The projection of the subject-predicate relation into the real world serves two purposes.

The properties of material objects, too, exist independently of our imagination, but they do not exist independently of the objects of which they are properties. More specifically, therefore, substance betoken the kind of independent existence that properties lack, the smile of the Cheshire cat notwithstanding. Hence Aristotle's definition.

Can the difference between two exactly similar objects reside in their substances? Obviously not. Asking how one substance — by itself, conceptually divested of its properties — can differ from another substance is like asking how one subject without predicates can differ from another subject without predicates. It can't. Substance, therefore, does not betoken individual existence. Individuality is strictly a matter of properties.

If there are no individual substances, then substance obviously cannot serve as the glue that binds together the properties of each object (without binding together the properties of all objects). The legitimate question of why certain physical properties always go together (for instance, being a fermion and having half-integral spin) cannot be answered in such a naive way.

But if one substance cannot differ from another, then there cannot be such a thing as another substance. There can only be one substance.

Now recall the conclusions of the previous article. Our theoretical division of the world into separate physical systems is a fiction. So, therefore, is the atomistic paradigm, according to which material objects are made up of individual substances. It is impossible to interpose a multitude of permanently self-identical and mutually distinct substances between the one substance that betokens existence and a multitude of existing properties. At bottom there is only one system (or substance), and this constitutes the universe and each of the apparently separate things that exist in it. This is what moves both northward and southward initially and both eastward and westward in the end.

Our conclusion that individuality is strictly a matter of properties, at which we arrived via an analysis of the way quantum mechanics assigns probabilities to measurement outcomes, is therefore not as revolutionary as it seems at first sight. It merely confirms what a sufficiently logical "logic" entails, which is that ultimately there can be only one substance.