Timed magnitude comparisons of numerical and nonnumerical expressions of uncertainty

Two experiments involving paired comparisons of numerical and nonnumerical expressions of uncertainty are reported. Subjects were timed under two opposing sets of instructions ("choose higher probability" vs. "choose lower probability"). Numerical comparisons were consistently faster and easier than their nonnumerical counterparts. Consistent distance and congruity effects were obtained, illustrating that both numerical and nonnumerical expressions of uncertainty contain subjective magnitude information, and suggesting that similar processes are employed in manipulating and comparing numerical and verbal terms. To account for the general pattern of results obtained, Holyoak's reference point model (1978) was generalized by explicitly including the vagueness of the nonnumerical expressions. This generalized model is based on the notion that probability expressions can be represented by membership functions (Wallsten, Budescu, Rapoport, Zwick, & Forsyth, 1986) from which measures of location for each word, and measures of overlap for each pair can be derived. A good level of fit was obtained for this model at the individual level.     

Spearman's law of diminishing returns: A statistical artifact?

Spearman's Law of Diminishing Returns (SLODR) is the idea that the structure of human cognitive ability is more differentiated and g a weaker determinant of cognitive performance at higher levels of ability. In this study, we distinguish between ‘traditional’ methods of testing SLODR and ‘contemporary’ methods of testing SLODR. It is the former set of methods from which the vast majority of the evidence base for SLODR derives. We demonstrated that it is easy to mimic SLODR and reverse SLODR effects in these traditional methods of assessing SLODR by using data with skewed observed variable distributions. The skewness magnitudes did not need to be large to produce these effects and they fell well within the range of values that are usually considered unproblematic for parametric statistic analysis. In simulated datasets, positive subtest skewness resulted in SLODR and negative subtest skewness resulted in reverse SLODR. In contemporary methods of testing SLODR, non-linear g-loadings or a skewed g are assumed to reflect evidence for SLODR. When we applied contemporary methods of testing SLODR to these data, there was evidence of heteroscedastic residuals but no evidence of non-linear g-loadings or skewed g distributions. We broadly replicated the effects of subtest skew from these simulated datasets in real data from the Minnesota Study of Twins Reared Apart. Results imply that traditional methods of assessing SLODR cannot distinguish between effects due to subtest characteristics that have nothing to do with differences in ability structure at different levels of g and true SLODR effects. This calls into question the empirical support for SLODR.     

Assessing Parameter Invariance in the BLIM: Bipartition Models

In knowledge space theory, the knowledge state of a student is the set of all problems he is capable of solving in a specific knowledge domain and a knowledge structure is the collection of knowledge states. The basic local independence model (BLIM) is a probabilistic model for knowledge structures. The BLIM assumes a probability distribution on the knowledge states and a lucky guess and a careless error probability for each problem. A key assumption of the BLIM is that the lucky guess and careless error probabilities do not depend on knowledge states (invariance assumption). This article proposes a method for testing the violations of this specific assumption. The proposed method was assessed in a simulation study and in an empirical application. The results show that (1) the invariance assumption might be violated by the empirical data even when the model’s fit is very good, and (2) the proposed method may prove to be a promising tool to detect invariance violations of the BLIM.     

Bayesian nonparametric model selection and model testing

This article examines a Bayesian nonparametric approach to model selection and model testing, which is based on concepts from Bayesian decision theory and information theory. The approach can be used to evaluate the predictive-utility of any model that is either probabilistic or deterministic, with that model analyzed under either the Bayesian or classical-frequentist approach to statistical inference. Conditional on an observed set of data, generated from some unknown true sampling density, the approach identifies the “best” model as the one that predicts a sampling density that explains the most information about the true density. Furthermore, in the approach, the decision is to reject a model when it does not explain enough information about the true density (according to a straightforward calibration of the Kullback-Leibler divergence measure). The posterior estimate of the true density is based on a Bayesian nonparametric prior that can give positive support to the entire space of sampling densities (defined on some sample space). This article also discusses the theoretical and practical advantages of the Bayesian nonparametric approach over all other types of model selection procedures, and over any model testing procedure that depends on interpreting a p-value. Finally, the Bayesian nonparametric approach is illustrated on four real data sets, in the comparison and testing of order-constrained models, cognitive models, models of choice-behavior, and a test of a general psychometric model.     

