The paper presents a formal model of the system of number representations as a multiplicity of mental number axes with a hierarchical structure. The hierarchy is determined by the mind as it acquires successive types of mental number axes generated by virtue of some algebraic mechanisms. Three types of algebraic structures, responsible for functioning these mechanisms, are distinguished: BASAN-structures, CASAN-structures and CAPPAN-structures. A foundational order holds between these structures. CAPPAN-structures are derivative from CASAN-structures which are (...) extensions of BASAN-structures. The constructed formal model unifies two competitive conceptions of cognitive arithmetic: namely, the conception of the mental number line and the conception of parallel individuation. The paper is the continuation of a paper entitled Representational structures of arithmetical thinking, in which rich empirical evidence supporting the model is presented. The main result achieved in the present paper may be philosophically interpreted as an attempt to formalize the Kantian conception of the pure idea of time, understood as the a priori form of human arithmetical thinking. In this way, our theory may be comprehended as a result of applying the hard method of logical reconstruction of fundamental epistemological categories. (shrink)

Human adults are thought to possess two dissociable systems to represent numbers: an approximate quantity system akin to a mental number line, and a verbal system capable of representing numbers exactly. Here, we study the interface between these two systems using an estimation task. Observers were asked to estimate the approximate numerosity of dot arrays. We show that, in the absence of calibration, estimates are largely inaccurate: responses increase monotonically with numerosity, but underestimate the actual numerosity. However, insertion (...) of a few inducer trials, in which participants are explicitly (and sometimes misleadingly) told that a given display contains 30 dots, is sufficient to calibrate their estimates on the whole range of stimuli. Based on these empirical results, we develop a model of the mapping between the numerical symbols and the representations of numerosity on the number line. (shrink)

Comments on an article by Feigenson et. al.(see record 2004-18473-007). Reviewing behavioral and neural data in children, humans and animals, Feigenson and colleagues distinguish two core systems for number representation. One system represents number in an exact way but has a fixed upper limit; the other system has no size limit but represents number only approximately. Both systems are claimed to have a phylogenetic origin and to constitute the basis for ontogenetic development. As such, each system's representational (...) principles are reflected in adult human performance: subitizing is ascribed to the exact system whereas symbolic number processing is based on a mapping to the approximate system. This last assumption is motivated by the robust finding that symbolic numbers are more difficult to discriminate with increasing size (the 'size effect'). However, it remains to be shown how this mapping can reconcile the inherently exact nature of a symbolic system with signatures of approximate processing such as the size effect. (PsycINFO Database Record (c) 2005 APA, all rights reserved). (shrink)

It has been argued that numbers are spatially organized along a "mental number line" that facilitates left-hand responses to small numbers, and right-hand responses to large numbers. We hypothesized that whenever the representations of visual and numerical space are concurrently activated, interactions can occur between them, before response selection. A spatial prime is processed faster than a numerical target, and consistent with our hypothesis, we found that such a spatial prime affects non-spatial, verbal responses more when the prime (...) follows a numerical target (backward priming) then when it precedes it (forward priming). This finding emerged both in a number-comparison and a parity judgment task, and cannot be ascribed to a "Spatial-Numerical Association of Response Codes" (SNARC). Contrary to some earlier claims, we therefore conclude that visuospatial-numerical interactions do occur, even before response selection. (shrink)

Comments on an article by Feigenson et. al.(see record 2004-18473-007). Reviewing behavioral and neural data in children, humans and animals, Feigenson and colleagues distinguish two core systems for number representation. One system represents number in an exact way but has a fixed upper limit; the other system has no size limit but represents number only approximately. Both systems are claimed to have a phylogenetic origin and to constitute the basis for ontogenetic development. As such, each system's representational (...) principles are reflected in adult human performance: subitizing is ascribed to the exact system whereas symbolic number processing is based on a mapping to the approximate system. This last assumption is motivated by the robust finding that symbolic numbers are more difficult to discriminate with increasing size (the 'size effect'). However, it remains to be shown how this mapping can reconcile the inherently exact nature of a symbolic system with signatures of approximate processing such as the size effect. (PsycINFO Database Record (c) 2005 APA, all rights reserved). (shrink)

