Is Every Cognitive Phenomenon Computable?
Fernando Rodriguez-Vergara, Phil Husbands
Mathematics February 2, 2026 DOI: 10.3390/math14030535 (opens in new tab)
Study at a glance
AI-extracted from the abstract| Characteristics | Theoretical or philosophical paper Peer reviewed |
|---|---|
| Keywords | Cognition Phenomenon Consciousness Relation database Limit mathematics Process computing Turing test Bounded function Cognitive science Cognitive psychology Conviction Turing machine Artificial intelligence Cognitive systems Epistemology Mental representation Super-recursive algorithm |
| Key points | Argues that the unresolved relationship between cognition and computation will define future research in artificial life, cognitive science, and artificial intelligence. |
Abstract
According to the Church–Turing thesis, the limit of what is computable is bounded by Turing machines. Following from this, given that general computable functions formally describe the notion of recursive mechanisms, it is sometimes argued that every organismic process that specifies consistent cognitive responses should be both limited to Turing machine capabilities and amenable to formalization. There is, however, a deep intuitive conviction permeating contemporary cognitive science, according to which mental phenomena, such as consciousness and agency, cannot be explained by resorting to this kind of framework. In spite of some exceptions, the overall tacit assumption is that whatever the mind is, it exceeds the reach of what is described by notions of computability. This issue, namely the nature of the relation between cognition and computation, becomes particularly pertinent and increasingly more relevant as a possible source of better understanding the inner workings of the mind, as well as the limits of artificial implementations thereof. Moreover, although it is often overlooked or omitted so as to simplify our models, it will probably define, or so we argue, the direction of future research on artificial life, cognitive science, artificial intelligence, and related fields.