Many philosophers and psychologists have attempted to elucidate the nature of mental representation by appealing to notions like isomorphism or abstract structural resemblance. The ‘structural representations’ that these theorists champion are said to count as representations by virtue of functioning as internal models of distal systems. In his 2007 book, Representation Reconsidered, William Ramsey endorses the structural conception of mental representation, but uses it to develop a novel argument against representationalism, the widespread view that cognition essentially involves the manipulation of (...) mental representations. Ramsey argues that although theories within the ‘classical’ tradition of cognitive science once posited structural representations, these theories are being superseded by newer theories, within the tradition of connectionism and cognitive neuroscience, which rarely if ever appeal to structural representations. Instead, these theories seem to be explaining cognition by invoking so-called ‘receptor representations’, which, Ramsey claims, aren’t genuine representations at all—despite being called representations, these mechanisms function more as triggers or causal relays than as genuine stand-ins for distal systems. I argue that when the notions of structural and receptor representation are properly explicated, there turns out to be no distinction between them. There only appears to be a distinction between receptor and structural representations because the latter are tacitly conflated with the ‘mental models’ ostensibly involved in offline cognitive processes such as episodic memory and mental imagery. While structural representations might count as genuine representations, they aren’t distinctively mental representations, for they can be found in all sorts of non-intentional systems such as plants. Thus to explain the kinds of offline cognitive capacities that have motivated talk of mental models, we must develop richer conceptions of mental representation than those provided by the notions of structural and receptor representation. (shrink)

Where does the mind stop and the rest of the world begin? The question invites two standard replies. Some accept the demarcations of skin and skull, and say that what is outside the body is outside the mind. Others are impressed by arguments suggesting that the meaning of our words "just ain't in the head", and hold that this externalism about meaning carries over into an externalism about mind. We propose to pursue a third position. We advocate a very different (...) sort of externalism: an _active externalism_, based on the active role of the environment in driving cognitive processes. (shrink)

The primary goal of this essay is to provide a comprehensive overview and analysis of the various relations between material artifacts and the embodied mind. A secondary goal of this essay is to identify some of the trends in the design and use of artifacts. First, based on their functional properties, I identify four categories of artifacts co-opted by the embodied mind, namely (1) embodied artifacts, (2) perceptual artifacts, (3) cognitive artifacts, and (4) affective artifacts. These categories can overlap and (...) so some artifacts are members of more than one category. I also identify some of the techniques (or skills) we use when interacting with artifacts. Identifying these categories of artifacts and techniques allows us to map the landscape of relations between embodied minds and the artifactual world. Second, having identified categories of artifacts and techniques, this essay then outlines some of the trends in the design and use of artifacts, focussing on neuroprosthetics, brain-computer interfaces, and personalisation algorithms nudging their users towards particular epistemic paths of information consumption. (shrink)

Structural representations are increasingly popular in philosophy of cognitive science. A key virtue they seemingly boast is that of meeting Ramsey's job description challenge. For this reason, structural representations appear tailored to play a clear representational role within cognitive architectures. Here, however, I claim that structural representations do not meet the job description challenge. This is because even our most demanding account of their functional profile is satisfied by at least some receptors, which paradigmatically fail the job description challenge. Hence, (...) the functional profile typically associated with structural representations does not identify representational posits. After a brief introduction, I present, in the second section of the paper, the job description challenge. I clarify why receptors fail to meet it and highlight why, as a result, they should not be considered representations. In the third section I introduce what I take to be the most demanding account of structural representations at our disposal, namely Gładziejewski's account. Provided the necessary background, I turn from exposition to criticism. In the first half of the fourth section, I equate the functional profile of structural representations and receptors. To do so, I show that some receptors boast, as a matter of fact, all the functional features associated with structural representations. Since receptors function merely as causal mediators, I conclude structural representations are mere causal mediators too. In the second half of the fourth section I make this conclusion intuitive with a toy example. I then conclude the paper, anticipating some objections my argument invites. (shrink)

