Identity and quantification

One way of posing the question of diachronic identity is to ask for an explanation of facts like

1. The xs compose the very same object at t₁ as the ys compose at t₂

where we do not use sameness or identity or similar concepts in the explanation.

This task turns out to be quite easy. The following is logically equivalent to (1) and does not use sameness or identity:

2. There is an object z such that the xs compose z at t₁ and the ys compose z at t₂.

This is a variant of the point made here.