ABSTRACT: Many cognitive scientists, having discovered that some computational-level characterization f of a cognitive capacity φ is intractable, invoke heuristics as algorithmic-level explanations of how cognizers compute f. We argue that such explanations are actually dysfunctional, and rebut five possible objections. We then propose computational-level theory revision as a principled and workable alternative.

ABSTRACT: The plausibility of so-called ‘rational explanations’ in cognitive science is often contested on the grounds of computational intractability. Some have argued that intractability is a pseudoproblem, however, because cognizers do not actually perform the rational calculations posited by rational models; rather, they only behave as if they do. Whether or not the problem of intractability is dissolved by this gambit critically depends, inter alia, on the semantics of the ‘as if’ connective. First, this paper examines the five most sensible explications in the literature, and concludes that none of them actually circumvents the problem. Hence, rational ‘as if’ explanations must obey the minimal computational constraint of tractability. Second, this paper describes how rational explanations could satisfy the tractability constraint. Our approach suggests a computationally unproblematic interpretation of ‘as if’ that is compatible with the original conception of rational analysis.

The problem that this paper examines is the specification of the intentional content in the attribution of psychological states. It will be argued that such a specification cannot be complete, both in the case of interpreting the minds of human beings, and in that of other animals. The incompleteness of the specification of the intentional content belongs to the physiology of mindreading, not to its pathology. In favor of this thesis are put forward both epistemological and computational arguments. From the epistemological point of view, it will be suggested that the complete specification of the intentional content makes the psychological attribution impossible. From the computational point of view, it will be argued that the completeness would also make the problem computationally intractable.

We possess the remarkable capacity to identify and understand relational similarities between the constituent parts of disparate wholes. The analogical mapping process underlying this capacity allows us to draw inferences about objects, actions, and events that we see as analogous to one another. This is believed to be a fundamental aspect of intelligence, found in language, creativity, problem solving, and reasoning. A better understanding of how the brain supports the analogical mapping process carries the potential to better understand the domains where it manifests. However, the most well known model of analogical mapping, called Structure-Mapping Theory, has been shown to be computationally intractable. This is problematic because, assuming that the brain is limited by finite computational resources, brain computation is constrained to be tractable. A solution to this problem has been proposed by van Rooij et al. (2008), who have proven that the computations postulated by SMT are tractable provided that the model parameter o (denoting the number of objects in the analogical match) is relatively small. This proposal yields the prediction that humans can quickly determine good analogical matches in situations where o is small. Moreover, it predicts that performance should deteriorate as o grows because of the inherent intractability of the postulated computations. In this thesis, we set out to test these predictions in a behavioral experiment. Participants were instructed to identify squares that correspond with one another on opposite sides of a divided screen. The results demonstrated that increasing the number of squares resulted in longer response times and less optimal analogical mappings. These findings are consistent with the model’s predictions, and provide support for the FPT-Cognition thesis.

Rejecting the claim as meaningless that human reasoning can approximate generally NP-hard Bayesian models—in the sense that the mind's actual " computations " come close to, or be like, inferences that Bayesian models dictate—this paper addresses whether a Bayesian model can nevertheless have normative pull on human reasoners in special cases. For such normative pull to arise, we argue, a well-defined and empirically supported approximation relation is required—but broadly absent—between human reasoning on the ground and the behavior of a non-NP-hard model. We discuss a responsible stance on this issue, and point to complexities that arise in specifying a suitable sense of approximation.

It is often assumed that the socio-cultural context positively influences mindreading performances. Among the available theories, mindshaping is proposed to consist of cultural mechanisms that make the social domain homogeneous and, hence, easier to interpret. Proponents of the mindshaping hypothesis claim that homogeneity is responsible for the computational tractability of mindreading, which is otherwise intractable. In this paper, we examine this core claim of mindshaping and investigate how homogeneity influences mindreading tractability. By taking action understanding as a case-study for mindreading, we formally operationalize mindshaping homogeneity in different ways with the goal of bridging the gap between informal claims and formal (in)tractability results. The analysis shows that only specific combinations of homogeneity may lead to tractable mindreading, whilst others do not. Additionally, the analysis reveals the possibility of a yet undiscovered mindshaping mechanism.