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.

The recognition that human minds/brains are finite systems with limited resources for computation has led some researchers to advance theTractable 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 theP‐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 theFPT‐Cognition thesisas 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)

Despite their success in describing and predicting cognitive behavior, the plausibility of so-called ‘rational explanations’ is often contested on the grounds of computational intractability. Several cognitive scientists have argued that such intractability is an orthogonal pseudoproblem, however, since rational explanations account for the ‘why’ of cognition but are agnostic about the ‘how’. Their central premise is that humans do not actually perform the rational calculations posited by their models, but only act as if they do. Whether or not the problem (...) of intractability is solved by recourse to ‘as if’ explanations critically depends, inter alia, on the semantics of the ‘as if’ connective. We examine the five most sensible explications in the literature, and conclude that none of them circumvents the problem. As a result, rational ‘as if’ explanations must obey the minimal computational constraint of tractability. (shrink)

This study addresses the dynamical nature of a “representation‐hungry” cognitive task involving an imagined action. In our experiment, participants were handed rods that systematically increased or decreased in length on subsequent trials. Participants were asked to judge whether or not they thought they could reach for a distant object with the hand‐held rod. The results are in agreement with a dynamical model, extended from Tuller, Case, Ding, and Kelso (1994). The dynamical effects observed in this study suggest that predictive judgments (...) regarding the possibility or impossibility of a certain action can be understood in terms of dynamically evolving basins of attraction instead of as depending on representational structures. (shrink)

Intractability is a growing concern across the cognitive sciences: while many models of cognition can describe and predict human behavior in the lab, it remains unclear how these models can scale to situations of real-world complexity. Cognition and Intractability is the first book to provide an accessible introduction to computational complexity analysis and its application to questions of intractability in cognitive science. Covering both classical and parameterized complexity analysis, it introduces the mathematical concepts and proof techniques that can be used (...) to test one's intuition of tractability. It also describes how these tools can be applied to cognitive modeling to deal with intractability, and its ramifications, in a systematic way. Aimed at students and researchers in philosophy, cognitive neuroscience, psychology, artificial intelligence, and linguistics who want to build a firm understanding of intractability and its implications in their modeling work, it is an ideal resource for teaching or self-study. (shrink)

Many compelling examples have recently been provided in which people can achieve impressive epistemic success, e.g. draw highly accurate inferences, by using simple heuristics and very little information. This is possible by taking advantage of the features of the environment. The examples suggest an easy and appealing naturalization of rationality: on the one hand, people clearly can apply simple heuristics, and on the other hand, they intuitively ought do so when this brings them high accuracy at little cost.. The ‘ought-can’ (...) principle is satisfied, and rationality is meaningfully normative. We show, however, that this naturalization program is endangered by a computational wrinkle in the adaptation process taken to be responsible for this heuristics-based (‘ecological’) rationality: for the adaptation process to guarantee even minimal rationality, it requires astronomical computational resources, making the problem intractable. We consider various plausible auxiliary assumptions in attempt to remove this obstacle, and show that they do not succeed; intractability is a robust property of adaptation. We discuss the implications of our findings for the project of naturalizing rationality. (shrink)

Advancement in cognitive science depends, in part, on doing some occasional ‘theoretical housekeeping’. We highlight some conceptual confusions lurking in an important attempt at explaining the human capacity for rational or coherent thought: Thagard & Verbeurgt’s computational-level model of humans’ capacity for making reasonable and truth-conducive abductive inferences (1998; Thagard, 2000). Thagard & Verbeurgt’s model assumes that humans make such inferences by computing a coherence function (f_coh), which takes as input representation networks and their pair-wise constraints and gives as output (...) a partition into accepted (A) and rejected (R) elements that maximizes the weight of satisfied constraints. We argue that their proposal gives rise to at least three difficult problems. (shrink)

Four articles in this issue of topiCS (volume 4, issue 1) argue against a computational approach in cognitive science in favor of a dynamical approach. I concur that the computational approach faces some considerable explanatory challenges. Yet the dynamicists’ proposal that cognition is self-organized seems to only go so far in addressing these challenges. Take, for instance, the hypothesis that cognitive behavior emerges when brain and body (re-)configure to satisfy task and environmental constraints. It is known that for certain systems (...) of constraints, no procedure can exist (whether modular, local, centralized, or self-organized) that reliably finds the right configuration in a realistic amount of time. Hence, the dynamical approach still faces the challenge of explaining how self-organized constraint satisfaction can be achieved by human brains and bodies in real time. In this commentary, I propose a methodology that dynamicists can use to try to address this challenge. (shrink)

