Is a final theory conceivable?

Abstract

Some physicists believe that a final theory, which will unify separate branches of theoretical physics, including quantum field theory and general relativity, is imminent. The physicists who expect such a theory typically assume that ultimate natural laws will be expressed by the same mathematical formalism which is associated with present-day physics. This view is questionable, because mathematics itself evolves and is not currently in a finished form. Historically, a succession of discoveries in physics has unveiled new laws of nature, each stage being made possible by the development of new mathematics. Evolutionary biology and interbehavioral psychology, ordinarily overlooked by the philosophy of science, reveal further inconsistencies inherent in the concept of a terminal stage of scientific discovery. Another troublesome implication of this notion has come to light recently: Finality of a conceptual scheme comprised of a finite number of natural laws is incompatible with recent developments in mathematical logic and the theory of computational irreducibility.