The traditional view of cognition as detached from emotions is recently being questioned. This study aimed to investigate the influence of emotional valence on the accuracy and bias in the representation of numbers on the mental number line (MNL). The study included 164 participants who were randomly assigned into two groups with induced positive and negative emotional valence using matched arousal film clips. Participants performed a computerised number-to-position (CNP) task to estimate the position of numbers on a (...) horizontal line. The results showed that participants in the positive valence group exhibited a rightward bias, while those in the negative valence group showed an opposite pattern. The analysis of mean absolute error revealed that the negative valence group had higher error rates compared to the positive valence group. Furthermore, the MNL estimation pattern analysis indicated that a two-cycle cyclic power model (CPM) best explained the data for both groups. These findings suggest that emotional valence influences the spatial representation of numbers on the MNL and affects accuracy in numerical estimations. Our findings are finally discussed in terms of body-specificity and the Brain’s Asymmetric Frequency Tuning (BAFT) theories. The study provides new insights into the interplay between emotions and numerical cognition. (shrink)

Nonsymbolic comparison tasks are commonly used to index the acuity of an individual's Approximate Number System (ANS), a cognitive mechanism believed to be involved in the development of number skills. Here we asked whether the time that an individual spends observing numerical stimuli influences the precision of the resultant ANS representations. Contrary to standard computational models of the ANS, we found that the longer the stimulus was displayed, the more precise was the resultant representation. We propose an adaptation (...) of the standard model, and suggest that this finding has significant methodological implications for numerical cognition research. (shrink)

A crucial aspect of the human mind is the ability to project the self along the time line to past and future. It has been argued that such self-projection is essential to re-experience past experiences and predict future events. In-depth analysis of a novel paradigm investigating mental time shows that the speed of this “self-projection” in time depends logarithmically on the temporal-distance between an imagined “location” on the time line that participants were asked to imagine and the location of (...) another imagined event from the time line. This logarithmic pattern suggests that events in human cognition are spatially mapped along an imagery mental time line. We argue that the present time-line data are comparable to the spatial mapping of numbers along the mental number line and that such spatial maps are a fundamental basis for cognition. (shrink)

Cohen Kadosh, Tzelgov, and Henik [Cohen Kadosh, R., Tzelgov, J., and Henik, A. (2008). A synesthetic walk on the number line: The size effect. Cognition, 106, 548-557] present a new paradigm to probe properties of the mental number line. They describe two experiments which they argue to be inconsistent with the exact small number model proposed by Verguts, Fias, and Stevens [Verguts, T., Fias, W., Stevens, M. (2005). A model of exact small-number representation. Psychonomic Bulletin (...) and Review, 12, 66-80]. We discuss the data, assumptions, and conclusions of Cohen Kadosh et al.'s paper in relation to existing models of numerical cognition. (shrink)

In this study, we directly contrast two approaches that have been proposed to explain the SNARC effect. The traditional direct mapping account suggests that a direct association exists between the position of a number on the mental number line and the location of the response. On the other hand, accounts are considered that propose an intermediate step in which numbers are categorized as either small or large between the number magnitude and the response representations. In a (...) magnitude comparison task, we departed from the usual bimanual left/right response dimension and instead introduced the unimanual close/far dimension. A spatial-numerical association was observed: small numbers were associated with a close response, while large numbers were associated with a far response, regardless of the movement direction (left/right). We discuss why these results cannot be explained by assuming a direct mapping from the representation of numbers on a mental number line to response locations and discuss how the results can be explained by the alternative accounts. (shrink)

Are small and large numbers represented similarly or differently on the mental number line? The size effect was used to argue that numbers are represented differently. However, recently it has been argued that the size effect is due to the comparison task and is not derived from the mental number line per se. Namely, it is due to the way that the mental number line is mapped onto the task-relevant output component. Here synesthesia was (...) used to disentangle these two alternatives. In two naming experiments a digit-color synesthete showed that the congruity effect was modulated by number size. These results support the existence of a mental number line with a vaguer numerical representation as numbers increase in size. In addition, the results show that in digit-color synesthesia, colors can evoke numerical representation automatically. (shrink)

