Definitively Identifying an Inherent Limitation to Actual Cognition
This work addresses a foundational issue in philosophy of mind and AI by providing a rigorous limitation on cognition without relying on empirically contradicted assumptions.
The paper tackles the problem of applying Gödel's incompleteness theorems to human cognition by avoiding unrealistic assumptions of infallibility and purely formal reasoning, and presents a novel methodology that establishes a definitive limitation applicable to real-world entities like individuals or groups.
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.