There are presently two leading foreign policy decision-making paradigms in vogue. The first is based on the classical or rational model originally posited by von Neumann and Morgenstern to explain microeconomic decisions. The second is based on the cybernetic perspective whose groundwork was laid by Herbert Simon in his early research on bounded rationality. In this paper we introduce a third perspective -- the poliheuristic theory of decision-making -- as an alternative to the rational actor and cybernetic paradigms in international (...) relations. This theory is drawn in large part from research on heuristics done in experimental cognitive psychology. According to the poliheuristic theory, policy makers use poly (many) heuristics while focusing on a very narrow range of options and dimensions when making decisions. Among them, the political dimension is noncompensatory. The paper also delineates the mathematical formulations of the three decision-making models. (shrink)

There are presently two leading foreign policy decision-making paradigms in vogue. The first is based on the classical or rational model originally posited by von Neumann and Morgenstern to explain microeconomic decisions. The second is based on the cybernetic perspective whose groundwork was laid by Herbert Simon in his early research on bounded rationality. In this paper we introduce a third perspective — thepoliheuristic theory of decision-making — as an alternative to the rational actor and cybernetic paradigms in international relations. (...) This theory is drawn in large part from research on heuristics done in experimental cognitive psychology. According to the poliheuristic theory, policy makers use poly (many) heuristics while focusing on a very narrow range of options and dimensions when making decisions. Among them, the political dimension is noncompensatory. The paper also delineates the mathematical formulations of the three decision-making models. (shrink)

Current understanding of the development of quantity representations is based primarily on performance in the number‐line task. We posit that the data from number‐line tasks reflect the observer's underlying representation of quantity, together with the cognitive strategies and skills required to equate line length and quantity. Here, we specify a unified theory linking the underlying psychological representation of quantity and the associated strategies in four variations of the number‐line task: the production and estimation variations of the bounded and unbounded (...) number‐line tasks. Comparison of performance in the bounded and unbounded number‐line tasks provides a unique and direct way to assess the role of strategy in number‐line completion. Each task produces a distinct pattern of data, yet each pattern is hypothesized to arise, at least in part, from the same underlying psychological representation of quantity. Our model predicts that the estimated biases from each task should be equivalent if the different completion strategies are modeled appropriately and no other influences are at play. We test this equivalence hypothesis in two experiments. The data reveal all variations of the number‐line task produce equivalent biases except for one: the estimation variation of the bounded number‐line task. We discuss the important implications of these findings. (shrink)

This study tested a structural model of cognitive-emotional explanatory variables to explain performance in mathematics. The predictor variables assessed were related to students’ level of development of early mathematical competencies (EMCs), specifically, relational and numerical competencies, predisposition toward mathematics, and the level of logical intelligence in a population of primary school Chilean students (n = 634). This longitudinal study also included the academic performance of the students during a period of four years as a variable. The sampled students (...) were initially assessed by means of an Early Numeracy Test (ENT), and, subsequently, they were administered a Likert-type scale to measure their predisposition toward mathematics (EPMAT) and a basic test of logical intelligence (TILE). The results of these tests were used to analyse the interaction of all the aforementioned variables by means of a structural equations model. This combined interaction model was able to predict 64.3% of the variability of observed performance. Preschool students' performance in EMCs was a strong predictor for achievement in mathematics for students between 8 to 11 years of age. Therefore, this paper highlights the importance of EMCs and the modulating role of predisposition toward mathematics. Also, this paper discusses the educational role of these findings, as well as possible ways to improve negative predispositions toward mathematical tasks in the school domain. (shrink)

This article argues that many, if not most, behavior descriptions and sequencing are in essence an interpretation of signs, and are evaluated as sequences of signs by researchers. Thus, narrative analysis, as developed by Barthes and others, seems best suited to be used in behavioral/biosemiotic studies rather than mathematical modeling, and is very similar to some classic ethology methods. As our brain interprets behaviors as signs and attributes meaning to them, narrative analysis seems more suitable than mathematical modeling (...) to describe and study behavior. Mathematical models are, on many occasions, extremely reductionist and simplifying because of computational and/or numerical representation limitations that lead to errors and straitjacketing interpretations of reality. Since actual animals are not as optimal in real life as our mathematical models, here it is proposed that we should consider logical/verbal models and semantic interpretations as equally or even better suited for behavioral analysis, and refrain from enforcing mathematical modeling as the only way to study and understand biological problems, especially those of a behavioral and biosemiotic nature. (shrink)

Theory of Mind (ToM) is the term used for our ability to predict and explain the behaviour of ourselves and others. Accounts of this theory have so far fallen into two competing types: Simulation Theory and 'Theory Theory'. In contrast with Theory Theory, Simulation Theory argues that we predict behaviour not by employing a model of people, but by replicating others' thoughts and feelings. This book presents a novel defence of Simulation Theory, reviewing the major challenges against it and positing (...) the theory as the most effective method for exploring how we know each other and ourselves. Drawing on key research in the field, chapters reopen the debates surrounding Theory of Mind and cover a variety of topics including schizophrenia with implications for experimental social psychology. In the past, one of the greatest criticisms against Simulation Theory is that it cannot explain systematic error in Theory of Mind. This book explores the rapidly developing heuristics and biases programme, pioneered by Kahneman and Tversky, to suggest that a novel bias mismatch defence available to Simulation Theory explains these systematic errors. Simulation Theory: A psychological and philosophical consideration will appeal to a range of researchers and academics, including psychologists from the fields of cognitive, social and developmental psychology, as well as philosophers, psychotherapists and practitioners looking for further research on Theory of Mind. The book will also be of relevance to those interested in autism, since it offers a new approach to Theory of Mind which explains central symptoms in autistic subjects. (shrink)

This book is devoted to the study of human thought, its systemic structure, and the historical development of mathematics both as a product of thought and as a fascinating case analysis. After demonstrating that systems research constitutes the second dimension of modern science, the monograph discusses the yoyo model, a recent ground-breaking development of systems research, which has brought forward revolutionary applications of systems research in various areas of the traditional disciplines, the first dimension of science. After the systemic structure (...) of thought is factually revealed, mathematics, as a product of thought, is analyzed by using the age-old concepts of actual and potential infinities. In an attempt to rebuild the system of mathematics, this volume first provides a new look at some of the most important paradoxes, which have played a crucial role in the development of mathematics, in proving what these paradoxes really entail. Attention is then turned to constructing the logical foundation of two different systems of mathematics, one assuming that actual infinity is different than potential infinity, and the other that these infinities are the same. This volume will be of interest to academic researchers, students and professionals in the areas of systems science, mathematics, philosophy of mathematics, and philosophy of science. (shrink)