Empirical philosophers of science aim to base their philosophical theories on observations of scientific practice. But since there is far too much science to observe it all, how can we form and test hypotheses about science that are sufficiently rigorous and broad in scope, while avoiding the pitfalls of bias and subjectivity in our methods? Part of the answer, we claim, lies in the computational tools of the digital humanities, which allow us to analyze large volumes of scientific literature. Here (...) we advocate for the use of these methods by addressing a number of large-scale, justificatory concerns—specifically, about the epistemic value of journal articles as evidence for what happens elsewhere in science, and about the ability of DH tools to extract this evidence. Far from ignoring the gap between scientific literature and the rest of scientific practice, effective use of DH tools requires critical reflection about these relationships. (shrink)

Predictive processing (PP) has been repeatedly presented as a unificatory account of perception, action, and cognition. In this paper, we argue that this is premature: As a unifying theory, PP fails to deliver general, simple, homogeneous, and systematic explanations. By examining its current trajectory of development, we conclude that PP remains only loosely connected both to its computational framework and to its hypothetical biological underpinnings, which makes its fundamentals unclear. Instead of offering explanations that refer to the same set of (...) principles, we observe systematic equivocations in PP‐based models, or outright contradictions with its avowed principles. To make matters worse, PP‐based models are seldom empirically validated, and they are frequently offered as mere just‐so stories. The large number of PP‐based models is thus not evidence of theoretical progress in unifying perception, action, and cognition. On the contrary, we maintain that the gap between theory and its biological and computational bases contributes to the arrested development of PP as a unificatory theory. Thus, we urge the defenders of PP to focus on its critical problems instead of offering mere re‐descriptions of known phenomena, and to validate their models against possible alternative explanations that stem from different theoretical assumptions. Otherwise, PP will ultimately fail as a unified theory of cognition. (shrink)

It is a common view among philosophers of science that theoretical virtues (also known as epistemic or cognitive values), such as simplicity and consistency, play an important role in scientific practice. In this article, I set out to study the role that theoretical virtues play in scientific practice empirically. I apply the methods of data science, such as text mining and corpus analysis, to study large corpora of scientific texts in order to uncover patterns of usage. These patterns of usage, (...) in turn, might shed some light on the role that theoretical virtues play in scientific practice. Overall, the results of this empirical study suggest that scientists invoke theoretical virtues explicitly, albeit rather infrequently, when they talk about models (less than 30%), theories (less than 20%), and hypotheses (less than 15%) in their published works. To the extent that they are mentioned in scientific publications, the results of this study suggest that accuracy, consistency, and simplicity are the theoretical virtues that scientists invoke more frequently than the other theoretical virtues tested in this study. Interestingly, however, depending on whether they talk about hypotheses, theories, or models, scientists may invoke one of those theoretical virtues more than the others. (shrink)

Replicability and reproducibility of computational models has been somewhat understudied by “the replication movement.” In this paper, we draw on methodological studies into the replicability of psychological experiments and on the mechanistic account of explanation to analyze the functions of model replications and model reproductions in computational neuroscience. We contend that model replicability, or independent researchers' ability to obtain the same output using original code and data, and model reproducibility, or independent researchers' ability to recreate a model without original code, (...) serve different functions and fail for different reasons. This means that measures designed to improve model replicability may not enhance (and, in some cases, may actually damage) model reproducibility. We claim that although both are undesirable, low model reproducibility poses more of a threat to long-term scientific progress than low model replicability. In our opinion, low model reproducibility stems mostly from authors' omitting to provide crucial information in scientific papers and we stress that sharing all computer code and data is not a solution. Reports of computational studies should remain selective and include all and only relevant bits of code. (shrink)

