The first thing that comes to my mind is to consider probability distributions over partitions, and find the lowest-valued one of those. The weights could be interpreted as credences that a given partition is in fact “the correct one”. After all, I doubt we have a specific idea of the boundary between two given objects—we can’t map which atom is part of which object, even if we had microscopic vision and could see the atoms. The border is fuzzy. Seems like a distribution over partitions would thus do better than a single partition.
Ah, but then the problem is, how do you score them? Hmm. I may need to think about this. It’s the kind of mathematical puzzle I like playing with.
The first thing that comes to my mind is to consider probability distributions over partitions, and find the lowest-valued one of those. The weights could be interpreted as credences that a given partition is in fact “the correct one”. After all, I doubt we have a specific idea of the boundary between two given objects—we can’t map which atom is part of which object, even if we had microscopic vision and could see the atoms. The border is fuzzy. Seems like a distribution over partitions would thus do better than a single partition.
Ah, but then the problem is, how do you score them? Hmm. I may need to think about this. It’s the kind of mathematical puzzle I like playing with.