Aristotelianism, classical theism and presentism

A fundamental commitment of Aristotelianism seems to be that all reality supervenes on substances and accidents. If according to worlds w₁ and w₂ there are the same substances and accidents, then w₁ = w₂.

But this seems incompatible with presentism. For given indeterminism, there is a world just like the actual one but which tomorrow will diverge from ours. The fact that tomorrow the other world will diverge from ours, however, does not make any difference as to what substances and accidents presently exist, and hence, given presentism, to what substances and accidents exist simpliciter.

It is usual for presentists to posit tensed properties like being such that yesterday you mowed the lawn or being such that tomorrow you will mow the lawn. But the future-tensed property, at least, is not a good candidate for being an Aristotelian accident. Aristotelian accidents are real qualities of things. So that won’t help the Aristotelian presentist.

Here’s another way to put the problem. According to Aristotelianism, facts cannot change without a change in the substance and accidents. But this is not compatible with presentism. Now imagine that there is only one substance, a radioactive atom that will decay in a week. Suppose this substance undergoes no other changes besides that decay. Then today it is a fact that the atom will decay in seven days. Tomorrow this will no longer be a fact—instead, it will be a fact that the atom will decay in six days. Thus, the facts will change between today and tomorrow. But no substances or accidents will come in or out of existence between today and tomorrow, as we supposed that the decay—which is a week away—is the only change that will happen.

There is a simple solution for the Aristotelian, and it is one that Aristotle himself opted for: accept open futurism, i.e., a temporal logic on which there are no facts of the matter about undetermined future events. Assuming this is the only option, the above arguments show that:

1. (Presentism + Aristotelianism) implies open future.

However, given the doctrinal understanding of omniscience in classical theism:

2. Classical theism implies the denial of open future.

We can get a variety of implications from 1 and 2. The one that I like the antecedent of is:

3. (Classical theism + Aristotelianism) implies the denial of presentism.