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.

在讨论心理学理论主题时，通常会根据心理学与物理科学不同的假设来撰写文章，因为我们没有支持累积的、渐进式科学的理论。在这篇简短的文章中，我将讨论一个反例：Shepard 泛化定律及其在过去 3 年中启发的各种贝叶斯扩展。以谢泼德定律为例，我认为心理学理论构建不是一个统计问题，数学形式主义有利于理论，测量和理论有着复杂的关系，重写旧理论可以产生新的见解，理论增长可以推动实证工作. 虽然我一般认为数学心理学的工具对心理学理论家很有价值，