We argue that the search for the ultimate theory of physics can be modelled mathematically as the search for an algebraic system with the property that the set of all its representations forms an algebraic system isomorphic to the original. The simplest examples of algebraic systems with this property are identified with corresponding theories of physics. The philosophical setting is developed in the form of a Kantian-like thesis.

The preprint version dated November 1987 was sent to Canadian Philosophy Journal where a very enthusiastic referee liked the ideas but asked me to explain it with reference to Kant. After I did that, the referee changed his mind but did say that time would tell if my ideas were right ... see my revisit of these ideas 20 years later in my chapter of my book On Space and Time.