What Is Computational Knowledge And How Do We Acquire It?

. The goal of foundational thinking in computer science is to understand the methods and practices of working programmers; we might even be able to improve upon those practices. The investigation outlined here applies the methods of constructive mathematics 'a l`a A. N. Kolmogoroff, L. E. J. Brouwer and Errett Bishop to contemporary computer science. The major approach is to use Kolmogoroff's interpretation of the predicate calculus. This investigation includes an attempt to merge contemporary thoughts on computability and computing semantics with the language of mental constructions proposed by Brouwer. This necessarily forces us to ask about the psychology of language. I present a definition of algorithms that links language, constructive mathematics, and logic. Using the concept of an abstract family of algorithms (Hennie) and principles of constructivity, a definition of problem solving. The constructive requirements for an algorithm are developed and presented. Given this framewor..