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)

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 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)

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)

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)

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)

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)

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)

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)

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)

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.

Persian possesses a number of stative complex predicates with _dâshtan_ ‘to have’ that express certain kinds of mental state. I propose that these _possessive experiencer complex predicates_ be given a formal semantic treatment involving possession of a portion of an abstract quality by an individual, as in the analysis of property concept lexemes due to Francez and Koontz-Garboden (Language 91(3):533–563, 2015 ; Natural Language and Linguistic Theory 34:93–106, 2016 ; Semantics and morphosyntactic variation: Qualities and the grammar of (...) property concepts, Oxford University Press, 2017 ). Augmented with an analysis of prepositional phrases introducing the target of the mental state and an approach to gradability in terms of measure functions (Wellwood in Measuring predicates, PhD dissertation, University of Maryland, College Park, 2014 ), the analysis explains various properties of possessive experiencer complex predicates, including the behavior of target phrases, the ability of the non-verbal element to be modified by a range of adjectives, the direct participation of the non-verbal element in comparative constructions, and the ability of degree expressions to modify both the non-verbal element and the VP containing the complex predicate. Theoretically, the analysis ties transitive mental state expressions to the grammar and semantics of property concept sentences, which are expressed via possessive morphosyntax cross-linguistically, and connects with syntactic proposals that independently argue for a universal underlyingly possessive morphosyntax for mental state predicates (Noonan in Case and syntactic geometry, PhD dissertation, McGill University, 1992 ; Hale and Keyser in Prolegomenon to a theory of argument structure, MIT Press, 2002 ). The work here also motivates modifications to Francez and Koontz-Garboden’s original proposal, and opens new questions in the original empirical domain of the analysis of possessive predicating strategies for the expression of property concept sentences. (shrink)

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)

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)

It is generally accepted that there is something special about reasoning by using mental images. The question of how it is special, however, has never been satisfactorily spelled out, despite more than thirty years of research in the post-behaviorist tradition. This article considers some of the general motivation for the assumption that entertaining mental images involves inspecting a picture-like object. It sets out a distinction between phenomena attributable to the nature of mind to what is called the cognitive (...) architecture, and ones that are attributable to tacit knowledge used to simulate what would happen in a visual situation. With this distinction in mind, the paper then considers in detail the widely held assumption that in some important sense images are spatially displayed or are depictive, and that examining images uses the same mechanisms that are deployed in visual perception. I argue that the assumption of the spatial or depictive nature of images is only explanatory if taken literally, as a claim about how images are physically instantiated in the brain, and that the literal view fails for a number of empirical reasons – for example, because of the cognitive penetrability of the phenomena cited in its favor. Similarly, while it is arguably the case that imagery and vision involve some of the same mechanisms, this tells us very little about the nature of mental imagery and does not support claims about the pictorial nature of mental images. Finally, I consider whether recent neuroscience evidence clarifies the debate over the nature of mental images. I claim that when such questions as whether images are depictive or spatial are formulated more clearly, the evidence does not provide support for the picture-theory over a symbol-structure theory of mental imagery. Even if all the empirical claims were true, they do not warrant the conclusion that many people have drawn from them: that mental images are depictive or are displayed in some (possibly cortical) space. Such a conclusion is incompatible with what is known about how images function in thought. We are then left with the provisional counterintuitive conclusion that the available evidence does not support rejection of what I call the “null hypothesis”; namely, that reasoning with mental images involves the same form of representation and the same processes as that of reasoning in general, except that the content or subject matter of thoughts experienced as images includes information about how things would look. (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)

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.

The present paper constitutes a development of the position that illness, whether bodily or mental, should be analyzed as an incapacitating failure of bodily or mental capacities, respectively, to realize their functions. The paper undertakes this development by responding to two critics. It addresses first Szasz’s continued claims that (1) physical illness is the paradigm concept of illness and (2) a philosophical analysis of mental illness does not shed any light on the social and legal role of (...) the idea. Then, in reply to Wakefield, the aim is to defend the account as an interpretation of Aristotle and to argue that this Aristotelian view of mental illness is preferable to one that rests on a supposed value free account of human function. More generally the discussion points to the fact that both Wakefield and Szasz rely on a number of metaphysical assumptions about the supposedly empirical nature of medical diagnosis, about the relation between facts and values, and about mind and body (among others), which are open to challenge. In particular the paper indicates an aristotelian approach to the fusion, in the natural world, of so-called facts and values, and the relevance of this fusion to the analysis of the concept of illness. This suggests the debate over distinct conceptions of that concept must both illumine and be illuminated by these deeper metaphysical questions. (shrink)

We assessed the automaticity of spatial-numerical and spatial-musical associations by testing their intentionality and load sensitivity in a dual-task paradigm. In separate sessions, 16 healthy adults performed magnitude and pitch comparisons on sung numbers with variable pitch. Stimuli and response alternatives were identical, but the relevant stimulus attribute (pitch or number) differed between tasks. Concomitant tasks required retention of either color or location information. Results show that spatial associations of both magnitude and pitch are load sensitive and that the (...) spatial association for pitch is more powerful than that for magnitude. These findings argue against the automaticity of spatial mappings in either stimulus dimension. (shrink)

In this surprising book, Allan V. Horwitz argues that our current conceptions of mental illness as a disease fit only a small number of serious psychological conditions and that most conditions currently regarded as mental illness are cultural constructions, normal reactions to stressful social circumstances, or simply forms of deviant behavior.

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)

The side-effect effect, in which an agent who does not speci␣cally intend an outcome is seen as having brought it about intentionally, is thought to show that moral factors inappropriately bias judgments of intentionality, and to challenge standard mental state models of intentionality judgments. This study used matched vignettes to dissociate a number of moral factors and mental states. Results support the view that mental states, and not moral factors, explain the side-effect effect. However, the critical (...) mental states appear not to be desires as proposed in standard models, but rather ‘deeper’ evaluative states including values and core evaluative attitudes. (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)