In this paper, we argue that several recent ‘wide’ perspectives on cognition (embodied, embedded, extended, enactive, and distributed) are only partially relevant to the study of cognition. While these wide accounts override traditional methodological individualism, the study of cognition has already progressed beyond these proposed perspectives towards building integrated explanations of the mechanisms involved, including not only internal submechanisms but also interactions with others, groups, cognitive artifacts, and their environment. The claim is substantiated with reference to recent developments in the (...) study of “mindreading” and debates on emotions. We claim that the current practice in cognitive (neuro)science has undergone, in effect, a silent mechanistic revolution, and has turned from initial binary oppositions and abstract proposals towards the integration of wide perspectives with the rest of the cognitive (neuro)sciences. (shrink)

Philosophy of science is expanding via the introduction of new digital data and tools for their analysis. The data comprise digitized published books and journal articles, as well as heretofore unpublished material such as images, archival text, notebooks, meeting notes, and programs. The growth in available data is matched by the extensive development of automated analysis tools. The variety of data sources and tools can be overwhelming. In this article, we survey the state of digital work in the philosophy of (...) science, showing what kinds of questions can be answered and how one can go about answering them. (shrink)

There are at least twelve major virtues of good theories: evidential accuracy, causal adequacy, explanatory depth, internal consistency, internal coherence, universal coherence, beauty, simplicity, unification, durability, fruitfulness, and applicability. These virtues are best classified into four classes: evidential, coherential, aesthetic, and diachronic. Each virtue class contains at least three virtues that sequentially follow a repeating pattern of progressive disclosure and expansion. Systematizing the theoretical virtues in this manner clarifies each virtue and suggests how they might have a coordinated and cumulative (...) role in theory formation and evaluation across the disciplines—with allowance for discipline specific modification. An informal and flexible logic of theory choice is in the making here. Evidential accuracy, according to my systematization, is not a largely isolated trait of good theories, as some have made it out to be. Rather, it bears multifaceted relationships, constituting significant epistemic entanglements, with other theoretical virtues. (shrink)

AbtractTechnologies both new and old provide us with a wide range of cognitive artifacts that change the structure of our cognitive tasks. After a brief analysis of past classifications of these artifacts, I shall elaborate a new way of classifying them developed by focusing on an aspect that has been previously overlooked, namely the possible relationships between these objects and the cognitive processes they involve. Cognitive artifacts are often considered as objects that simply complement our cognitive capabilities, but this “complementary (...) view” seems to be an oversimplification. Assuming an “interaction-centered approach”, this article identifies three essential ways in which cognitive artifacts carry out their function: complementing, constituting and substituting our cognitive processes, and builds a taxonomy of these objects that is grounded on these relations. In so doing, it also addresses the chaotic set of different micro-functions carried out by cognitive artifacts, which have not thus far been dealt with, sorting these functions into three corresponding categories. The second part of the article analyzes in greater detail how cognitive artifacts work in our cognitive life, identifying a new kind of functions, called semi-proper functions, and providing a new definition of cognitive artifact based on the previous analysis of these objects. (shrink)

In this paper I examine the notion of ‘artifact’ and related notions in the dominant version of extended cognition theory grounded on extended functionalism. Although the term is ubiquitous in the literature, it is far from clear what ECT means by it. How are artifacts conceptualized in ECT? Is ‘artifact’ a meaningful and useful category for ECT? If the answer to the previous question is negative, should we worry? Is it important for ECT to have a coherent theory of artifacts? (...) And what are the demands and constraints that ECT imposes on this theory? I distinguish between two aspects of ECT, one narrow, aligned with extended functionalism ; and one broad or pluralistic, in which EF is combined with other theoretical resources in the context of diverse research programs. I begin by determining the problems in conceptualizing artifacts from EF. Then I address the question of why a concept of artifact may be relevant to ECT. Next, I examine the efforts of Richard Heersmink to combine ECT with dominant theories of artifacts in the philosophy of technology. I argue that both approaches fail to yield a meaningful notion of artifact, let alone one of ‘cognitive’ artifact. Finally, I argue that narrow ECT places rather strong constraints on a theory of artifacts, since it locates the specificity of ‘artifact’ in material aspects of realization that are, by definition, outside its theoretical purview. I examine, then discard, the possibility that a materialist and objectivist theory of artifacts may be of help. And finally I briefly explore some ways in which a broad, pluralistic ECT may address some of these shortcomings. (shrink)

Published research findings are sometimes refuted by subsequent evidence, says Ioannidis, with ensuing confusion and disappointment.

