Four tensions concerning mathematical modeling in psychology.

CONTENTS WHY SHOULD MATHEMA'IICS PI-AY A ROLE IN PSYCHOLOGY? ............................ Structure. Pattern. and Process ........................................................................................... What Keeps Mathematical Psvchology . from Being an 0.xvmoron Y ................................... FOUR DISTINCTIONS .......................................................................................................... . Phenomenological versus Process Models: Unopened and Opened Black Boxes .............. Descriptive versus Normative Models ............................................................................... Dynamic versus Static Moakling ......................................................................................... Noise versus Models of Structure ......................................................................................... EXAMPLES OF PHENOMENOLOGICAL AND PROCESS MODELS ............................... Phenomenological Models ............................................................................................ Process Models ................................................................................................................. Invariance qf Mechanisms Across Situations ...................................................................... A DESCRIPTIVEYNORM ATJVE EXAMPLE. . DECISION MAKING ................................... Normative Principles oj' Preferencc~ ................................................................................ Normative Principles of Framing ...................................................................................... A Descriptive Principle ...................................................................................................... Rankand Sign-dependent Representations ....................................................................... DYNAMIC AND SOMEWHAT DYNAMIC MODELS ......................................................... Models of Incremental Change .................... . ............................................................. Concepts and Memory ..................................... . .......................................................... Problems of Testing Models of' Change ............................................................................. STRUCTURE AND NOISE . , ........................................................................................ Statistical Modeling ............................. , ......................................................... ............ Probabilistic . Mc)dr;tl.s ........................................................................................................