The equations at the top of this page are the two most important principles of the theory of abstract objects. In this document, we try to give you some idea of what these principles say. The theory of abstract objects is a metaphysical theory. Whereas physics attempts a systematic description of fundamental and complex concrete objects, metaphysics attempts a systematic description of fundamental and complex abstract objects.
Abstract objects are the objects that are presupposed by our scientific conceptual framework.
For example, when doing natural science, we presuppose that we can use the natural numbers to count concrete objects, and that we can use the real numbers to measure them in various ways. As part of our scientific investigations, we presuppose that objects behave in certain ways because they have certain properties , and that natural laws govern not just actual objects that have certain properties, but any physically possible object having those properties. So metaphysics investigates numbers, laws, properties, possibilities, etc., as entities in their own right, since they seem to be presupposed by our very understanding of the scientific enterprise. The theory of abstract objects attempts to organize these objects within a systematic and axiomatic framework. It would be a mistake to think that a theory postulating abstract objects is incompatible with our theories of natural science, which seem to presuppose that the only things that exist are the things governed by our true scientific theories.