In this paper, we propose a new mathematical model of retrieval of intentions from long-term memory. We model retrieval as a stochastic race between a plurality of potentially relevant intentions stored in long-term memory. Psychological theories are dominated by two opposing conceptions of the role of memory in temporally extended agency – as when a person has to remember to make a phone call in the afternoon because, in the morning, she promised she would do so. According to the (...) Working Memory conception, remembering to make the phone call is explained in terms of the construction and maintenance of intentions in working-memory. According to the Long-Term Memory conception, we should explain the episode in terms of an ability to store intentions in long-term memory. The two conceptions predict different processing profiles. The aim of this paper is to present a new mathematical model of the type of memory mechanism that could realise the long-term memory representations of intentions necessary for the Long-Term Memory conception. We present and illustrate the formal model and propose a new type of experimental paradigm that could allow us to test which of the two conceptions provides the best explanation of the role of memory in temporally extended agency. (shrink)

We discuss foundational issues of quantum information biology —one of the most successful applications of the quantum formalism outside of physics. QIB provides a multi-scale model of information processing in bio-systems: from proteins and cells to cognitive and social systems. This theory has to be sharply distinguished from “traditional quantum biophysics”. The latter is about quantum bio-physical processes, e.g., in cells or brains. QIB models the dynamics of information states of bio-systems. We argue that the information interpretation of quantum (...) mechanics is the most natural interpretation of QIB. Biologically QIB is based on two principles: adaptivity; openness. These principles are mathematically represented in the framework of a novel formalism— quantum adaptive dynamics which, in particular, contains the standard theory of open quantum systems. (shrink)

In this article my primary intention is to engage in a discussion on the inherent constraints of models, taken as models of theories, that reaches beyond the epistemological level. Naturally the paper takes into account the ongoing debate between proponents of the syntactic and the semantic view of theories and that between proponents of the various versions of scientific realism, reaching down to the most fundamental, subjective level of discourse. In this approach, while allowing for a limited discussion of physical (...) and positive science models, I am primarily focused on the structure and ontology of mathematical models, in particular Cohen’s forcing models and to a lesser extent Gödel’s constructible universe, to the extent that these were designed to answer questions bearing on the scope, the capacity and ultimately the ontology of models themselves, therefore influencing in one or the other way the status of models in general. This status, it is argued, is largely defined by the way models subsume a set-theoretical structure whose constraints, reducible to an extra-linguistic level of discourse, may implicitly condition the epistemic status of models as representations of axiomatic theories. In the last section I deal extensively with the inner constraints of theories as subjectively originated in a less technical philosophically oriented discussion with certain prompts from phenomenology. (shrink)

Children learn and use various strategies to solve math problems. One way children's math learning can be supported is through their use of and exposure to hand gestures. Children's self-produced gestures can reveal unique, math-relevant knowledge that is not contained in their speech. Additionally, these gestures can assist with their math learning and problem solving by supporting their cognitive processes, such as executive function. The gestures that children observe during math instructions are also linked to supporting cognition. Specifically, children (...) are better able to learn, retain, and generalize knowledge about math when that information is presented within the gestures that accompany an instructor's speech. To date, no conceptual model provides an outline regarding how these gestures and the math environment are connected, nor how they may interact with children's underlying cognitive capacities such as their executive function. In this review, we propose a new model based on an integration of the information processing approach and theory of embodied cognition. We provide an in-depth review of the related literature and consider how prior research aligns with each link within the proposed model. Finally, we discuss the utility of the proposed model as it pertains to future research endeavors. (shrink)

Proof requires a dialogue between agents to clarify obscure inference steps, fill gaps, or reveal implicit assumptions in a purported proof. Hence, argumentation is an integral component of the discovery process for mathematical proofs. This work presents how argumentation theories can be applied to describe specific informal features in the development of proof-events. The concept of proof-event was coined by Goguen who described mathematical proof as a public social event that takes place in space and time. This new (...) meta-methodological concept is designed to cover not only “traditional” formal proofs but all kinds of proofs and inference steps, including incomplete or purported proofs. Our approach attempts to make proof-events more comprehensive to express the complete trajectory of a mathematical proof-event until the ultimate validation of the proving outcome. Thus, we advance an extended version of proof-event calculus which is built on argumentation theories designed to capture the internal and external structure of collaborative mathematical practice and highlight the relationship between proof, human reasoning, and cognitive processes. In addition, another area in which argumentation can make a significant contribution is dealing with the defeasible knowledge of the Web which is a product of its open and ubiquitous nature. This approach seems to be sufficient for the presentation of Web-based proving processes as manifested in the case of the Mini-Polymath 4 project. (shrink)

Intelligent mental representations of physical, cognitive and social environments allow humans to navigate enormous search spaces, whose sizes vastly exceed the number of neurons in the human brain. This allows us to solve a wide range of problems, such as the Traveling Salesperson Problem, insight problems, as well as mathematics and physics problems. As an area of research, problem solving has steadily grown over time. Researchers in Artificial Intelligence have been formulating theories of problem solving for the last 70 (...) years. Psychologists, on the other hand, have focused their efforts on documenting the observed behavior of subjects solving problems. This book represents the first effort to merge the behavioral results of human subjects with formal models of the causative cognitive mechanisms. The first coursebook to deal exclusively with the topic, it provides a main text for elective courses and a supplementary text for courses such as cognitive psychology and neuroscience. (shrink)

