Mindcraft is a series of opinion posts on current issues in cognitive science by Brains Blog founder Gualtiero Piccinini. Do you agree? Disagree? Please contribute on the discussion board below! If you’d like to write a full-length response, please contact editor Dan Burnston.
I have written an article proving that allocentric navigation of the sort enabled in vertebrates by the hippocampal-entorhinal complex under the control of the prefrontal cortex is in principle (under standard idealizations) computationally universal. The navigation may occur either online (in the environment) or offline (in the animal’s head). The article is forthcoming in the Journal of Biological Physics. A preprint is available here.
I consider this an important breakthrough in the foundations of the mind sciences, because it gets as close as you can possibly get to a mathematical refutation of the most influential arguments for classical symbolic theories of cognition and paves the way for a research program that aims to explain cognition, including language, symbolic cognition, and propositional thought, in terms of a broadly navigational architecture. I am pursuing that research program in a separate book manuscript that is nearly finished.
Here is a key passage from the article that explains its significance:
“This conclusion [i.e., that allocentric navigation is computationally universal] bears on a familiar line of criticism according to which nonclassical neurocomputational architectures cannot by themselves explain the productivity, systematicity, compositionality, or generality of cognition and therefore require supplementation by a classical symbolic architecture [e.g., Fodor & Pylyshyn, 1988; Gallistel & King, 2009]. It also bears on contemporary debates over whether the available evidence warrants assigning representational functions to neural states [e.g., Krakauer & Ramsey, 2026]. The present results show that navigation-based architectures have sufficient representational and computational power. This entails that such architectures can, in principle, realize arbitrarily complex computable transformations, including transformations exhibiting the kinds of productivity, systematicity, and compositionality often taken to require a classical symbolic architecture.
The same conclusion also bears on a second and opposite source of pressure. Radical enactivist, ecological, and dynamicist approaches emphasize embodied agent–environment coupling and have often been developed as alternatives to orthodox explanations in terms of internal computation and representation [Brooks, 1991; Chemero, 2009; Gibson, 1979; Hutto & Myin, 2013; Port & van Gelder, 1995; Thelen & Smith, 1994; van Gelder, 1995; Varela et al., 1991]. The present results do not vindicate a return to classical internal symbol manipulation. Allocentric navigation is itself embodied, action-oriented, dynamically controlled, and often environmentally embedded. What the results show, rather, is that even architectures situated in all these ways can naturally be analyzed in terms of representational and computational power [cf. Piccinini, 2022]. Once an allocentric navigation system includes stable map-like states, landmark relations, stored item information, local transitions, and controllable movement or simulated movement through a map, its operations can, at the relevant level of analysis, be described as computations over representations and assessed for the class of transformations they can realize. Thus, the relevant contrast is not between classical symbolic computation and no computation or representation at all. A navigation-based architecture can be nonclassical, embodied, and dynamically controlled while still having the same computability-theoretic power as classical symbolic models.
Together, these points open the possibility of explaining higher cognition, including symbolic processing itself, in terms of cognitive map-based computation. Cognitive maps do not normally store and process symbols in any linguistic or language-like sense. What they store is information about the allocentric relations among locations, landmarks, and other items located within the map, together with operations that may be performed on such items. The present results show that those resources are sufficient for universal computation. Symbolic processing therefore need not be treated as architecturally basic but may instead be reconstrued in terms of map-like resources already known to exist in the brain.”
An interdisciplinary conference on how a broadly navigational architecture can explain propositional thought is also about to occur at Mizzou on October 16-7, 2026.
This distinction becomes crucial once the formal result is given explanatory significance for biological cognition. Living cognitive systems are autopoietically and ultimately autocatalytically organized. Their causal organization is not exhausted by factorized transitions between states, because the causal role of each component depends on a recursively maintained organization of the whole system.
A Turing-completeness proof can establish the computational power of an abstracted architecture. But once this architecture is proposed as an explanation of higher biological cognition, a further question arises: does the factorized computational description capture the causal organization by which cognition is actually generated?
In epistemological terms, the model gives us a map of possible transformations. The living organism is the landscape whose organization has to be explained. A proof about the map is not yet an explanation of the landscape.