Formal Models and Mathematical Thinking: Towards a Scientific Epistemology of Psychology
Keywords:
Mathematical formalization, formal models, mathematical psychology, falsification, dynamic model, Bayesian inference, clinical psychology, psychological networks, epistemology of psychologyAbstract
This essay argues that psychology requires mathematical thinking in a broad sense to strengthen its scientific character. It is argued that reducing mathematics to a purely numerical domain in school education limits the capacity for formal reasoning among professionals and students, thereby encouraging the acceptance of discourses lacking verifiable structure within clinical practice. Drawing on the distinction between verbal models and formal models, the essay demonstrates how mathematization, whether through equations, probabilistic models, logical structures, or topological frameworks, makes it possible to explicate assumptions, generate predictions, and subject hypotheses to falsification. Examples of applications are presented, including a hypothetical logistic model relating situational uncertainty to prosocial behavior, and a dynamic model inspired by nonlinear physics to describe therapist and patient interactions. The paper also discusses the feasibility of incorporating non numerical formalisms, such as those proposed in certain contemporary interpretations of psychoanalysis, within the scientific framework, provided that they are expressed as coherent and testable structures. It is concluded that mathematical formalization does not replace the human dimension of clinical practice; rather, it complements it by providing greater operational clarity, predictive capacity, and epistemological accountability.
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