In computational complexity theory, decision problems are divided into complexity classes based on the amount of computational resources it takes for algorithms to solve them. In theoretical computer science, it is commonly accepted that only functions for solving problems in the complexity class P, solvable by a deterministic Turing machine in polynomial time, are considered to be tractable. In cognitive science and philosophy, this tractability result has been used to argue that only functions in P can feasibly work as (...) computational models of human cognitive capacities. One interesting area of computational complexity theory is descriptive complexity, which connects the expressive strength of systems of logic with the computational complexity classes. In descriptive complexity theory, it is established that only first-order (classical) systems are connected to P, or one of its subclasses. Consequently, second-order systems of logic are considered to be computationally intractable, and may therefore seem to be unfit to model human cognitive capacities. This would be problematic when we think of the role of logic as the foundations of mathematics. In order to express many important mathematical concepts and systematically prove theorems involving them, we need to have a system of logic stronger than classical first-order logic. But if such a system is considered to be intractable, it means that the logical foundation of mathematics can be prohibitively complex for human cognition. In this paper I will argue, however, that this problem is the result of an unjustified direct use of computational complexity classes in cognitive modelling. Placing my account in the recent literature on the topic, I argue that the problem can be solved by considering computational complexity for humanly relevant problem solving algorithms and input sizes. (shrink)

Following a previous article published in Biological Theory, in this study we present a mathematical theory for a science of qualities as directly perceived by living organisms, and based on morphological patterns. We address a range of qualitative phenomena as observables of a psychological system seen as an impredicative system. The starting point of our study is the notion that perceptual phenomena are projections of underlying invariants, objects that remain unchanged when transformations of a certain class under consideration are (...) applied. The study develops with the observables, the entailed total order and metric, whence the algebra and the geometry of such a science, presenting a formal phenomenological model for phenomena that are not rigidly Euclidean. We show how non-Euclidean perception can have many useful Euclidean formalizations, as well as locally-homeomorphic-to-Euclidean-space models. The mathematical models we provide are tested on the basis of results from experimental psychology, in particular from the field of color, time, and space perception. (shrink)

This study uses personality and psychology health characteristics of high school students as intermediary variables to study how cognitive ability affects academic performance, and analyzes memory, information processing, presentation, logical reasoning, and thinking transformation ability in high school students. In this study, the structural equation model was used to analyze the mediating effect, and the bootstrap method was used to test the significance of the mediating effect. The participants were 572 high school students from Beijing, China. They completed (...) a survey that included questions on cognitive ability, personality characteristics, and psychology health. This study uses structural equation modeling for mediation analysis. Through the analysis of four models of comprehensive academic performance, Chinese academic performance, mathematics academic performance, and English academic performance, the results of the study showed that cognitive ability has a significant effect on academic performance, and personality characteristics and psychology health play a partially mediating role between cognitive ability and English academic performance. The mediation effect is about 40%. (shrink)

Quantum cognition research applies abstract, mathematical principles of quantum theory to inquiries in cognitive science. It differs fundamentally from alternative speculations about quantum brain processes. This topic presents new developments within this research program. In the introduction to this topic, we try to answer three questions: Why apply quantum concepts to human cognition? How is quantum cognitive modeling different from traditional cognitive modeling? What cognitive processes have been modeled using a quantum account? In addition, a (...) brief introduction to quantum probability theory and a concrete example is provided to illustrate how a quantum cognitive model can be developed to explain paradoxical empirical findings in psychological literature. (shrink)

This book presents a comprehensive review of the emerging theories from cognitive science that integrate both decision processes and choice behavior.

Contemporary psychological research that studies how people apply mathematics has largely viewed mathematics as a computational tool for deriving an answer. The tacit assumption has been that people first understand a situation, and then choose which computations to apply. We examine an alternative assumption that mathematics can also serve as a tool that helps one to construct an understanding of a situation in the first place. Three studies were conducted with 6th‐grade children in the context of proportional situations because early (...) proportional reasoning is a premier example of where mathematics may provide new understanding of the world. The children predicted whether two differently‐sized glasses of orange juice would taste the same when they were filled from a single carton of juice made from concentrate and water. To examine the relative contributions and interactions of situational and mathematical knowledge, we manipulated the formal features of the problem display (e.g., diagram vs. photograph) and the numerical complexity (e.g., divisibility) of the containers and the ingredient ratios. When the problem was presented as a diagram with complex numbers, or “realistically” with easy numbers, the children predicted the glasses would taste different because one glass had more juice than the other. But, when the problem was presented realistically with complex numbers, the children predicted the glasses would taste the same on the basis of empirical knowledge (e.g., “Juice can't change by itself”). And finally, when the problem was presented as a diagram with easy numbers, the children predicted the glasses would taste the same on the basis of proportional relations. These complex interactions illuminate how mathematical and empirical knowledge can jointly constrain the construction of a new understanding of the world. We propose that mathematics helped in the case of successful proportional reasoning because it made a complex empirical situation cognitively tractable, and thereby helped the children construct mental models of that situation. We sketch one aspect of the mental models that are constructed in the domain of quantity—a preference for specificity—that helps explain the current findings. (shrink)

The first systematic collaboration between cognitive scientists and sports psychologists considers the mind–body relationship from the perspective of athletic skill and sports practice. This landmark work is the first systematic collaboration between cognitive scientists and sports psychologists that considers the mind–body relationship from the perspective of athletic skill and sports practice. With twenty-six chapters by leading researchers, the book connects and integrates findings from fields that range from philosophy of mind to sociology of sports. The chapters show not (...) only that sports can tell scientists how the human mind works but also that the scientific study of the human mind can help athletes succeed. Sports psychology research has always focused on the themes, notions, and models of embodied cognition; embodied cognition, in turn, has found striking confirmation of its theoretical claims in the psychological accounts of sports performance and athletic skill. Athletic skill is a legitimate form of intelligence, involving cognitive faculties no less sophisticated and complex than those required by mathematical problem solving. After presenting the key concepts necessary for applying embodied cognition to sports psychology, the book discusses skill disruption ; sensorimotor skill acquisition and how training correlates to the development of cognitive faculties; the intersubjective and social dimension of sports skills, seen in team sports; sports practice in cultural and societal contexts; the notion of “affordance” and its significance for ecological psychology and embodied cognition theory; and the mind's predictive capabilities, which enable anticipation, creativity, improvisation, and imagination in sports performance. Contributors Ana Maria Abreu, Kenneth Aggerholm, Salvatore Maria Aglioti, Jesús Ilundáin-Agurruza, Duarte Araújo, Jürgen Beckmann, Kath Bicknell, Geoffrey P. Bingham, Jens E. Birch, Gunnar Breivik, Noel E. Brick, Massimiliano L. Cappuccio, Thomas H. Carr, Alberto Cei, Anthony Chemero, Wayne Christensen, Lincoln J. Colling, Cassie Comley, Keith Davids, Matt Dicks, Caren Diehl, Karl Erickson, Anna Esposito, Pedro Tiago Esteves, Mirko Farina, Giolo Fele, Denis Francesconi, Shaun Gallagher, Gowrishankar Ganesh, Raúl Sánchez-García, Rob Gray, Denise M. Hill, Daniel D. Hutto, Tsuyoshi Ikegami, Geir Jordet, Adam Kiefer, Michael Kirchhoff, Kevin Krein, Kenneth Liberman, Tadhg E. MacIntyre, Nelson Mauro Maldonato, David L. Mann, Richard S. W. Masters, Patrick McGivern, Doris McIlwain, Michele Merritt, Christopher Mesagno, Vegard Fusche Moe, Barbara Gail Montero, Aidan P. Moran, David Moreau, Hiroki Nakamoto, Alberto Oliverio, David Papineau, Gert-Jan Pepping, Miriam Reiner, Ian Renshaw, Michael A. Riley, Zuzanna Rucinska, Lawrence Shapiro, Paula Silva, Shannon Spaulding, John Sutton, Phillip D. Tomporowski, John Toner, Andrew D. Wilson, Audrey Yap, Qin Zhu, Christopher Madan. (shrink)

