Keynote speaker: Gregory Cox - Estes early career award lecture

Models and Meaning: Coming Out as a Mathematical Psychologist I love introducing myself to laypeople as a "mathematical psychologist" because they often view the term as an inherent contradiction between the strict formal world of mathematical and computational models on the one hand and the fuzzy ineffable realm of the mind on the other. By embracing that apparent conflict, I think mathematical psychology is in a unique position to help advance the science of cognition beyond the recent crises which have exposed issues in our experimental and statistical methods. Mathematical psychology has already played a large part in developing tools that expand access to Bayesian statistics and psychometrics, but I think it has an even more valuable part to play in advancing the psychological theories our methods are meant to test---by imbuing formal models with meaning and enabling meaning to be expressed via formal models. In this talk, I consider a number of issues I have encountered in developing mathematical models to express cognitive theories. These issues manifest, like mathematical psychology itself, as tensions between seemingly opposing ends of a continuum. These include some specific issues related to my own areas of research, like the tension between episodic and semantic memory; the tension between associations and the items they bind together; and the tension between neural and cognitive levels of description. They also include broader issues like the tension between statistical/descriptive models and causal/mechanistic models; the tension between quantitative fit and explanatory power; and the tension between models as psychometric tools versus expressions of theory. I make no attempt to resolve these tensions. Instead, I argue that the value of mathematical psychology lies in providing the language to articulate these tensions and to enable researchers to decide for themselves where they fall along these various continua in a given scientific context---to express what they mean in terms of models and to use models to help them explore what they mean.