The Precision Trap: On the Idealization of Mathematics in Psychology

Calls for greater precision and mathematization in psychology are often motivated by the hope that they will help overcome the field's theoretical problems. While mathematics undoubtedly contributes to scientific progress, this paper questions the idea that an increase in mathematization, in itself, constitutes progress. First, it examines the tradeoffs of precision, arguing that making a theory more precise can change what is being studied, reduce its functionality, and sometimes lend an unwarranted authority to its claims. It also considers examples of non-mathematical yet successful psychological approaches. Second, the paper introduces the Mathematization Bind. Under a realist standard, mathematical precision cannot, by itself, establish that a theory has moved closer to Reality, as the history of the luminiferous aether illustrates. Under a pragmatic standard, the value of mathematics depends on what it enables us to accomplish, relative to the goals of inquiry. Neither perspective justifies treating greater mathematization as scientific progress by default. The paper also questions the tendency to regard an idealized image of physics as the model of scientific maturity. It concludes that the appropriate role and degree of mathematization in psychology should be determined by what it actually contributes to scientific inquiry, rather than by expectations about what a mature science ought to look like.