This book describes a novel methodology for studying algorithmic skills, intended as cognitive activities related to rule-based symbolic transformation, and argues that some human computational abilities may be interpreted and analyzed as genuine examples of extended cognition. It shows that the performance of these abilities relies not only on innate neurocognitive systems or language-related skills, but also on external tools and general agent–environment interactions. Further, it asserts that a low-level analysis, based on a set of core neurocognitive systems linking (...) numbers and language, is not sufficient to explain some specific forms of high-level numerical skills, like those involved in algorithm execution. To this end, it reports on the design of a cognitive architecture for modeling all the relevant features involved in the execution of algorithmic strategies, including external tools, such as paper and pencils. The first part of the book discusses the philosophical premises for endorsing and justifying a position in philosophy of mind that links a modified form of computationalism with some recent theoretical and scientific developments, like those introduced by the so-called dynamical approach to cognition. The second part is dedicated to the description of a Turing-machine-inspired cognitive architecture, expressly designed to formalize all kinds of algorithmic strategies. (shrink)

The prominence of Bayesian modeling of cognition has increased recently largely because of mathematical advances in specifying and deriving predictions from complex probabilistic models. Much of this research aims to demonstrate that cognitive behavior can be explained from rational principles alone, without recourse to psychological or neurological processes and representations. We note commonalities between this rational approach and other movements in psychology – namely, Behaviorism and evolutionary psychology – that set aside mechanistic explanations or make use (...) of optimality assumptions. Through these comparisons, we identify a number of challenges that limit the rational program's potential contribution to psychological theory. Specifically, rational Bayesian models are significantly unconstrained, both because they are uninformed by a wide range of process-level data and because their assumptions about the environment are generally not grounded in empirical measurement. The psychological implications of most Bayesian models are also unclear. Bayesian inference itself is conceptually trivial, but strong assumptions are often embedded in the hypothesis sets and the approximation algorithms used to derive model predictions, without a clear delineation between psychological commitments and implementational details. Comparing multiple Bayesian models of the same task is rare, as is the realization that many Bayesian models recapitulate existing (mechanistic level) theories. Despite the expressive power of current Bayesian models, we argue they must be developed in conjunction with mechanistic considerations to offer substantive explanations of cognition. We lay out several means for such an integration, which take into account the representations on which Bayesian inference operates, as well as the algorithms and heuristics that carry it out. We argue this unification will better facilitate lasting contributions to psychological theory, avoiding the pitfalls that have plagued previous theoretical movements. (shrink)

This study applied cognitive diagnostic models to assess students’ learning progressions in energy. A Q-matrix was proposed based on existing literature about learning progressions of energy in the physical science domain and the Trends in International Mathematics and Science Study assessment framework. The Q-matrix was validated by expert review and real data analysis. Then, the deterministic inputs, noisy ‘and’ gate model with hierarchical relations was applied to data from three jurisdictions that had stable, defined science curricula. The results suggested (...) that the hypothesized learning progression was consistent with the observed progression in understanding the energy concept. We also found similarities in students’ attribute mastery across the three jurisdictions. In addition, we examined the instructional sensitivity of the selected item. We discuss several curriculum-related issues and student misconceptions that may affect students’ learning progressions and mastery patterns in different regions of the world. (shrink)

Technology-based assessment offers unique possibilities for collecting data about students’ cognitive development and using this data to provide students and teachers with feedback to improve learning. The aim of this study was to show how the psychological dimension of learning can be assessed in everyday educational practice through technology-based assessment in reading, mathematics and science. We analyzed three related aspects of the assessments: cognitive development, gender differences and vertical scaling. The sample for the study was drawn from primary (...) school students in Grades 1–8 (aged 7 to 14) in Hungary. There were 1500 to 2000 students in each grade cohort. Online tests were constructed from 1638 items from the reading, mathematics and science domains in the eDia system. The results confirmed empirically that the disciplinary, application and psychological dimensions of learning can be empirically distinguished. Students’ cognitive development was the most steady (and effective) in mathematics where the greatest development happened in the first years of schooling. Path models suggested that the psychological dimension of learning can be predicted at a moderate level based on students’ level of school knowledge consisting of the disciplinary and application dimensions of learning as latent constructs. The predictive power was almost the same in both of the dimensions. Generally, girls developed faster in the psychological dimension of reading, mathematics and science learning; however, the size of gender differences varied by age and domain. This study (1) provides evidence that the psychological dimension of learning can be made visible even in an educational context and (2) highlights the importance of the explicit development of the psychological dimension of learning during school lessons, and (3) shows that there are gender differences in the developmental level of the psychological dimension of learning in favour of girls, but it varies by grade and domain. (shrink)

