The recognition that human minds/brains are finite systems with limited resources for computation has led some researchers to advance the Tractable Cognition thesis: Human cognitive capacities are constrained by computational tractability. This thesis, if true, serves cognitive psychology by constraining the space of computational‐level theories of cognition. To utilize this constraint, a precise and workable definition of “computational tractability” is needed. Following computer science tradition, many cognitive scientists and psychologists define computational tractability as polynomial‐time computability, leading to the P‐Cognition thesis. (...) This article explains how and why the P‐Cognition thesis may be overly restrictive, risking the exclusion of veridical computational‐level theories from scientific investigation. An argument is made to replace the P‐Cognition thesis by the FPT‐Cognition thesis as an alternative formalization of the Tractable Cognition thesis (here, FPT stands for fixed‐parameter tractable). Possible objections to the Tractable Cognition thesis, and its proposed formalization, are discussed, and existing misconceptions are clarified. (shrink)

In this commentary, I advocate for strict relations between Marr's levels of analysis. Under a strict relationship, each level is exactly implemented by the subordinate level. This yields two benefits. First, it brings consistency for multilevel explanations. Second, similar to how a sculptor chisels away superfluous marble, a modeler can chisel a computational-level model by applying constraints. By sculpting the model, one restricts the set of possible algorithmic- and implementational-level theories.