, Volume 13, Issue 1, pp 51-60

Philosophy, mathematics, science and computation

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Abstract

Attempts to lay a foundation for the sciences based on modern mathematics are questioned. In particular, it is not clear that computer science should be based on set-theoretic mathematics. Set-theoretic mathematics has difficulties with its own foundations, making it reasonable to explore alternative foundations for the sciences. The role of computation within an alternative framework may prove to be of great potential in establishing a direction for the new field of computer science.

Whitehead's theory of reality is re-examined as a foundation for the sciences. His theory does not simply attempt to add formal rigor to the sciences, but instead relies on the methods of the biological and social sciences to construct his world-view. Whitehead's theory is a rich source of notions that are intended to explain every element of experience. It is a product of Whitehead's earlier attempt to provide a mathematical foundation for the physical sciences and is still consistent with modern physics.

A computer simulation language is, in fact, a theory of reality; one that is often based on extremely simplistic notions. Simulation languages have evolved from the various programming languages and not from the development of their underlying world-view. The use of an established theory of reality, such as Whitehead's, as the basis of a simulation language is proposed as a way of extending the usefulness of computer simulation as an experimental tool for the theory.

The λσ simulation language is a first step in this direction. Based on Whitehead's notion of concrescence and a formalization in the typed λ-calculus, λσ provides a notation and method for the construction and simulation of real-world phenomena. Both philosophy and computer science stand to benefit from such an attempt. Whitehead's theory gains a testing tool, while computer science gains a significantly more advanced simulation language.

In philosophical discussion, the merest hint of dogmatic certainty as to the finality of statement is an exhibition of folly. A. N. Whitehead,Process and Reality.