Realist Conceptualism and Computability

Abstract

This paper formulates an interpretation of computability from the perspective of realist conceptualism. The key notion within this theory is that of a computable concept, where a concept is a cognitive capacity of a certain sort. Differences and connections between the conceptualist interpretation and the classical one, customarily referred to as the theory of effective computability, for which the key concept is that of an algorithm, are shown in the text. Consequences of the idea that the content of computable concepts can be expressed in algorithms are explored. An appendix briefly outlines how the present conceptualist approach differs from two other non-classical interpretations of computability, the intuitionist and the representationist.