If Mathematical Psychology Did Not Exist We Might Need to Invent It: A Comment on Theory Building in Psychology

It is commonplace, when discussing the subject of psychological theory, to write articles from the assumption that psychology differs from the physical sciences in that we have no theories that would support cumulative, incremental science. In this brief article I discuss one counterexample: Shepard's law of generalization and the various Bayesian extensions that it inspired over the past 3 decades. Using Shepard's law as a running example, I argue that psychological theory building is not a statistical problem, mathematical formalism is beneficial to theory, measurement and theory have a complex relationship, rewriting old theory can yield new insights, and theory growth can drive empirical work. Although I generally suggest that the tools of mathematical psychology are valuable to psychological theorists, I also comment on some limitations to this approach.