Single cell recordings in monkeys provide strong evidence for an important role of the motor system in action understanding. This evidence is backed up by data from studies of the (human) mirror neuron system using neuroimaging or TMS techniques, and behavioral experiments. Although the data acquired from single cell recordings are generally considered to be robust, several debates have shown that the interpretation of these data is far from straightforward. We will show that research based on single-cell recordings allows for (...) unlimited content attribution to mirror neurons. We will argue that a theoretical analysis of the mirroring process, combined with behavioral and brain studies, can provide the necessary limitations. A complexity analysis of the type of processing attributed to the mirror neuron system can help formulate restrictions on what mirroring is and what cognitive functions could, in principle, be explained by a mirror mechanism. We argue that processing at higher levels of abstraction needs assistance of non-mirroring processes to such an extent that subsuming the processes needed to infer goals from actions under the label ?mirroring? is not warranted. (shrink)

People cannot understand intentions behind observed actions by direct simulation, because goal inference is highly context dependent. Context dependency is a major source of computational intractability in traditional information-processing models. An embodied embedded view of cognition may be able to overcome this problem, but then the problem needs recognition and explication within the context of the new, layered cognitive architecture.

Barbey & Sloman (B&S) advocate a dual-process (two-system) approach by comparing it with an alternative perspective (ecological rationality), claiming that the latter is unwarranted. Rejecting this alternative approach cannot serve as sufficient evidence for the viability of the former.

Theory of mind refers to the human capacity for reasoning about others’ mental states based on observations of their actions and unfolding events. This type of reasoning is notorious in the cognitive science literature for its presumed computational intractability. A possible reason could be that it may involve higher-order thinking. To investigate this we formalize theory of mind reasoning as updating of beliefs about beliefs using dynamic epistemic logic, as this formalism allows to parameterize ‘order of thinking.’ We prove that (...) theory of mind reasoning, so formalized, indeed is intractable. Using parameterized complexity we prove, however, that the ‘order parameter’ is not a source of intractability. We furthermore consider a set of alternative parameters and investigate which of them are sources of intractability. We discuss the implications of these results for the understanding of theory of mind. (shrink)

Paul ThagardCambridge, MA: MIT press, 2006313 pages, ISBN: 026220164X (hbk); $36.00Can human beliefs and inferences be understood as a form of coherence maximization? This question underlies much o...

This paper focuses on the cognitive/computational and evolutionary levels. It describes three proposals to make cognition computationally tractable, namely: Resource Rationality, the Adaptive Toolbox and Massive Modularity. While each of these proposals appeals to evolutionary considerations to dissolve the intractability of cognition, Rich, Blokpoel, de Haan, and van Rooij argue that, in each case, the intractability challenge is not resolved, but just relocated to the level of evolution.

This paper focuses on the cognitive/computational and evolutionary levels. It describes three proposals to make cognition computationally tractable, namely: Resource Rationality, the Adaptive Toolbox and Massive Modularity. While each of these proposals appeals to evolutionary considerations to dissolve the intractability of cognition, Rich, Blokpoel, de Haan, and van Rooij argue that, in each case, the intractability challenge is not resolved, but just relocated to the level of evolution.

Bayesian models are often criticized for postulating computations that are computationally intractable (e.g., NP-hard) and therefore implausibly performed by our resource-bounded minds/brains. Our letter is motivated by the observation that Bayesian modelers have been claiming that they can counter this charge of “intractability” by proposing that Bayesian computations can be tractably approximated. We would like to make the cognitive science community aware of the problematic nature of such claims. We cite mathematical proofs from the computer science literature that show intractable (...) Bayesian computations, such as postulated in existing Bayesian models, cannot be tractably approximated. This does not mean that human brains do not (or cannot) implement the type of algorithms that Bayesian modelers are advancing, but it does mean that proposing that they do by itself does nothing to parry the charge of intractability, because the postulated algorithms are as intractable (i.e., require exponential time) as the computations they try to approximate. Besides our negative message for the community, our letter also makes a positive contribution by referring to a methodology that Bayesian modelers can use to try and parry the charge of intractability in a mathematically sound way. (shrink)

Leech et al. present a connectionist algorithm as a model of (the development) of analogizing, but they do not specify the algorithm's associated computational-level theory, nor its computational complexity. We argue that doing so may be essential for connectionist cognitive models to have full explanatory power and transparency, as well as for assessing their scalability to real-world input domains.