In this book, T. L. Short corrects widespread misconceptions of Peirce's theory of signs and demonstrates its relevance to contemporary analytic philosophy of language, mind and science. Peirce's theory of mind, naturalistic but nonreductive, bears on debates of Fodor and Millikan, among others. His theory of inquiry avoids foundationalism and subjectivism, while his account of reference anticipated views of Kripke and Putnam. Peirce's realism falls between 'internal' and 'metaphysical' realism and is more satisfactory than either. His pragmatism is not verificationism; (...) rather, it identifies meaning with potential growth of knowledge. Short distinguishes Peirce's mature theory of signs from his better-known but paradoxical early theory. He develops the mature theory systematically on the basis of Peirce's phenomenological categories and concept of final causation. The latter is distinguished from recent and similar views, such as Brandon's, and is shown to be grounded in forms of explanation adopted in modern science. (shrink)

How is it that thoroughly physical material beings such as ourselves can think, dream, feel, create and understand ideas, theories and concepts? How does mere matter give rise to all these non-material mental states, including consciousness itself? An answer to this central question of our existence is emerging at the busy intersection of neuroscience, psychology, artificial intelligence, and robotics.In this groundbreaking work, philosopher and cognitive scientist Andy Clark explores exciting new theories from these fields that reveal minds like ours to (...) be prediction machines - devices that have evolved to anticipate the incoming streams of sensory stimulation before they arrive. These predictions then initiate actions that structure our worlds and alter the very things we need to engage and predict. Clark takes us on a journey in discovering the circular causal flows and the self-structuring of the environment that define "the predictive brain." What emerges is a bold, new, cutting-edge vision that reveals the brain as our driving force in the daily surf through the waves of sensory stimulation. (shrink)

There have been recent disagreements in the philosophy of neuroscience regarding which sorts of scientific models provide mechanistic explanations, and which do not. These disagreements often hinge on two commonly adopted, but conflicting, ways of understanding mechanistic explanations: what I call the “representation-as” account, and the “representation-of” account. In this paper, I argue that neither account does justice to neuroscientific practice. In their place, I offer a new alternative that can defuse some of these disagreements. I argue that individual models (...) do not provide mechanistic explanations by themselves. Instead, individual models are always used to complement a huge body of background information and pre-existing models about the target system. With this in mind, I argue that mechanistic explanations are distributed across sets of different, and sometimes contradictory, scientific models. Each of these models contributes limited, but essential, information to the same mechanistic explanation, but none can be considered a mechanistic explanation in isolation of the others. (shrink)

According to the predictive coding theory of cognition , brains are predictive machines that use perception and action to minimize prediction error, i.e. the discrepancy between bottom–up, externally-generated sensory signals and top–down, internally-generated sensory predictions. Many consider PCT to have an explanatory scope that is unparalleled in contemporary cognitive science and see in it a framework that could potentially provide us with a unified account of cognition. It is also commonly assumed that PCT is a representational theory of sorts, in (...) the sense that it postulates that our cognitive contact with the world is mediated by internal representations. However, the exact sense in which PCT is representational remains unclear; neither is it clear that it deserves such status—that is, whether it really invokes structures that are truly and nontrivially representational in nature. In the present article, I argue that the representational pretensions of PCT are completely justified. This is because the theory postulates cognitive structures—namely action-guiding, detachable, structural models that afford representational error detection—that play genuinely representational functions within the cognitive system. (shrink)

