This chapter looks back to the pioneering studies that prefigured the emergence of cognitive science, subsequently converging into this new interdisciplinary field in the late 1970s. The first section addresses a key turning point in psychology. Whereas behaviorism holds that all explicit behaviors are the product of conditioning, it became clear that animals can manipulate representations of the environment to solve complex problems without reinforcement. The second section introduces the Turing machine developed by Turing in the 1930s, illustrating that purely mechanical procedures can process information algorithmically. The idea of a computable machine contributed to the birth of computer science and provided a model for thinking about how the mind processes information. Chomsky's transformational grammar offers a classic example of a computable model of how complex sentences convey information as a function of basic syntax rules. Finally, Miller and Broadbent's findings on attention support applying the information-processing model in psychology. These pioneering researchers were the first to lay out some of what were to be the basic concepts of cognitive science.

Chapter 4 focuses in the methodological and instrumental contrasts between artificial economics and mainstream economics. It discusses the mathematical methods of mainstream economics (centered around the use of optimization methods and systems of equations representations) versus the computational methods of artificial economics (characterized by the use of algorithms, software, and computer hardware). Presents basic notions on algorithms, recursion, and Turing machines. And discusses the methodological and instrumental differences between artificial economics and mainstream economics as derived from differences between classical mathematics and constructive mathematics.

Computability is discussed here at length, beingthe prime example of what Gödel callsformalism independence in his 1946 Princeton Bicentennial Lecture. The emergence of the concept of human effective calculability and of its formal counterpart---simply computability---is traced in the work of Gödel, Chucrh, Hilbert and Bernays, and finally Turing. The reception of Turing’s work on the part of Church and Kleene as well as on the part of Gödel is chronicled.