A long‐standing debate in the study of human communication centers on the degree to which communicators tune their communicative signals (e.g., speech, gestures) for specific addressees, as opposed to taking a neutral or egocentric perspective. This tuning, called recipient design, is known to occur under special conditions (e.g., when errors in communication need to be corrected), but several researchers have argued that it is not an intrinsic feature of human communication, because that would be computationally too demanding. In this study, (...) we contribute to this debate by studying a simple communicative behavior, communicative pointing, under conditions of successful (error‐free) communication. Using an information‐theoretic measure, called legibility, we present evidence of recipient design in communicative pointing. The legibility effect is present early in the movement, suggesting that it is an intrinsic part of the communicative plan. Moreover, it is reliable only from the viewpoint of the addressee, suggesting that the motor plan is tuned to the addressee. These findings suggest that recipient design is an intrinsic feature of human communication. (shrink)

In terms of Groenendijk and Stokhof’s (1984) formalization of exhaustive interpretation, many conversational implicatures can be accounted for. In this paper we justify and generalize this approach. Our justification proceeds by relating their account via Halpern and Moses’ (1984) non-monotonic theory of ‘only knowing’ to the Gricean maxims of Quality and the first sub-maxim of Quantity. The approach of Groenendijk and Stokhof (1984) is generalized such that it can also account for implicatures that are triggered in subclauses not entailed by (...) the whole complex sentence. (shrink)

We offer philosophical motivations for a method we call Virtual World Cognitive Science (VW CogSci), in which researchers use virtual embodied agents that are embedded in virtual worlds to explore questions in the field of Cognitive Science. We focus on questions about mental and linguistic representation and the ways that such computational modeling can add rigor to philosophical thought experiments, as well as the terminology used in the scientific study of such representations. We find that this method forces researchers to (...) take a god’s-eye view when describing dynamical relationships between entities in minds and entities in an environment in a way that eliminates the need for problematic talk of belief and concept types, such as the belief that cats are silly, and the concept CAT, while preserving belief and concept tokens in individual cognizers’ minds. We conclude with some further key advantages of VW CogSci for the scientific study of mental and linguistic representation and for Cognitive Science more broadly. (shrink)

In this classic work of feminist political thought, Iris Marion Young challenges the prevailing reduction of social justice to distributive justice.

This paper analyses the phenomenology and epistemology of chatbots such as ChatGPT and Bard. The computational architecture underpinning these chatbots are large language models (LLMs), which are generative AI (Artificial Intelligence) systems trained on a massive dataset of text extracted from the Web. We conceptualise these LLMs as multifunctional computational cognitive artifacts, used for various cognitive tasks such as translating, summarizing, answering questions, information-seeking, and much more. Phenomenologically, LLMs can be experienced as a “quasi-other”; when that happens, users anthropomorphise them. (...) For most users, current LLMs are black boxes, i.e., for the most part, they lack data transparency and algorithmic transparency. They can, however, be phenomenologically and informationally transparent, in which case there is an interactional flow. Anthropomorphising and interactional flow can, in some users, create an attitude of (unwarranted) trust towards the output LLMs generate. We conclude this paper by drawing on the epistemology of trust and testimony to examine the epistemic implications of these dimensions. Whilst LLMs generally generate accurate responses, we observe two epistemic pitfalls. Ideally, users should be able to match the level of trust that they place in LLMs to the degree that LLMs are trustworthy. However, both their data and algorithmic opacity and their phenomenological and informational transparency can make it difficult for users to calibrate their trust correctly. The effects of these limitations are twofold: users may adopt unwarranted attitudes of trust towards the outputs of LLMs (which is particularly problematic when LLMs hallucinate), and the trustworthiness of LLMs may be undermined. (shrink)

The novelist blends philosophy and metaphysics to examine the nature and origin of Plato's hostile views toward art and its role in life.

