A Renewed Challenge to Anti-criterialism

In virtue of what do things persist through time? Are there criteria of their identities through time? Anti-criterialists say no. One prominent challenge to anti-criterialism comes in two steps. The first step is to show that anti-criterialists are committed specifically to the claim that there are no informative metaphysically sufficient conditions for identity through time. The second step is to show that this commitment yields absurd results. Each step of this challenge is open to objection. However, in what follows, I will refortify this challenge to anti-criterialism by offering new reasons to take each step.