The acquisition of mental verbs: A systematic investigation of the first reference to mental state

It is generally recognized that the ability to contemplate and communicate about the knowledge, beliefs, and goals of oneself and others is a benchmark of human cognition. Yet, little is known about the beginnings of this ability, in large measure because methods for accurately assessing very young children's ability have been unavailable. Here we present the results of using a method of convergent analyses of naturally occurring speech to assess the young child's ability to contemplate and communicate about mental state. The first study describes the frequency and function of verbs of mental reference such as think and know in the speech of one child from 2;4 to 4;0. The second examines shorter samples of speech collected from 30 two-year-olds over a 6 month period. Results from both studies suggest that the earliest uses of mental verbs are for conversational functions rather than for mental reference. First attempts at mental reference begin to appear in some children's speech in the second half of the third year. Since most of the children studied exhibited the linguistic knowledge necessary to make reference to mental states, we conclude that the absence of such reference earlier suggests that still younger children lack awareness of such states, or at the very least, an understanding of their appropriateness as topics of conversation.     

Personality and reasoning ability during retirement age: Report from a Swedish population-based longitudinal study

We examined the association between personality and level and change in reasoning ability in a population-based sample of older adults (62–68 years) using a three-year annual follow-up longitudinal study design (HEARTS; N = 3851). Personality traits were measured using the Mini-IPIP scale and reasoning using a short form of Raven’s Matrices. Findings from a structural equation model, controlling for age, education, and sex, revealed that higher levels on extraversion, conscientiousness, and neuroticism were associated with lower reasoning ability (βs: −0.17 to −0.09). Higher levels of openness were associated with better reasoning (β: 0.16). We found no association with rate of change. This evidence replicates previous findings demonstrating that personality traits are associated with individual differences in cognition among older adults.     

Exploiting illusory effects to disclose similarities in numerical and luminance processing

Recent studies have suggested that numerical and physical magnitudes are similarly processed by a generalized magnitude system. The present study investigates the number?Cluminance interaction, taking advantage of illusory effects in a cued line bisection task with numerical or nonnumerical flankers and varying levels of luminance. The results showed that both dimensions influenced bisection performance. Whereas numbers (Experiment 1) induced a systematic shift of the subjective midpoint toward the larger digit, luminance (Experiment 2) modulated the bisection performance toward the darker flanker. By combining these two illusions (Experiments 3 and 4), the two dimensions interfered with each other. This pattern of results suggests overlapping representations for physical and numerical magnitudes and highlights the value of illusory effects in cognitive research.     

$${\in_K}$$: a Non-Fregean Logic of Explicit Knowledge

We present a new logic-based approach to the reasoning about knowledge which is independent of possible worlds semantics. \({\in_K}\) (Epsilon-K) is a non-Fregean logic whose models consist of propositional universes with subsets for true, false and known propositions. Knowledge is, in general, not closed under rules of inference; the only valid epistemic principles are the knowledge axiom K _i φ → φ and some minimal conditions concerning common knowledge in a group. Knowledge is explicit and all forms of the logical omniscience problem are avoided. Various stronger epistemic properties such as positive and/or negative introspection, the K-axiom, closure under logical connectives, etc. can be restored by imposing additional semantic constraints. This yields corresponding sublogics for which we present sound and complete axiomatizations. As a useful tool for general model constructions we study abstract versions of some 3-valued logics in which we interpret truth as knowledge. We establish a connection between \({\in_K}\) and the well-known syntactic approach to explicit knowledge proving a result concerning equi-expressiveness. Furthermore, we discuss some self-referential epistemic statements, such as the knower paradox, as relaxations of variants of the liar paradox and show how these epistemic “paradoxes” can be solved in \({\in_K}\). Every specific \({\in_K}\)-logic is defined as a certain extension of some underlying classical abstract logic.     