Miller (1956) summarized evidence that people can remember about seven chunks in short-term memory (STM) tasks. However, that number was meant more as a rough estimate and a rhetorical device than as a real capacity limit. Others have since suggested that there is a more precise capacity limit, but that it is only three to five chunks. The present target article brings together a wide variety of data on capacity limits suggesting that the smaller capacity limit is real. Capacity (...) limits will be useful in analyses of information processing only if the boundary conditions for observing them can be carefully described. Four basic conditions in which chunks can be identified and capacity limits can accordingly be observed are: (1) when information overload limits chunks to individual stimulus items, (2) when other steps are taken specifically to block the recoding of stimulus items into larger chunks, (3) in performance discontinuities caused by the capacity limit, and (4) in various indirect effects of the capacity limit. Under these conditions, rehearsal and long-term memory cannot be used to combine stimulus items into chunks of an unknown size; nor can storage mechanisms that are not capacity-limited, such as sensory memory, allow the capacity-limited storage mechanism to be refilled during recall. A single, central capacity limit averaging about four chunks is implicated along with other, noncapacity-limited sources. The pure STM capacity limit expressed in chunks is distinguished from compound STM limits obtained when the number of separately held chunks is unclear. Reasons why pure capacity estimates fall within a narrow range are discussed and a capacity limit for the focus of attention is proposed. Key Words: attention; enumeration; information chunks; memory capacity; processing capacity; processing channels; serial recall; short-term memory; storage capacity; verbal recall; working memory capacity. (shrink)

The current consensus among most researchers is that natural number is not built solely upon a foundation of mental magnitudes. On their way to the conclusion that magnitudes do not form any part of that foundation, Rips et al. pass rather quickly by theories suggesting that mental magnitudes might play some role. These theories deserve a closer look.

ion is instrumental for our understanding of how numbers are cognitively represented. We propose that the notion of abstraction becomes testable from within the framework of simulated cognition. We describe mental simulation as embodied, grounded, and situated cognition, and report evidence for number representation at each of these levels of abstraction.

Aimed at philsophy graduates this book investigates mental content in a systematic way and advances a number of claims about how mental content states are related to the body and the world. Internalism is the thesis that they are; externalism is the theory that they are not.

On a now orthodox view, humans and many other animals possess a “number sense,” or approximate number system, that represents number. Recently, this orthodox view has been subject to numerous critiques that question whether the ANS genuinely represents number. We distinguish three lines of critique – the arguments from congruency, confounds, and imprecision – and show that none succeed. We then provide positive reasons to think that the ANS genuinely represents numbers, and not just non-numerical confounds (...) or exotic substitutes for number, such as “numerosities” or “quanticals,” as critics propose. In so doing, we raise a neglected question: numbers of what kind? Proponents of the orthodox view have been remarkably coy on this issue. But this is unsatisfactory since the predictions of the orthodox view, including the situations in which the ANS is expected to succeed or fail, turn on the kind of number being represented. In response, we propose that the ANS represents not only natural numbers, but also non-natural rational numbers. It does not represent irrational numbers, however, and thereby fails to represent the real numbers more generally. This distances our proposal from existing conjectures, refines our understanding of the ANS, and paves the way for future research. (shrink)

Mature representations of number are built on a core system of numerical representation that connects to spatial representations in the form of a ‘mental number line’. The core number system is functional in early infancy, but little is known about the origins of the mapping of numbers onto space. Here we show that preverbal infants transfer the discrimination of an ordered series of numerosities to the discrimination of an ordered series of line lengths. Moreover, infants construct (...) relationships between individual numbers and line lengths that vary positively, but not between numbers and lengths that vary inversely. These findings provide evidence for an early developing predisposition to relate representations of numerical magnitude and spatial length. A central foundation of mathematics, science and technology therefore emerges prior to experience with language, symbol systems, or measurement devices. (shrink)

Mental health generally refers to an individual’s thoughts, feelings and actions, particularly when he faced with life challenges and stresses. A good mental health isn’t just the absence of mental health problems. It is the achievement and the maintenance of psychological well-being. Mental Health is the state of one’s peace of mind, happiness and harmony brought out by one’s level of adjustment with himself and his environment. In describing mental health, Anwar said, “…mental health (...) is the health of one’s mind which can prove a potent determinant of one’s integrated personality and balanced behavour identified on the basis of the level of his adjustment to himself, others and with the environment. A mentally healthy individual possesses a number of characteristics which influence his life positively and help him in achieving his goals of life effectively. He has adequate ability to make adjustments in the changed circumstances and situations. His intellectual powers are adequately developed. He is able to think independently and take proper decision at the proper time. He tries to accomplish his work as effectively as possible but he does not prove to be an extremist by becoming a perfectionist. Though these characteristics are expected from a mentally healthy individual, but these should be taken as essential and necessary conditions for the maintenance of proper mental health and thus absence of one or the other characteristic does not necessarily mean negation of mental health. Good mental health is not just the absence of mental problems. Being mentally healthy is much more than free of depression, anxiety or other psychological issues.”1 In this paper an attempt is made to discuss about the mental health policies and issues in India. (shrink)

