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Visheshas the the distinctive items in the metaphysics of the orthodx Hindu philosphy Vaisheshika (which just means "the guys with visheshas"). According to this school, the physical universe is compose entirely of atoms of various types. Each atom of a given type is exactly like every other atom of that type in all its physical characteristics. Every larger physical thing in the universe is identified by what atoms compose it and how they are arranged. In order, then, to identify any thing, we must be able to identify atoms. This cannot be done by physical characteristics, so there must be something else in each atom whose sole purpose is to make it this atom, rather than that one. This is its vishesha.
In logic, this critter is sometimes taken analogically as what allows us to identify the same (or the corresponding) thing across worlds, especially when the shift involves major changes in properties ("If Socrates were a 17th century Irish washerwoman..."). This task has similarly been tried with analogical uses of quiddity, haeceity, and pudgala. Technically it is just a function on worlds that picks a critter in each one in its range. We may put some restrictions on these functions ("essentialism") or not -- usually not, to be on the safe side.
Viewed in this way, visheshas are pretty good analogies -- they do not depend upon any characteristic of the thing to be assigned. But they are in the world, whereas the cross-world identifier is transcendental. The same objection applies to quiddity and haeceity, with the additional problem that they rely on something the thing is or does to identify it. Pudgala, "person," sems to work best and was actually devised for the transworld identity -- what coonects a heap of properties at one moment to a heap at the next so that they are said to be "the same thing" even though basic Buddhism is that there is nothing in the world that endures more than three partless instants. The suggestion that it is a causal relation that makes the connection is negated by another Buddhist claim: that each thing at one moment is caused by everything at the previous moment. So, to talk of "the same thing" requires that the relator be transcendental -- not in any world -- and not reliant on any property of the thing, since the proeprties may change radically at transmigration.
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