This paper takes an embodied and extended cognition perspective to ER integration – a cognitive process through which a learner integrates external representations (ERs) in a domain, with her internal (mental) model, as she interacts with, uses, understands and transforms between those ERs. In the paper, I argue for a theoretical as well as empirical shift in future investigations of ER integration, by proposing a model of cognitive mechanisms underlying the process, based on recent advances in extended and (...) embodied cognition. I present this new model in contrast to the still dominant classical cognitivist (information processing) approaches to ER integration, and the educational technology intervention designs such approaches inspire. I then exemplify this distinction between the information processing model and the new model through a case of arithmetic problem solving. Corroborative neuroscience evidence presented in relation to this case provides empirical support for the new model by showing how bodily actions (sensorimotor mechanisms) are critical to ER integration and learning. Finally, as educational implications of the new model, I demonstrate the need for: (i) re-viewing the development of ER integration and expertise as fine-tuning of the learner's action or sensorimotor system, and (ii) a shift of focus in new-media intervention design principles based on this newer understanding of ER integration in science, technology, engineering and mathematics. (shrink)

In the mid-twentieth century, the identity of those who oversaw the UK electricity grid tentatively and slowly began to shift from those who joined the electricity industry directly from secondary school to a university-educated elite with a higher level of technical education. At the same time, electricity infrastructure became increasingly centralised, leading to the creation of a national grid in 1938, meaning that control of electricity became concentrated in the hands of an ever-smaller group and increasing the stakes in debates (...) over strategy. By using the case studies of power engineer Paul Schiller and mathematician Maurice Davies, this paper traces how the boundaries of what mathematics could or could not be used for were renegotiated between factions within the UK electricity industry. Schiller unsuccessfully attempted to use mathematics, including the authority of academic mathematicians, to reinforce controversial arguments about the strategic direction of the industry in the 1940s. Such arguments failed to resonate with a class of, as Schiller put it, “practical men” that still held considerable influence. Davies on the other hand was employed by the industry in the 1950s to improve efficiency, and was able to implement lasting measures in this effort by using the weather to forecast electricity demand, and successfully defended the usefulness of his work in the 1970s against colleagues who felt that forecasting could be done better with mathematical models without weather inputs. The contrast between these two stories shows how the influence of mathematical thinking was contingent upon existing power dynamics, and reinforce how the history of mathematics should be socially embedded. (shrink)

Searching for information is critical in many situations. In medicine, for instance, careful choice of a diagnostic test can help narrow down the range of plausible diseases that the patient might have. In a probabilistic framework, test selection is often modeled by assuming that people's goal is to reduce uncertainty about possible states of the world. In cognitive science, psychology, and medical decision making, Shannon entropy is the most prominent and most widely used model to formalize probabilistic uncertainty (...) and the reduction thereof. However, a variety of alternative entropy metrics (Hartley, Quadratic, Tsallis, Rényi, and more) are popular in the social and the natural sciences, computer science, and philosophy of science. Particular entropy measures have been predominant in particular research areas, and it is often an open issue whether these divergences emerge from different theoretical and practical goals or are merely due to historical accident. Cutting across disciplinary boundaries, we show that several entropy and entropy reduction measures arise as special cases in a unified formalism, the Sharma–Mittal framework. Using mathematical results, computer simulations, and analyses of published behavioral data, we discuss four key questions: How do various entropy models relate to each other? What insights can be obtained by considering diverse entropy models within a unified framework? What is the psychological plausibility of different entropy models? What new questions and insights for research on human information acquisition follow? Our work provides several new pathways for theoretical and empirical research, reconciling apparently conflicting approaches and empirical findings within a comprehensive and unified information‐theoretic formalism. (shrink)

According to one of the most powerful paradigms explaining the meaning of the concept of natural number, natural numbers get a large part of their conceptual content from core cognitive abilities. Carey’s bootstrapping provides a model of the role of core cognition in the creation of mature mathematical concepts. In this paper, I conduct conceptual analyses of various theories within this paradigm, concluding that the theories based on the ability to subitize (i.e., to assess anexactquantity of the elements (...) in a collection without counting them), or on the ability to approximate quantities (i.e., to assess anapproximatequantity of the elements in a collection without counting them), or both, fail to provide a conceptual basis for bootstrapping the concept of an exact natural number. In particular, I argue that none of the existing theories explains one of the key characteristics of the natural number structure: the equidistances between successive elements of the natural numbers progression. I suggest that this regularity could be based on another innate cognitive ability, namely sensitivity to the regularity of rhythm. In the final section, I propose a new position within the core cognition paradigm, inspired by structuralist positions in philosophy of mathematics. (shrink)

The creation of paraconsistent logics have expanded the boundaries of formal logic by introducing coherent systems that tolerate contradictions without triviality. Thanks to their novel approach and rigorous formalization they have already found many applications in computer science, linguistics and mathematics. As a natural next step, some philosophers have also tried to answer the question if human everyday reasoning could be accurately modelled with paraconsistent logics. The purpose of this article is to argue against the notion that human reasoning is (...) paraconsistent. Numerous findings in the area of cognitive psychology and cognitive neuroscience go against the hypothesis that humans tolerate contradictions in their inferences. Humans experience severe stress and confusion when confronted with contradictions. Experiments on the ways in which humans process contradictions point out that the first thing humans do is remove or modify one of the contradictory statements. From an evolutionary perspective, contradiction is useless and even more dangerous than lack of information because it takes up resources to process. Furthermore, it appears that when logicians, anthropologists or psychologists provide examples of contradictions in human culture and behaviour, their examples very rarely take the form of: \\). Instead, they are often conditional statements, probabilistic judgments, metaphors or seemingly incompatible beliefs. At different points in time humans are definitely able to hold contradictory beliefs, but within one reasoning leading to a particular behaviour, contradiction is never tolerated. (shrink)

Models based on causal capacities, or independent causal influences/mechanisms, are widespread in the sciences. This paper develops a natural mathematical framework for representing such capacities by extending and generalizing previous results in cognitive psychology and machine learning, based on observations and arguments from prior philosophical debates. In addition to its substantial generality, the resulting framework provides a theoretical unification of the widely-used noisy-OR/AND and linear models, thereby showing how they are complementary rather than competing. This unification helps (...) to explain many of the shared cognitive and mathematical properties of those models. (shrink)

