An exercise in vacuity

I’ve been thinking what an Aristotelian would say about the thesis that the normative supervenes on the non-normative. That thesis holds that:

1. any two possible worlds that have the same non-normative facts have the same normative facts.

So, the first question I asked myself was: What sorts of non-normative facts are there on the Aristotelian view of the world? First, every fact involving a natural kind is normative, since natural kind concepts are normative concepts—sheep are the sorts of things that should have four legs (among other things) and electrons are the sorts of things that should repel other electrons (among other things). Second, because natural kind membership is essential, it seems that any facts about particulars will also be normative, since all particulars other than God (and by divine simplicity there are no non-normative facts about God) are essentially members of natural kinds. Could there at least be some non-normative facts about how many objects exist? I don’t think so. For to exist is to be a substance, or to be related appropriately to a substance (say, by being an accident of a substance). But a part of what it is to be a substance is to have a form which governs how one ought to behave, and that’s normative. So existential facts are normative, too.

In fact, it’s looking to me like there are no non-normative facts on an Aristotelian view. Hence, if (1) were to hold, we would have to have:

2. any two possible worlds have the same normative facts.

But since all facts are normative, it would follow that:

3. any two possible worlds have the same facts.

But since possible worlds are distinguished by their facts, we see that on an Aristotelian view, the supervenience thesis basically says:

4. there is only one possible world.

And that’s false.