Orthogonal factors of mental ability? A response to Hampshire et al.

We respond to the main points raised by Hampshire et al. (2014). First, we note that the simulation study of Hampshire et al. (2012) was based on the assumption that individual differences in the capacities of the three proposed brain networks are mutually independent. However, this orthogonality cannot be assumed even if those networks are anatomically and functionally distinct. We also consider further the implications of our finding that a blended variable or task-mixing model of the structure of mental ability would require nearly every mental ability task to load on nearly every factor of mental ability. We explain that such a result is implausible and favors more parsimonious models that include a g factor.     

Interactional expertise as a third kind of knowledge

Between formal propositional knowledge and embodied skill lies ‘interactional expertise’—the ability to converse expertly about a practical skill or expertise, but without being able to practice it, learned through linguistic socialisation among the practitioners. Interactional expertise is exhibited by sociologists of scientific knowledge, by scientists themselves and by a large range of other actors. Attention is drawn to the distinction between the social and the individual embodiment theses: a language does depend on the form of the bodies of its members but an individual within that community can learn the language without the body. The idea has significance for our understanding of colour-blindness, deafness and other abilities and disabilities. They say that love's a word, a word we've only heard the meaning of.     

Epistemic expressivism and the argument from motivation

This paper explores in detail an argument for epistemic expressivism, what we call the Argument from Motivation. While the Argument from Motivation has sometimes been anticipated, it has never been set out in detail. The argument has three premises, roughly, that certain judgments expressed in attributions of knowledge are intrinsically motivating in a distinct way (P1); that motivation for action requires desire-like states or conative attitudes (HTM); and that the semantic content of knowledge attributions cannot be specified without reference to the intrinsically motivating judgments that such attributions express (P2). We argue that these premises entail a version of ecumenical expressivism. Since the argument from motivation has not been explicitly stated before, there is no current discussion of the argument. In this paper we therefore consider and reject various objections that one might propose to the argument, including some that stem from the idea that knowledge is factive, or that knowledge involves evidence that rules out relevant alternatives. Other objections to (P1) specifically might be derived from cases of apparent lack of epistemic motivation considered in in Kvanvig (The value of knowledge and the pursuit of understanding, 2003) and Brown (Nous 42(2):167–189, 2008), as well as from general forms of externalism about epistemic motivation. We consider these and find them wanting. Finally, the paper offers some critical remarks about the prospect of denying (P2).     

Is motor knowledge part and parcel of the concepts of manipulable artifacts? Clues from a case of upper limb aplasia

The sensory-motor theory of conceptual representations assumes that motor knowledge of how an artifact is manipulated is constitutive of its conceptual representation. Accordingly, if we assume that the richer the conceptual representation of an object is, the easier that object is identified, manipulable artifacts that are associated with motor knowledge should be identified more accurately and/or faster than manipulable artifacts that are not (everything else being equal). In this study, we tested this prediction by investigating the identification of manipulable artifacts in an individual, DC, who was totally deprived of hand motor experience due to upper limb aplasia. This condition prevents him from interacting with most manipulable artifacts, for which he thus has no motor knowledge at all. However, he had motor knowledge for some of them, which he routinely uses with his feet. We contrasted DC’s performance in a timed picture naming task for manipulable artifacts for which he had motor knowledge versus those for which he had no motor knowledge. No detectable advantage on DC’s naming performance was found for artifacts for which he had motor knowledge compared to those for which he did not. This finding suggests that motor knowledge is not part of the concepts of manipulable artifacts.     

