exist any more”.
I think any such algorithm should be able to cope with both “the flower doesn’t exist any more” and “the flower is now two flowers”. I don’t understand this one well enough to make suggestions.
This is a good point. For all three of these (new ship from old parts, mitosis, and two flowers) the algorithm’s answer would be that there are multiple admissible notions of what-the-relevant-object-is, i.e. multiple locally-minimal boundaries consistent with the initial conditions. And indeed, human intuition also recognizes that there are multiple reasonable notions of what-the-object-is. Different object-notions would be relevant to different queries (i.e. different sets of variables considered “far away”).
E.g. in the strong ship of Theseus problem, low-level internal structure of the materials carries over from old to new ship, but their exact connections might not (i.e. nails might be in different places or boards in different order or even just new pitch on the hull). One ship-notion considers anything depending on those connections to be “nearby” (so that information can be safely thrown away), while the other ship-notion considers at least some things depending on those connections to be “far away” (so that information cannot be safely thrown away). On the other hand, if the ship is perfectly reconstructed down to a molecular level, then all of the information is carried over from old to new, and then the algorithm would unambiguously say it’s the same ship.