Non-transitive identity in the quantum realm: Many worlds, one identity relation
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4th Lisbon International Conference on Philosophy of Science
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According to the Many Worlds Interpretation (MWI), a world-system initially in a superposition of two states, after measurement results in two worlds where each state obtains respectively: world A splits into world B and C. The issue here is that the transitivity of identity fails because A=B, A=C, but B?C.
Two approaches are studied. Wallace?s (2012) worlds as four-dimensional entities stretched over time, so that the relationship is not one of identity but of one temporal parthood, I think results in odd worm-like unintuitive entities.
In the second approach, I consider Bader (2021) which rejects that identity is a one-to-many relation. For him the initial world is identical to only one of the two resulted worlds and this as a brute fact, that carries no further explanation. But I find this to be insufficient because of its explanation is asymmetrical.
My account of world identity is paraconsistent, and in sense also more intuitive: following measurement, if world C was annihilated right after, it would be the case that world A just is world B (and vice versa). This follows the normal progression of identity and preservation account.
I follow Priest?s (2010) logical framework which defines identity as the material biconditional: t0=t1 is defined as ?P(Pt0?Pt1). This logic has values t (true only), f (false only) and b (both true and false) and the material biconditional is not transitive, so identity is not as well. To see this, consider A that is b, B that is t, and C that is f. In this case we have A?B, A?C but ¬(B?C).
Also, in this setting, logical explosion does not follow from the failure of transitivity.
Giving up the transitivity of identity is hard to accept, but paraconsistent identity further provides explanation for cases of fission and vagueness.