Inferring the intentional states of autonomous virtual agents

Inferring the mental states of other agents, including their goals and intentions, is a central problem in cognition. A critical aspect of this problem is that one cannot observe mental states directly, but must infer them from observable actions. To study the computational mechanisms underlying this inference, we created a two-dimensional virtual environment populated by autonomous agents with independent cognitive architectures. These agents navigate the environment, collecting “food” and interacting with one another. The agents’ behavior is modulated by a small number of distinct goal states: attacking, exploring, fleeing, and gathering food. We studied subjects’ ability to detect and classify the agents’ continually changing goal states on the basis of their motions and interactions. Although the programmed ground truth goal state is not directly observable, subjects’ responses showed both high validity (correlation with this ground truth) and high reliability (correlation with one another). We present a Bayesian model of the inference of goal states, and find that it accounts for subjects’ responses better than alternative models. Although the model is fit to the actual programmed states of the agents, and not to subjects’ responses, its output actually conforms better to subjects’ responses than to the ground truth goal state of the agents.     

On the language specificity of basic number processing: transcoding in a language with inversion and its relation to working memory capacity

Transcoding Arabic numbers from and into verbal number words is one of the most basic number processing tasks commonly used to index the verbal representation of numbers. The inversion property, which is an important feature of some number word systems (e.g., German einundzwanzig [one and twenty]), might represent a major difficulty in transcoding and a challenge to current transcoding models. The mastery of inversion, and of transcoding in general, might be related to nonnumerical factors such as working memory resources given that different elements and their sequence need to be memorized and manipulated. In this study, transcoding skills and different working memory components in Austrian (German-speaking) 7-year-olds were assessed. We observed that inversion poses a major problem in transcoding for German-speaking children. In addition, different components of working memory skills were differentially correlated with particular transcoding error types. We discuss how current transcoding models could account for these results and how they might need to be adapted to accommodate inversion properties and their relation to different working memory components.     

Genetic Testing and Parkinson Disease: Assessment of Patient Knowledge,Attitudes, and Interest

The most common genetic contributor to late-onset Parkinson disease (PD) is the LRRK2 gene. In order to effectively integrate LRRK2 genetic testing into clinical practice, a strategy tailored to the PD population must be developed. We assessed 168 individuals with PD for baseline knowledge of genetics, perceived risk, and interest and opinions regarding genetic counseling and testing. Most participants felt that they were familiar with general genetics terms but overall knowledge levels were low, with an average score of 55%. The majority of participants thought it was likely they inherited a PD gene (72%), believed genetic testing for PD would be useful (86%), and were interested in genetic testing (59%) and genetic counseling (56%). However, only a few participants had heard of any genetic tests for PD (29%) or LRRK2 (10%). There appears to be a significant level of interest in genetics and genetic testing within the PD population, but a considerable deficit in genetics knowledge and an over-estimation of risk. Genetic education and counseling tools to address these needs were developed to provide patients with the ability to make informed and knowledgeable genetic testing decisions.     

How much does number matter to a monkey (Macaca mulatta)?

Although many animal species can represent numerical values, little is known about how salient number is relative to other object properties for nonhuman animals. In one hypothesis, researchers propose that animals represent number only as a last resort, when no other properties differentiate stimuli. An alternative hypothesis is that animals automatically, spontaneously, and routinely represent the numerical attributes of their environments. The authors compared the influence of number versus that of shape, color, and surface area on rhesus monkeys' (Macaca mulatta) decisions by testing them on a matching task with more than one correct answer: a numerical match and a nonnumerical (color, surface area, or shape) match. The authors also tested whether previous laboratory experience with numerical discrimination influenced a monkey's propensity to represent number. Contrary to the last-resort hypothesis, all monkeys based their decisions on numerical value when the numerical ratio was favorable.     

