Pragmatism, mathematical models, and the scientific ideal of prediction and control

•Models primarily derived from the observation of functional relations do indeed contribute to the scientific value of theories and explanations, even though the final form of the models appears to be highly indirect and abstract.•Models not primarily so derived invite less effective and frequently mentalistic theories and explanations of behavior.•Models may be evaluated in terms of both (a) the verbal processes responsible for their origin and development and (b) the prediction and control engendered by the theories and explanations that incorporate the models, however indirect and abstract that prediction and control may be.•Technological application and theoretical contemplation may be viewed as continuous and overlapping forms of scientific activity, rather than dichotomous and mutually exclusive.

Mathematical models are often held to be valuable, if not necessary, for theories and explanations in the quantitative analysis of behavior. The present review suggests that mathematical models primarily derived from the observation of functional relations do indeed contribute to the scientific value of theories and explanations, even though the final form of the models appears to be highly abstract. However, mathematical models not primarily so derived risk being essentialist in character, based on a particular view of formal causation. Such models invite less effective and frequently mentalistic theories and explanations of behavior. Models may be evaluated in terms of both (a) the verbal processes responsible for their origin and development and (b) the prediction and control engendered by the theories and explanations that incorporate the models, however indirect or abstract that prediction and control may be. Overall, the present review suggests that technological application and theoretical contemplation may be usefully viewed as continuous and overlapping forms of scientific activity, rather than dichotomous and mutually exclusive.