Review of John Von Neumann and Norbert Wiener: From Mathematics to the Technologies of Life and Death by Steve J. Heims. MIT Press, 547 pages, $19.95

This paper examines the grounding of George Spencer Brown’s notion of a distinction, particularly the ultimate distinctions in intension (the elementary) and extension (the universal), It discusses the consequent notions of inside and outside, and discovers that they are apparent, the consequence of the difference between the self and the external observer. The necessity for the constant redrawing of the distinction is shown to create “things”. The form of all things is identical and continuous. This is reflected in the distinction’s similarity to the Möbius strip rather than the circle. There is no inside, no outside except through the notion of the external observer. At the extremes, the edges dissolve. The elementary and.the universal thus re-enter each other. “Your inside is out and your outside is in.”

A theoretical model is proposed that explicates the generation of conceptual structures from unitary sensory objects to abstract constructs that satisfy the criteria generally stipulated for concepts of “number”: independence from sensory properties, unity of composites consisting of units, and potential numerosity. The model is based on the assumption that attention operates not as a steady state but as a pulselike phenomenon that can, but need not, be focused on sensory signals in the central nervous system. Such a view of attention is compatible with recent findings in the neurophysiology of perception and provides, in conjunction with Piaget’s postulate of empirical and reflective abstraction, a novel approach to the analysis of concepts that seem indispensable for the development of numerical operations.

Key words: philosophy of mathematics, cognition, development

Key words: radical constructivism, cognition