Our successful engagement with the world is plausibly underwritten by our sensitivity to affordances in our immediate environment. The considerable literature on affordances focuses almost exclusively on affordances for bodily actions such as gripping, walking or eating. I propose that we are also sensitive to affordances for mental actions such as attending, imagining and counting. My case for this ‘Mental Affordance Hypothesis’ is motivated by a series of examples in which our sensitivity to mental affordances mirrors our (...) sensitivity to bodily affordances. Specifically, subjects perceive opportunities to perform a mental action and their doing so leads, under the right conditions, to the automatic preparation of that action. I conclude by sketching a mental affordance research program that would reinforce my case for the Mental Affordance Hypothesis and establish its ramifications for a number of debates across philosophy and psychology. (shrink)

I argue that the human mind includes an innate domain-specific system for representing precise small numerical quantities. This theory contrasts with object-tracking theories and with domain-general theories that only make use of mental models. I argue that there is a good amount of evidence for innate representations of small numerical quantities and that such a domain-specific system has explanatory advantages when infants’ poor working memory is taken into account. I also show that the mental models approach requires previously (...) unnoticed domain-specific structure and consequently that there is no domain-general alternative to an innate domain-specific small number system. (shrink)

Johnson-Laird's mental models theory claims that reasoning is a semantic process of construction and manipulation of models in working memory of limited capacity. Accordingly, both a deduction and a given interpretation of a premise would be all the harder the higher the number of models they require. The purpose of the present experiment was twofold. First, it aimed to demonstrate that the interpretation of if...then conditional sentences in children (third, sixth, and ninth graders) evolves as a function of (...) the number of models the children can produce. We proposed a theory of conditional reasoning development that hypothesises a developmental trend of three successive levels of interpretations underlain by one, two, and then three models, i.e. conjunctive, biconditional, and conditional respectively. Second, we aimed to show that these different levels correlate with working memory capacities: the higher the working memory span, the higher the number of models underlying the conditional interpretation. These two hypotheses were verified, supporting the mental models theory. The results are compared with the rival theory of mental logic. (shrink)

Many philosophers treat mental imagery as a kind of perceptual representation – it is either a perceptual state, or a representation of a perceptual state. In the sciences, writers point to mental imagery by way of a standard gloss – mental imagery is said to be (often, early) perceptual processing not directly caused by sensory stimuli (Kosslyn et al. 1995). Philosophers sometimes adopt this gloss, which I will call the basic view. Bence Nanay endorses it, and appeals (...) to it in a number of places to argue that mental imagery plays various functional or explanatory roles, as well as to argue that some mental phenomena should be seen as forms of mental imagery. In places he goes even further, relying on this view of mental imagery to explain how mental imagery is a unified kind despite heterogeneous appearances, and using this view to support his claim that mental imagery is a natural kind. Nanay’s book – which is a both a useful introduction to the many ways that mental imagery appears in discussions across philosophy, neuroscience, and psychology, as well as an extended argument for the multi-faceted relevance of mental imagery to a range of projects in the philosophy of mind and psychology – thus also serves as a nice test case for whether this basic view of mental imagery is good enough to aid theorizing across philosophy and the sciences. I think not. I will illustrate why by looking at two areas. First, I will discuss Nanay’s argument regarding mental imagery and object files. Second, I will discuss an issue Nanay raises, regarding the relationship between mental and motor imagery. A longer discussion might look to many more areas – as already mentioned, Nanay’s book covers a wide range of mental phenomena – with the same lesson emerging. The nature of mental imagery cannot be fully understood without facing an array of choice points, many of which push us to make commitments beyond the basic view. (shrink)

Human mental workload is arguably the most invoked multidimensional construct in Human Factors and Ergonomics, getting momentum also in Neuroscience and Neuroergonomics. Uncertainties exist in its characterization, motivating the design and development of computational models, thus recently and actively receiving support from the discipline of Computer Science. However, its role in human performance prediction is assured. This work is aimed at providing a synthesis of the current state of the art in human mental workload assessment through considerations, definitions, (...) measurement techniques as well as applications, Findings suggest that, despite an increasing number of associated research works, a single, reliable and generally applicable framework for mental workload research does not yet appear fully established. One reason for this gap is the existence of a wide swath of operational definitions, built upon different theoretical assumptions which are rarely examined collectively. A second reason is that the three main classes of measures, which are self-report, task performance, and physiological indices, have been used in isolation or in pairs, but more rarely in conjunction all together. Multiple definitions complement each another and we propose a novel inclusive definition of mental workload to support the next generation of empirical-based research. Similarly, by comprehensively employing physiological, task-performance, and self-report measures, more robust assessments of mental workload can be achieved. (shrink)