The idea of perfection.--On God and Good.--The sovereignty of good over other concepts.

In this paper, we explain why the antecedent of a biscuit conditional is relevant to its consequent by extending Douvenʼs evidential support theory of conditionals making use of utilities. By this extension, we can also explain why a biscuit conditional gives rise to the inference that the consequence is (most likely) true. Finally, we account for the intuition that (indicative) biscuit sentences are false when the antecedent is false and allow for counterfactual biscuits.

A much discussed topic in the theory of choice is how a preference order among options can be derived from the assumption that the notion of ' choice' is primitive. Assuming a choice function that selects elements from each finite set of options, Arrow (Económica 26: 121-127,1959) already showed how we can generate a weak ordering by putting constraints on the behavior of such a function such that it reflects utility maximization. Arrow proposed that rational agents can be modeled by (...) such choice functions. Arrow's standard model of rationality has been criticized in economics and gave rise to approaches of bounded rationality. Two standard assumptions of rationality will be given up in this paper. First, the idea that agents are utility optimizers (Simon). Second, the idea that the relation of ' indifference' gives rise to an equivalence relation. To account for the latter, Luce (Econometrica 24: 178-191, 1956) introduced semi-orders. Extending some ideas of Van Benthem (Pac Philos Q 63: 193-203, 1982), we will show how to derive semi-orders (and so-called interval orders) based on the idea that agents are utility satisficers rather than utility optimizers. (shrink)

The appropriateness, or acceptability, of a conditional does not just ‘go with’ the corresponding conditional probability. A condition of dependence is required as well. In this paper a particular notion of dependence is proposed. It is shown that under both a forward causal and a backward evidential reading of the conditional, this appropriateness condition reduces to conditional probability under some natural circumstances. Because this is in particular the case for the so-called diagnostic reading of the conditional, this analysis might help (...) to explain some of Douven and Verbrugge’s empirical observations. (shrink)

Contains papers presented at the Thirteenth Amsterdam Colloquium in formal semantics, pragmatics and logic, which was held in Amsterdam, December 17-19, 2001.

In this paper an approach to the exhaustive interpretation of answers is developed. It builds on a proposal brought forward by Groenendijk and Stokhof (1984). We will use the close connection between their approach and McCarthy's (1980, 1986) predicate circumscription and describe exhaustive interpretation as an instance of interpretation in minimal models, well-known from work on counterfactuals (see for instance Lewis (1973)). It is shown that by combining this approach with independent developments in semantics/pragmatics one can overcome certain limitations of (...) Groenenedijk and Stokhof's (1984) proposal. In the last part of the paper we will provide a Gricean motivation for exhaustive interpretation building on work of Schulz (to appear) and van Rooij and Schulz (2004). (shrink)

Cimpian et al. observed that we accept generic statements of the form ‘Gs are f’ on relatively weak evidence, but that if we are unfamiliar with group G and we learn a generic statement about it, we still treat it inferentially in a much stronger way: all Gs are f. This paper makes use of notions like ‘representativeness’, ‘contingency’ and ‘relative difference’ from psychology to provide a uniform semantics of generics that explains why people accept generics based on weak evidence. (...) The spirit of the approach has much in common with Leslie’s cognition-based ideas about generics, but the semantics will be grounded on a strengthening of Cohen’s relative readings of generic sentences. In contrast to Leslie and Cohen, we propose a uniform semantic analysis of generics. The basic intuition is that a generic of the form ‘Gs are f’ is true because f is typical for G, which means that f is valuably associated with G. We will make use of Kahneman and Tversky’s Heuristics and Biases approach, according to which people tend to confuse questions about probability with questions about representativeness, to explain pragmatically why people treat many generic statements inferentially in a much stronger way. (shrink)

In terms of Groenendijk and Stokhofs (1984) formalization of exhaustive interpretation, many conversational implicatures can be accounted for. In this paper we justify and generalize this approach. Our justification proceeds by relating their account via Halpern and Moses (1984) non-monotonic theory of only knowing to the Gricean maxims of Quality and the first sub-maxim of Quantity. The approach of Groenendijk and Stokhof (1984) is generalized such that it can also account for implicatures that are triggered in subclauses not entailed by (...) the whole complex sentence. (shrink)