The goal of this paper is to develop a systematic taxonomy of cognitive artifacts, i.e., human-made, physical objects that functionally contribute to performing a cognitive task. First, I identify the target domain by conceptualizing the category of cognitive artifacts as a functional kind: a kind of artifact that is defined purely by its function. Next, on the basis of their informational properties, I develop a set of related subcategories in which cognitive artifacts with similar properties can be grouped. In this (...) taxonomy, I distinguish between three taxa, those of family, genus, and species. The family includes all cognitive artifacts without further specifying their informational properties. Two genera are then distinguished: representational and non-representational (or ecological) cognitive artifacts. These genera are further divided into species. In case of representational artifacts, these species are iconic, indexical, or symbolic. In case of ecological artifacts, these species are spatial or structural. Within species, token artifacts are identified. The proposed taxonomy is an important first step towards a better understanding of the range and variety of cognitive artifacts and is a helpful point of departure, both for conceptualizing how different artifacts augment or impair cognitive performance and how they transform and are integrated into our cognitive system and practices. (shrink)

The standard objection against naturalised epistemology is that it cannot account for normativity in epistemology (Putnam 1982; Kim 1988). There are different ways to deal with it. One of the obvious ways is to say that the objection misses the point: It is not a bug; it is a feature, as there is nothing interesting in normative principles in epistemology. Normative epistemology deals with norms but they are of no use in prac-tice. They are far too general to be guiding (...) principles of research, up to the point that they even seem vacuous (see Knowles 2003). In this chapter, my strategy will be different and more in spirit of the founding father of naturalized epistemology, Quine, though not faithful to the letter. I focus on methodological prescriptions supplied by cogni-tive science in re-engineering of cognitive architectures. Engineering norms based on mechanism design weren’t treated as seriously as they should in epistemology, and that is why I will develop a sketch of a framework for researching them, starting from analysing cognitive sci-ence as engineering in section 3, then showing functional normativity in section 4, to eventually present functional engineering models of cogni-tive mechanisms as normative in section 5. Yet before showing the kind of engineering normativity specific for these prescriptions, it is worth-while to review briefly the role of normative methodology and the levels of norm complexity in it, and show how it follows Quine’s steps. (shrink)

In the study of cognitive processes, limitations on computational resources (computing time and memory space) are usually considered to be beyond the scope of a theory of competence, and to be exclusively relevant to the study of performance. Starting from considerations derived from the theory of computational complexity, in this paper I argue that there are good reasons for claiming that some aspects of resource limitations pertain to the domain of a theory of competence.

This paper analyzes epistemological and ontological dimensions of Human-Computer Interaction (HCI) through an analysis of the functions of computer systems in relation to their users. It is argued that the primary relation between humans and computer systems has historically been epistemic: computers are used as information-processing and problem-solving tools that extend human cognition, thereby creating hybrid cognitive systems consisting of a human processor and an artificial processor that process information in tandem. In this role, computer systems extend human cognition. Next, (...) it is argued that in recent years, the epistemic relation between humans and computers has been supplemented by an ontic relation. Current computer systems are able to simulate virtual and social environments that extend the interactive possibilities found in the physical environment. This type of relationship is primarily ontic, and extends to objects and places that have a virtual ontology. Increasingly, computers are not just information devices, but portals to worlds that we inhabit. The aforementioned epistemic and ontic relationships are unique to information technology and distinguish human-computer relationships from other human-technology relationships. (shrink)

An examination of the emergence of the phenomenon of deductive argument in classical Greek mathematics.

The cognitive foundations of geometry have puzzled academics for a long time, and even today are mostly unknown to many scholars, including mathematical cognition researchers. -/- Foundations of Geometric Cognition shows that basic geometric skills are deeply hardwired in the visuospatial cognitive capacities of our brains, namely spatial navigation and object recognition. These capacities, shared with non-human animals and appearing in early stages of the human ontogeny, cannot, however, fully explain a uniquely human form of geometric cognition. In the book, (...) Hohol argues that Euclidean geometry would not be possible without the human capacity to create and use abstract concepts, demonstrating how language and diagrams provide cognitive scaffolding for abstract geometric thinking, within a context of a Euclidean system of thought. -/- Taking an interdisciplinary approach and drawing on research from diverse fields including psychology, cognitive science, and mathematics, this book is a must-read for cognitive psychologists and cognitive scientists of mathematics, alongside anyone interested in mathematical education or the philosophical and historical aspects of geometry. (shrink)