This paper is devoted to some generalizations of explanatory potential of connectionist approaches to theoretical problems of the philosophy of mind. Are considered both strong, and weaknesses of neural network models. Connectionism has close methodological ties with modern neurosciences and neurophilosophy. And this fact strengthens its positions, in terms of empirical naturalistic approaches. However, at the same time this direction inherits weaknesses of computational approach, and in this case all system of anticomputational critical arguments becomes applicable to the connectionst models (...) of mind. The last developments in the field of deep learning gave rich empirical material for cognitive sciences. Multilayered networks, mathematical models of associative dynamics of learning, self-organizing neuronets and all that allow to explain the principles of human conceptual organizing and after this to emulate these processes in computer systems. At all engineering achievements of this technology there is a traditional criticism from representatives of cognitive psychology who cannot accept a thesis about learning ability of a neuronet on the basis of redistribution of scales. Process of learning of natural intelligence, according to cognitive models, happens due to attraction of knowledge broadcast in a symbolical form (mental representations, concepts) at the expense of the systems of output knowledge expressed in the propositional contents. Some philosophical aspects of «neural metaphor» in modern cognitive sciences create the problem field which demands comprehensive understanding, the first step towards which is taken in this work. (shrink)

In this contribution, we emphasize the relevance of mathematical approaches to the study of the first-person perspective. We briefly discuss why this is necessary and why mathematics plays a special role when it comes to integrating scientific (empirical) and philosophical (conceptual) projects. We also sketch some potential ways that mathematics could be used in phenomenology, based on a selection of four “phenomenological primitives” that characterize constitution: intentionality, minimal subjectivity, lifeworld, and time-consciousness. We also spell out a minimal topological toy (...) model and refer to some contemporary approaches using modern mathematics (e.g. category theory). We then discuss how this could be usefully applied to the (neuro)scientific study of consciousness and throughout stress the need to highlight (and formalize) phenomenology’s transcendental character. (shrink)

Mathematical developments in probabilistic inference have led to optimism over the prospects for Bayesian models of cognition. Our target article calls for better differentiation of these technical developments from theoretical contributions. It distinguishes between Bayesian Fundamentalism, which is theoretically limited because of its neglect of psychological mechanism, and Bayesian Enlightenment, which integrates rational and mechanistic considerations and is thus better positioned to advance psychological theory. The commentaries almost uniformly agree that mechanistic grounding is critical to the success of the (...) Bayesian program. Some commentaries raise additional challenges, which we address here. Other commentaries claim that all Bayesian models are mechanistically grounded, while at the same time holding that they should be evaluated only on a computational level. We argue this contradictory stance makes it difficult to evaluate a model's scientific contribution, and that the psychological commitments of Bayesian models need to be made more explicit. (shrink)

Bayesian reverse-engineering is a research strategy for developing three-level explanations of behavior and cognition. Starting from a computational-level analysis of behavior and cognition as optimal probabilistic inference, Bayesian reverse-engineers apply numerous tweaks and heuristics to formulate testable hypotheses at the algorithmic and implementational levels. In so doing, they exploit recent technological advances in Bayesian artificial intelligence, machine learning, and statistics, but also consider established principles from cognitive psychology and neuroscience. Although these tweaks and heuristics are highly pragmatic in (...) character and are often deployed unsystematically, Bayesian reverse-engineering avoids several important worries that have been raised about the explanatory credentials of Bayesian cognitive science: the worry that the lower levels of analysis are being ignored altogether; the challenge that the mathematical models being developed are unfalsifiable; and the charge that the terms ‘optimal’ and ‘rational’ have lost their customary normative force. But while Bayesian reverse-engineering is therefore a viable and productive research strategy, it is also no fool-proof recipe for explanatory success. (shrink)

The ability to improve in speed and accuracy as a result of repeating some task is an important hallmark of intelligent biological systems. Although gradual behavioral improvements from practice have been modeled in spiking neural networks, few such models have attempted to explain cognitive development of a task as complex as addition. In this work, we model the progression from a counting-based strategy for addition to a recall-based strategy. The model consists of two networks working in parallel: a slower (...) basal ganglia loop and a faster cortical network. The slow network methodically computes the count from one digit given another, corresponding to the addition of two digits, whereas the fast network gradually “memorizes” the output from the slow network. The faster network eventually learns how to add the same digits that initially drove the behavior of the slower network. Performance of this model is demonstrated by simulating a fully spiking neural network that includes basal ganglia, thalamus, and various cortical areas. Consequently, the model incorporates various neuroanatomical data, in terms of brain areas used for calculation and makes psychologically testable predictions related to frequency of rehearsal. Furthermore, the model replicates developmental progression through addition strategies in terms of reaction times and accuracy, and naturally explains observed symptoms of dyscalculia. (shrink)

In experiments of games, players frequently make choices which are regarded as irrational in game theory. In papers of Khrennikov (Information Dynamics in Cognitive, Psychological and Anomalous Phenomena. Fundamental Theories of Physics, Kluwer Academic, Norwell, 2004; Fuzzy Sets Syst. 155:4–17, 2005; Biosystems 84:225–241, 2006; Found. Phys. 35(10):1655–1693, 2005; in QP-PQ Quantum Probability and White Noise Analysis, vol. XXIV, pp. 105–117, 2009), it was pointed out that statistics collected in such the experiments have “quantum-like” properties, which can not be explained (...) in classical probability theory. In this paper, we design a simple quantum-like model describing a decision-making process in a two-players game and try to explain a mechanism of the irrational behavior of players. Finally we discuss a mathematical frame of non-Kolmogorovian system in terms of liftings (Accardi and Ohya, in Appl. Math. Optim. 39:33–59, 1999). (shrink)

Holobionts, consisting of a host and diverse microbial symbionts, function as distinct biological entities anatomically, metabolically, immunologically, and developmentally. Symbionts can be transmitted from parent to offspring by a variety of vertical and horizontal methods. Holobionts can be considered levels of selection in evolution because they are well-defined interactors, replicators/reproducers, and manifestors of adaptation. An initial mathematical model is presented to help understand how holobionts evolve. The model offered combines the processes of horizontal symbiont transfer, within-host symbiont proliferation, vertical (...) symbiont transmission, and holobiont selection. The model offers equations for the population dynamics and evolution of holobionts whose hologenomes differ in gene copy number, not in allelic or loci identity. The model may readily be extended to include variation among holobionts in the gene identities of both symbionts and host. (shrink)