Individual differences in the tendency to see the expected

Prior knowledge has been shown to facilitate the incorporation of visual stimuli into awareness. We adopted an individual differences approach to explore whether a tendency to ‘see the expected’ is general or method-specific. We administered a binocular rivalry task and manipulated selective attention, as well as induced expectations via predictive context, self-generated imagery, expectancy cues, and perceptual priming. Most prior manipulations led to a facilitated awareness of the biased percept in binocular rivalry, whereas strong signal primes led to a suppressed awareness, i.e., adaptation. Correlations and factor analysis revealed that the facilitatory effect of priors on visual awareness is closely related to attentional control. We also investigated whether expectation-based biases predict perceptual abilities. Adaptation to strong primes predicted improved naturalistic change detection and the facilitatory effect of weak primes predicted the experience of perceptual anomalies. Taken together, our results indicate that the facilitatory effect of priors may be underpinned by an attentional mechanism but the tendency to ‘see the expected’ is method-specific.     

Decision Making under Strict Uncertainty: An Experimental Test of Competitive Criteria

In decisions under strict uncertainty individual decision makers have to choose one of a finite number of alternatives with complete information about their outcomes but in the absence of any information about the probabilities of the various states of nature. We report two experiments with multiple decision tasks in which subjects were instructed to rank the alternatives (Experiment 1), or choose the best one (Experiment 2). We test the major decision rules (criteria) which have been proposed for this case in the normative literature with special attention on Hurwicz′s "optimism-pessimism" criterion which is the only one that can accommodate individual differences. Although none of the criteria can account for the results of the majority of the subjects, choices made by a sizable minority of the subjects′ are consistent with Hurwicz′s model. There is no evidence for a systematic relationship between the model′s single "optimism-pessimism" parameter (inferred form choices) and, independently derived, individual measures of optimism (obtained from responses to personality scales). We conclude with a discussion of the difficulty of experimentally implementing strict uncertainty.     

A computational perspective on social attachment

Humans depend on social relationships for survival and wellbeing throughout life. Yet, individuals differ markedly in their ability to form and maintain healthy social relationships. Here we use a simple mathematical model to formalize the contention that a person’s attachment style is determined by what they learn from relationships early in life. For the sake of argument, we therefore discount individual differences in the innate personality or attachment style of a child, assuming instead that all children are simply born with an equivalent, generic, hardwired desire and instinct for social proximity, and a capacity to learn. In line with the evidence, this innate endowment incorporates both simple bonding instincts and a capacity for cognitively sophisticated beliefs and generalizations. Under this assumption, we then explore how distinct attachment styles might emerge through interaction with the child’s early caregivers. Our central question is, how an apparently adaptive capacity to learn can yield enduring maladaptive attachment styles that generalize to new relationships. We believe extensions of our model will ultimately help clarify the complex interacting mechanisms – both acquired and innate – that underpin individual differences in attachment styles. While our model is relatively abstract, we also attempt some connection to known biological mechanisms of attachment.     

From specific examples to general knowledge in language learning

The extraction of general knowledge from individual episodes is critical if we are to learn new knowledge or abilities. Here we uncover some of the key cognitive mechanisms that characterise this process in the domain of language learning. In five experiments adult participants learned new morphological units embedded in fictitious words created by attaching new affixes (e.g., -afe) to familiar word stems (e.g., “sleepafe is a participant in a study about the effects of sleep”). Participants’ ability to generalise semantic knowledge about the affixes was tested using tasks requiring the comprehension and production of novel words containing a trained affix (e.g., sailafe). We manipulated the delay between training and test (Experiment 1), the number of unique exemplars provided for each affix during training (Experiment 2), and the consistency of the form-to-meaning mapping of the affixes (Experiments 3–5). In a task where speeded online language processing is required (semantic priming), generalisation was achieved only after a memory consolidation opportunity following training, and only if the training included a sufficient number of unique exemplars. Semantic inconsistency disrupted speeded generalisation unless consolidation was allowed to operate on one of the two affix-meanings before introducing inconsistencies. In contrast, in tasks that required slow, deliberate reasoning, generalisation could be achieved largely irrespective of the above constraints. These findings point to two different mechanisms of generalisation that have different cognitive demands and rely on different types of memory representations.