The aim of this paper is to discuss the concept of distributed cognition in the context of classic questions posed by mainstream cognitive science. We support our remarks by appealing to empirical evidence from the fields of cognitive science and ethnography. Particular attention is paid to the structure and functioning of a cognitive system, as well as its external representations. We analyze the problem of how far we can push the study of human cognition without taking into account what is (...) underneath an individual’s skin. In light of our discussion, a distinction between DCog and the extended mind becomes important. (shrink)

In Things That Make Us Smart, Donald A. Norman explores the complex interaction between human thought and the technology it creates, arguing for the development of machines that fit our minds, rather than minds that must conform to the machine.Humans have always worked with objects to extend our cognitive powers, from counting on our fingers to designing massive supercomputers. But advanced technology does more than merely assist with thought and memory—the machines we create begin to shape how we think and, (...) at times, even what we value. Norman, in exploring this complex relationship between humans and machines, gives us the first steps towards demanding a person-centered redesign of the machines that surround our lives. (shrink)

SummaryStarting with Descartes, epistemology has been almost entirely based on first person knowledge. We must begin, according to the usual story, with what is most certain: knowledge of our own sensations and thoughts. In one way or another we then progress, if we can, to knowledge of an objective external world. There is then the final, tenuous, step to knowledge of other minds.In this paper I argue for a total revision of this picture. All propositional thought, whether positive or skeptical, (...) whether of the inner or of the outer, requires possession of the concept of objective truth, and this concept is accessible only to those creatures in communication with others. Third person knowledge – knowledge of other minds – is thus conceptually basic. But such knowledge is impossible without knowledge of a shared world of objects in a shared time and space. Thus the acquisition of knowledge is not based on a progression from the subjective to the objective; it emerges holistically, and is interpersonal from the start. (shrink)

What is a scientific theory? This book considers this fundamental question by presenting a range of options and the issues they raise. It draws comparisons between theories and artworks and proposes that we should stop thinking of theories as things altogether.

In this paper, we focus on the development of geometric cognition. We argue that to understand how geometric cognition has been constituted, one must appreciate not only individual cognitive factors, such as phylogenetically ancient and ontogenetically early core cognitive systems, but also the social history of the spread and use of cognitive artifacts. In particular, we show that the development of Greek mathematics, enshrined in Euclid’s Elements, was driven by the use of two tightly intertwined cognitive artifacts: the use of (...) lettered diagrams; and the creation of linguistic formulae. Together, these artifacts formed the professional language of geometry. In this respect, the case of Greek geometry clearly shows that explanations of geometric reasoning have to go beyond the confines of methodological individualism to account for how the distributed practice of artifact use has stabilized over time. This practice, as we suggest, has also contributed heavily to the understanding of what mathematical proof is; classically, it has been assumed that proofs are not merely deductively correct but also remain invariant over various individuals sharing the same cognitive practice. Cognitive artifacts in Greek geometry constrained the repertoire of admissible inferential operations, which made these proofs inter-subjectively testable and compelling. By focusing on the cognitive operations on artifacts, we also stress that mental mechanisms that contribute to these operations are still poorly understood, in contrast to those mechanisms which drive symbolic logical inference. (shrink)

