Definitively Identifying an Inherent Limitation to Actual Cognition (1905.13010v2)

Abstract: A century ago, discoveries of a serious kind of logical error made separately by several leading mathematicians led to acceptance of a sharply enhanced standard for rigor within what ultimately became the foundation for Computer Science. By 1931, Godel had obtained a definitive and remarkable result: an inherent limitation to that foundation. The resulting limitation is not applicable to actual human cognition, to even the smallest extent, unless both of these extremely brittle assumptions hold: humans are infallible reasoners and reason solely via formal inference rules. Both assumptions are contradicted by empirical data from well-known Cognitive Science experiments. This article investigates how a novel multi-part methodology recasts computability theory within Computer Science to obtain a definitive limitation whose application to human cognition avoids assumptions contradicting empirical data. The limitation applies to individual humans, to finite sets of humans, and more generally to any real-world entity.