The remarkable successes of the physical sciences have been built on highly general quantitative laws, which serve as the basis for understanding an enormous variety of specific physical systems. How far is it possible to construct universal principles in the cognitive sciences, in terms of which specific aspects of perception, memory, or decision making might be modelled? Following Shepard (e.g., 1987), it is argued that some universal principles may be attainable in cognitive science. Here, 2 examples are proposed: the simplicity principle (which states that the cognitive system prefers patterns that provide simpler explanations of available data); and the scale-invariance principle, which states that many cognitive phenomena are independent of the scale of relevant underlying physical variables, such as time, space, luminance, or sound pressure. This article illustrates how principles may be combined to explain specific cognitive processes by using these principles to derive SIMPLE, a formal model of memory for serial order (Brown, Neath, & Chater, 2007), and briefly mentions some extensions to models of identification and categorization. This article also considers the scope and limitations of universal laws in cognitive science. (Contains 6 figures, 2 tables and 15 notes.)