This interdisciplinary volume brings together expert researchers coming from primatology, anthropology, ethology, philosophy of cognitive sciences, neurophysiology, mathematics and psychology to discuss both the foundations of non-human primate and human social cognition as well as the means there currently exist to study the various facets of social cognition. The first part focusses on various aspects of social cognition across primates, from the relationship between food and social behaviour to the connection with empathy and communication, offering a multitude of (...) innovative approaches that range from field-studies to philosophy. The second part details the various epistemic and methodological means there exist to study social cognition, in particular how to ascertain the proximal and ultimate mechanisms of social cognition through experimental, modelling and field studies. In the final part, the mechanisms of cultural transmission in primate and human societies are investigated, and special attention is given to how the evolution of cognitive capacities underlie primates’ abilities to use and manufacture tools, and how this in turn influences their social ecology. A must-read for both, young scholars as well as established researchers! (shrink)

Stibbard-Hawkes' taphonomic findings are valuable, and his call for caution warranted, but the hazards he raises are being mitigated by a multi-pronged approach; current research on behavioural/cognitive modernity is not based solely on material chronology. Theories synthesize data from archaeology, anthropology, psychology, neuroscience, and genetics, and predictions arising from these theories are tested with mathematical and agent-based models.

In the paper I discuss the problem of the nature of the relationship between objects and their properties. There are three contexts of the problem: of comparison, of change and of interaction. Philosophical explanations of facts indicated in the three contexts need reference to properties and to a proper understanding of a relationship between them and their bearers. My aim is to get closer to this understanding with the use of some models but previously I present the substantialist theory of (...) object and shortly argue for its main theses. The two models enabling us the understanding of the subject–properties structure are: the plastic stuff model and the functional model. On the ground of the first a subject is compared to a piece of plastic stuff which is informed by different shapes. Properties are ways how a subject is, they “give” some “figure” to a subject. The core idea of the second model is that essences (performing the role of subjects) are immanent functional laws governing correlations of properties. As such they are similar to mathematical functions which are saturated by values. The relationship between a subject and properties can be grasped by analogy to such a saturation. (shrink)

The frame concept from linguistics, cognitive science and artificial intelligence is a theoretical tool to model how explicitly given information is combined with expectations deriving from background knowledge. In this paper, we show how the frame concept can be fruitfully applied to analyze the notion of mathematical understanding. Our analysis additionally integrates insights from the hermeneutic tradition of philosophy as well as Schmid’s ideal genetic model of narrative constitution. We illustrate the practical applicability of our theoretical analysis through (...) a case study on extremal proofs. Based on this case study, we compare our analysis of proof understanding to Avigad’s ability-based analysis of proof understanding. (shrink)

The prime purpose of this paper is, first, to restore to discourse-bound occasion sentences their rightful central place in semantics and secondly, taking these as the basic propositional elements in the logical analysis of language, to contribute to the development of an adequate logic of occasion sentences and a mathematical foundation for such a logic, thus preparing the ground for more adequate semantic, logical and mathematical foundations of the study of natural language. Some of the insights elaborated in (...) this paper have appeared in the literature over the past thirty years, and a number of new developments have resulted from them. The present paper aims atproviding an integrated conceptual basis for this new development in semantics. In Section 1 it is argued that the reduction by translation of occasion sentences to eternal sentences, as proposed by Russell and Quine, is semantically and thus logically inadequate. Natural language is a system of occasion sentences, eternal sentences being merely boundary cases. The logic hasfewer tasks than is standardly assumed, as it excludes semantic calculi, which depend crucially on information supplied by cognition and context and thus belong to cognitive psychology rather than to logic. For sentences to express a proposition and thus be interpretable and informative, they must first be properly anchored in context. A proposition has a truth value when it is, moreover, properly keyed in the world, i.e. is about a situation in the world. Section 2 deals with the logical properties of natural language. It argues that presuppositional phenomena require trivalence and presents the trivalent logic PPC3, with two kinds of falsity and two negations. It introduces the notion of -space for a sentence A as the basis of logical model theory, and the notion of P A /, functioning as a `private' subuniverse for A/A. The trivalent Kleene calculus is reinterpreted as a logical account of vagueness, rather than of presupposition. PPC3 and the Kleene calculus are refinements of standard bivalent logic and can be combined into one logical system. In Section 3 the adequacy of PPC3 as a truth-functional model of presupposition is considered more closely and given a Boolean foundation. In a noncompositional extended Boolean algebra, three operators are defined: 1a for the conjoined presuppositions of a, ã for the complement of a within 1a, and â for the complement of 1a within Boolean 1. The logical properties of this extended Boolean algebra are axiomatically defined and proved for all possible models. Proofs are provided of the consistency and the completeness of the system. Section 4 is a provisional exploration of the possibility of using the results obtained for a new discourse-dependent account of the logic of modalities in natural language. The overall result is a modified and refined logical and model-theoretic machinery, which takes into account both the discourse-dependency of natural language sentences and the necessity of selecting a key in the world before a truth value can be assigned. (shrink)

By the end of his life Plato had rearranged the theory of ideas into his teaching about ideal numbers, but no written records have been left. The Ideal mathematics of Plato is present in all his dialogues. It can be clearly grasped in relation to the effective use of mathematical modelling. Many problems of mathematical modelling were laid in the foundation of the method by cutting the three-level idealism of Plato to the single-level “ideism” of Aristotle. For a (...) long time, the real, ideal numbers of Plato’s Ideal mathematics eliminates many mathematical problems, extends the capabilities of modelling, and improves mathematics. (shrink)

The aim of cognitive diagnosis is to classify respondents' mastery status of latent attributes from their responses on multiple items. Since respondents may answer some but not all items, item-level missing data often occur. Even if the primary interest is to provide diagnostic classification of respondents, misspecification of missing data mechanism may lead to biased conclusions. This paper proposes a joint cognitive diagnosis modeling of item responses and item-level missing data mechanism. A Bayesian Markov chain Monte Carlo method (...) is developed for model parameter estimation. Our simulation studies examine the parameter recovery under different missing data mechanisms. The parameters could be recovered well with correct use of missing data mechanism for model fit, and missing that is not at random is less sensitive to incorrect use. The Program for International Student Assessment 2015 computer-based mathematics data are applied to demonstrate the practical value of the proposed method. (shrink)