Objective Compare outcome of dogs that did and did not receive fresh frozen plasma (FFP) for treatment of pancreatitis. Design Retrospective case series between 1995 and 2005. Setting University referral hospital. Animals Seventy-four dogs were enrolled with a total of 77 Cases as 2 dogs had repeat episodes of pancreatitis. Diagnosis of pancreatitis was based on clinical signs, physical examination, and abdominal ultrasonographic examination. Interventions The medical database was searched for dogs with a diagnosis of pancreatitis. Information collected included signalment, (...) vital signs, CBC, use of FFP, length of stay, use of antimicrobials and supplemental nutrition, surgical intervention, preexisting illness, evidence of a coagulopathy and outcome. Outcome was compared between those patients that did and did not receive FFP. Measurements and Main Results Fifty-nine dogs survived to discharge. Two dogs with repeat pancreatitis survived to discharge after each episode. Thirteen dogs died and 2 were euthanized. FFP was administered to 20 dogs. Two dogs that were hospitalized for repeat pancreatitis did not receive FFP. Seven of 20 (35%) cases that received plasma died or were euthanized compared with 6 of 57 (12%) cases that did not receive plasma. Plasma administration was significantly related to outcome (P<0.001). Severity of illness scores were difficult to assign, however, dogs meeting criteria for systemic inflammatory response syndrome were not more likely to receive FFP. Other therapies included supplemental nutrition, antimicrobials, and surgical intervention, which did not affect outcome. Conclusions Mortality rate for those dogs receiving plasma was higher than those that did not. Severity of illness scores were difficult to assign; however, preexisting illness, evidence of systemic inflammatory response syndrome, and presence of a coagulopathy were not significantly different between the groups that did and did not receive FFP. No benefit for administration of FFP was noted. Additional investigation should be performed to confirm this result. 2009 Veterinary Emergency and Critical Care Society. (shrink)

The canonical history of mathematics suggests that the late 19th-century “arithmetization” of calculus marked a shift away from spatial-dynamic intuitions, grounding concepts in static, rigorous definitions. Instead, we argue that mathematicians, both historically and currently, rely on dynamic conceptualizations of mathematical concepts like continuity, limits, and functions. In this article, we present two studies of the role of dynamic conceptual systems in expert proof. The first is an analysis of co-speech gesture produced by mathematics graduate students while proving a theorem, (...) which reveals a reliance on dynamic conceptual resources. The second is a cognitive-historical case study of an incident in 19th-century mathematics that suggests a functional role for such dynamism in the reasoning of the renowned mathematician Augustin Cauchy. Taken together, these two studies indicate that essential concepts in calculus that have been defined entirely in abstract, static terms are nevertheless conceptualized dynamically, in both contemporary and historical practice. (shrink)

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)

This article proposes a theoretical framework for external representation based problem solving. The Tic‐Tac‐Toe and its isomorphs are used to illustrate the procedures of the framework as a methodology and test the predictions of the framework as a functional model. Experimental results show that the behavior in the Tic‐Tac‐Toe is determined by the directly available information in external and internal representations in terms of perceptual and cognitive biases, regardless of whether the biases are consistent with, inconsistent with, or irrelevant to (...) the task. It is shown that external representations are not merely inputs and stimuli to the internal mind and that they have much more important functions than mere memory aids. A representational determinism is suggested—the form of a representation determines what information can be perceived, what processes can be activated, and what structures can be discovered from the specific representation. (shrink)

Some philosophers have offered structural representations as an alternative to indicator-based representations. Motivating these philosophers is the belief that an indication-based analysis of representation exhibits two fatal inadequacies from which structural representations are spared: such an analysis cannot account for the causal role of representational content and cannot explain how representational content can be made determinate. In fact, we argue, indicator and structural representations are on a par with respect to these two problems. This should not be surprising, we contend, (...) given that the distinction between indicator and structural representations is better conceived as one involving degree rather than kind. (shrink)

In this article we propose a theoretical framework of distributed representations and a methodology of representational analysis for the study of distributed cognitive tasks—tasks that require the processing of information distributed across the internal mind and the external environment. The basic principle of distributed representations Is that the representational system of a distributed cognitive task is a set of internal and external representations, which together represent the abstract structure of the task. The basic strategy of representational analysis is to decompose (...) the representation of a hierarchical task into its component levels so that the representational properties at each level can be independently examined. The theoretical framework and the methodology are used to analyze the hierarchical structure of the Tower of Hanoi problem. Based on this analysis, four experiments are designed to examine the representational properties of the Tower of Hanoi. Finally, the nature of external representations is discussed. (shrink)