In recent years there has been increased recognition of the global burden of mental disorders, which in turn has led to the expansion of preventive initiatives at the community and population levels. The application of such public health approaches to mental health raises a number of important ethical questions. The aim of this collection is to address these newly emerging issues, with special attention to the principle of prevention and the distinctive ethical challenges in mental health. (...) The collection brings together an interdisciplinary group of experts in bioethics, mental health, public health, and global health. (shrink)

Adaptation to right-shifting prisms improves left neglect for mental number line bisection. This study examined whether adaptation affects the mental number line in normal participants. Thirty-six participants completed a mental number line task before and after adaptation to either: left-shifting prisms, right-shifting prisms or control spectacles that did not shift the visual scene. Participants viewed number triplets (e.g. 16, 36, 55) and determined whether the numerical distance was greater on the left or right (...) side of the inner number. Participants demonstrated a leftward bias (i.e. overestimated the length occupied by numbers located on the left side of the number line) that was consistent with the effect of pseudoneglect. The leftward bias was corrected by a short period of visuomotor adaptation to left-shifting prisms, but remained unaffected by adaptation to right-shifting prisms and control spectacles. The findings demonstrate that a simple visuomotor task alters the representation of space on the mental number line in normal participants. (shrink)

Mental model ascription – also called mindreading – is the process of inferring the mental states of others, which happens as a matter of course in social interactions. But although ubiquitous, mindreading is presumably a highly variable process: people mindread to different extents and with _different results._ We hypothesize that human mindreading ability relies on a large number of personal and contextual features: the inherent abilities of specific individuals, their current physical and mental states, their knowledge (...) of the domain of discourse, their familiarity with the interlocutor, the risks associated with an incorrect assessment of intent, and so on. This paper presents a theory of mindreading that models diverse artificial intelligent agents using an inventory of parameters and value sets that represent traits of humans and features of discourse contexts. Examples are drawn from Maryland Virtual Patient, a prototype system that will permit medical trainees to diagnose and treat cognitively modeled virtual patients with the optional assistance of a virtual tutor. Since real patients vary greatly with respect to physiological and cognitive features, so must a society of virtual patients. Modeling such variation is one of the goals of the overall OntoAgent program of research and development. (shrink)

Increased awareness of the importance of mental health for global health has led to a number of new initiatives, including influential policy instruments issued by the World Health Organization (WHO) and the United Nations (UN). This policy brief describes two WHO instruments, the Mental Health Action Plan for 2013–2020 (World Health Organization, 2013) and the Mental Health Atlas (World Health Organization, 2015), and presents a comparative analysis with the Sustainable Development Goals (SDGs) of the UN’s 2030 (...) Agenda for Sustainable Development (United Nations, 2015). The WHO’s Action Plan calls for several specific objectives and targets, with a focus on improving global mental health governance and service coverage. In contrast, the UN’s SDGs include only one goal specific to mental health, with a single indicator tracking suicide mortality rates. The discrepancy between the WHO and UN frameworks suggests a need for increased policy coherence. Improved global health governance can provide the basis for ensuring and accelerating progress in global mental health. (shrink)

Mental model ascription – also called mindreading – is the process of inferring the mental states of others, which happens as a matter of course in social interactions. But although ubiquitous, mindreading is presumably a highly variable process: people mindread to different extents and with different results. We hypothesize that human mindreading ability relies on a large number of personal and contextual features: the inherent abilities of specific individuals, their current physical and mental states, their knowledge (...) of the domain of discourse, their familiarity with the interlocutor, the risks associated with an incorrect assessment of intent, and so on. This paper presents a theory of mindreading that models diverse artificial intelligent agents using an inventory of parameters and value sets that represent traits of humans and features of discourse contexts. Examples are drawn from Maryland Virtual Patient, a prototype system that will permit medical trainees to diagnose and treat cognitively modeled virtual patients with the optional assistance of a virtual tutor. Since real patients vary greatly with respect to physiological and cognitive features, so must a society of virtual patients. Modeling such variation is one of the goals of the overall OntoAgent program of research and development. (shrink)

Over the past 50 years, philosophers and psychologists have perennially argued for the existence of analog mental representations of one type or another. This study critically reviews a number of these arguments as they pertain to three different types of mental representation: perceptual representations, imagery representations, and numerosity representations. Along the way, careful consideration is given to the meaning of “analog” presupposed by these arguments for analog mental representation, and to open avenues for future research.