Modern technology offers an increasing number of tools for teaching mathematics, but technology adoption in schools encounters many barriers. The Technology Acceptance Model explains that technology usage is dependent on intentions, which rest on perceived ease of use and perceived usefulness. Less is known about the relationship between intentions and actual behaviour. In the current study we show that the level of cognitive investment on the part of the teachers, captured by the construct of Need for Cognition (NC), is (...) crucial in the use of technology in mathematical instruction, while controlling for a variety of background factors. Furthermore NC moderates the relationship between intentions and technology use, such that high NC weakens the relationship between the perceived usefulness of technology in pedagogy and its actual use. (shrink)

The prime purpose of this paper is, first, to restore to discourse-bound occasion sentences their rightful central place in semantics and secondly, taking these as the basic propositional elements in the logical analysis of language, to contribute to the development of an adequate logic of occasion sentences and a mathematical (Boolean) foundation for such a logic, thus preparing the ground for more adequate semantic, logical and mathematical foundations of the study of natural language. Some of the insights elaborated (...) in this paper have appeared in the literature over the past thirty years, and a number of new developments have resulted from them. The present paper aims at providing an integrated conceptual basis for this new development in semantics. In Section 1 it is argued that the reduction by translation of occasion sentences to eternal sentences, as proposed by Russell and Quine, is semantically and thus logically inadequate. Natural language is a system of occasion sentences, eternal sentences being merely boundary cases. The logic has fewer tasks than is standardly assumed, as it excludes semantic calculi, which depend crucially on information supplied by cognition and context and thus belong to cognitive psychology rather than to logic. For sentences to express a proposition and thus be interpretable and informative, they must first be properly anchored in context. A proposition has a truth value when it is, moreover, properly keyed in the world, i.e. is about a situation in the world. Section 2 deals with the logical properties of natural language. It argues that presuppositional phenomena require trivalence and presents the trivalent logic ${\rm PPC}_{3}$ , with two kinds of falsity and two negations. It introduces the notion of Σ-space for a sentence A (or / A /, the set of situations in which A is true) as the basis of logical model theory, and the notion of / ${\bf P}^{A}$ / (the Σ-space of the presuppositions of A), functioning as a 'private' subuniverse for / A /. The trivalent Kleene calculus is reinterpreted as a logical account of vagueness, rather than of presupposition. ${\rm PPC}_{3}$ and the Kleene calculus are refinements of standard bivalent logic and can be combined into one logical system. In Section 3 the adequacy of ${\rm PPC}_{3}$ as a truth-functional model of presupposition is considered more closely and given a Boolean foundation. In a noncompositional extended Boolean algebra, three operators are defined: $1_{a}$ for the conjoined presuppositions of a, ã for the complement of a within $1_{a}$ , and â for the complement of $1_{a}$ within Boolean 1. The logical properties of this extended Boolean algebra are axiomatically defined and proved for all possible models. Proofs are provided of the consistency and the completeness of the system. Section 4 is a provisional exploration of the possibility of using the results obtained for a new discourse-dependent account of the logic of modalities in natural language. The overall result is a modified and refined logical and model-theoretic machinery, which takes into account both the discourse-dependency of natural language sentences and the necessity of selecting a key in the world before a truth value can be assigned. (shrink)

: The development of the interdisciplinary areas of cognitive, affective and action neurosciences contributes to the identification of neurobiological bases of conscious experience. The structure of consciousness was philosophically conceived a century ago as consisting of a subjective pole, the bearer of experiences, and an objective pole composed of experienced contents. In more recent formulations, Nagel refers to a “point of view”, in which qualitative experiences are anchored, while Velmans understands that phenomenal content is composed of mental representations “projected” (...) to the space external to the brains that construct them. In Freudian psychology, the conscious mind contains a tension between the Id and the Ego. How to relate this bipolar structure with the results of neuroscience? I propose the notion of projection [also used by Williford et al. ] as a bridge principle connecting the neurobiological systems of knowing, feeling and acting with the bipolar structure. The projective process is considered responsible for the generation of the sense of self and the sense of the world, composing an informational phenomenal field generated by the nervous system and experienced in the first-person perspective. After presenting the projective hypothesis, I discuss its philosophical status, relating it to the phenomenal and high-order thought approaches, and a mathematical model of projection. Eight ways of testing the status of the projective hypothesis are briefly mentioned. Resumo: O desenvolvimento de áreas interdisciplinares das neurociências, contribui para a identificação das bases neurobiológicas da experiência consciente. A estrutura intrínseca da experiência consciente foi filosoficamente concebida há um século como consistindo de um pólo subjetivo, o portador de experiências, e um pólo objetivo, composto dos conteúdos experimentados. Em formulações mais recentes, Thomas Nagel refere-se a um “ponto de vista”, no qual experiências qualitativas são ancoradas, enquanto Max Velmans entende que o conteúdo fenomenal é composto de representações mentais “projetadas” para o espaço externo ao cérebro que as constrói. Na psicologia freudiana, a mente consciente contém uma tensão entre o Id e o Ego. Como relacionar esta estrutura bipolar com os resultados da neurociência? Proponho a noção de projeção como princípio-ponte, conectando os sistemas neurobiológicos do saber, sentir e agir com a estrutura bipolar. O processo projetivo é considerado responsável pela geração do sentido do eu e do sentido do mundo, compondo um campo fenomenal informacional gerado pelo sistema nervoso e vivenciado na perspectiva da primeira pessoa. Após apresentar a hipótese projetiva, discuto seu status filosófico, relacionando-o às abordagens fenomenológicas, à teoria do pensamento de ordem superior e ao modelo matemático da projeção. Oito maneiras de testar o status da hipótese projetiva são brevemente mencionadas. (shrink)

Evidence Theory is a branch of mathematics that concerns combination of empirical evidence in an individual’s mind in order to construct a coherent picture of reality. Designed to deal with unexpected empirical evidence suggesting new possibilities, evidence theory is compatible with Shackle’s idea of decision-making as a creative act. This essay investigates this connection in detail, pointing to the usefulness of evidence theory to formalise and extend Shackle’s decision theory. In order to ease a proper framing of the issues involved, (...) evidence theory is compared with sub-additive probability theory and Ewens’s infinite alleles model. Furthermore, the original version of evidence theory is presented along with its most recent developments. (shrink)