Research on the cognitive abilities involved in decision making has shown that, under objective risk conditions (i.e., when explicit information about possible outcomes and risks is available), superior decisions are especially predicted by executive functions and exact number processing skills, also referred to as objective numeracy. So far, decision-making research has mainly focused on exact number processing skills, such as performing calculations or transformations of symbolic numbers. There is evidence that such exact numeric skills are based (...) on approximate number processing (ANP) skills, which enable quick and accurate processing of non-symbolic numbers (e.g. Chen and Li, 2014). Very few studies, however, have investigated ANP skills in the context of risky decision making and have analyzed direct associations among the aforementioned sub functions. Possible interactions between the closely related skills have not been considered. The current study (N = 128) examines interactions of ANP skills with executive functions and objective numeracy, in predicting risky choice behavior. ANP skills are represented by the accuracy in a dot-comparison task. Decision making is measured by two versions of the Game of Dice Task (GDT), which place different emphases on the reflection of potential risks. The results show two-way as well as three-way interactions between the measures of ANP skills, executive functions, and objective numeracy in predicting risky decisions in both GDT versions. The riskiest decisions were most frequently made in case of low scores in all of the three competencies, while good performance in any one of them resulted in significant reductions of disadvantageous decisions. The findings indicate that high ANP skills can positively affect choice behavior in individuals who have weaknesses in reflectively attributed skills, namely executive functions and objective numeracy. Potential compensatory effects and mechanisms of ANP in decision making are discussed. (shrink)

Subjects classified visible 2-digit numbers as larger or smaller than 55. Target numbers were preceded by masked 2-digit primes that were either congruent (same relation to 55) or incongruent. Experiments 1 and 2 showed prime congruency effects for stimuli never included in the set of classified visible targets, indicating subliminal priming based on long-term semantic memory. Experiments 2 and 3 went further to demonstrate paradoxical unconscious priming effects resulting from task context. For example, after repeated practice classifying 73 as larger (...) than 55, the novel masked prime 37 paradoxically facilitated the “larger” response. In these experiments task context could induce subjects to unconsciously process only the leftmost masked prime digit, only the rightmost digit, or both independently. Across 3 experiments, subliminal priming was governed by both task context and long-term semantic memory. (shrink)

Recent findings indicate that the constituting digits of multi-digit numbers are processed, decomposed into units, tens, and so on, rather than integrated into one entity. This is suggested by interfering effects of unit digit processing on two-digit number comparison. In the present study, we extended the computational model for two-digit number magnitude comparison of Moeller, Huber, Nuerk, and Willmes (2011a) to the case of three-digit number comparison (e.g., 371_826). In a second step, we evaluated how hundred-decade (...) and hundred-unit compatibility effects were moderated by varying the percentage of within-hundred (e.g., 539_582) and within-hundred-and-decade filler items (e.g., 483_489). From the results we predict that numerical distance as well as compatibility effects should indeed be modulated by the relevance of tens and units in three-digit number magnitude comparison: While in particular the hundred distance effect should decrease, we predict hundred-decade and hundred-unit compatibility effects to increase with the relevance of tens and units. (shrink)

A growing body of research has shown that symbolic number processing relates to individual differences in mathematics. However, it remains unclear which mechanisms of symbolic number processing are crucial—accessing underlying magnitude representation of symbols (i.e., symbol‐magnitude associations), processing relative order of symbols (i.e., symbol‐symbol associations), or processing of symbols per se. To address this question, in this study adult participants performed a dots‐number word matching task—thought to be a measure of symbol‐magnitude associations (numerical (...) magnitude processing)—a numeral‐ordering task that focuses on symbol‐symbol associations (numerical order processing), and a digit‐number word matching task targeting symbolic processing per se. Results showed that both numerical magnitude and order processing were uniquely related to arithmetic achievement, beyond the effects of domain‐general factors (intellectual ability, working memory, inhibitory control, and non‐numerical ordering). Importantly, results were different when a general measure of mathematics achievement was considered. Those mechanisms of symbolic number processing did not contribute to math achievement. Furthermore, a path analysis revealed that numerical magnitude and order processing might draw on a common mechanism. Each process explained a portion of the relation of the other with arithmetic (but not with a general measure of math achievement). These findings are consistent with the notion that adults’ arithmetic skills build upon symbol‐magnitude associations, and they highlight the effects that different math measures have in the study of numerical cognition. (shrink)

Recent years have witnessed an enormous increase in behavioral and neuroimaging studies of numerical cognition. Particular interest has been devoted toward unraveling properties of the representational medium on which numbers are thought to be represented. We have argued that a correct inference concerning these properties requires distinguishing between different input modalities and different decision/output structures. To back up this claim, we have trained computational models with either symbolic or nonsymbolic input and with different task requirements, and showed that this allowed (...) for an integration of the existing data in a consistent manner. In later studies, predictions from the models were derived and tested with behavioral and neuroimaging methods. Here we present an integrative review of this work. (shrink)

The study has two objectives: to introduce grip force recording as a new technique for studying embodied numerical processing; and to demonstrate how three competing accounts of numerical magnitude representation can be tested by using this new technique: the Mental Number Line, A Theory of Magnitude and Embodied Cognition account. While 26 healthy adults processed visually presented single digits in a go/no-go n-back paradigm, their passive holding forces for two small sensors were recorded in both hands. Spontaneous and (...) unconscious grip force changes related to number magnitude occurred in the left hand already 100–140 ms after stimulus presentation and continued systematically. Our results support a two-step model of number processing where an initial stage is related to the automatic activation of all stimulus properties whereas a later stage consists of deeper conscious processing of the stimulus. This interpretation generalizes previous work with linguistic stimuli and elaborates the timeline of embodied cognition. We hope that the use of grip force recording will advance the field of numerical cognition research. (shrink)

This paper aims to show that Selim Berker’s widely discussed prime number case is merely an instance of the well-known generality problem for process reliabilism and thus arguably not as interesting a case as one might have thought. Initially, Berker’s case is introduced and interpreted. Then the most recent response to the case from the literature is presented. Eventually, it is argued that Berker’s case is nothing but a straightforward consequence of the generality problem, i.e., the problematic aspect of (...) the case for process reliabilism (if any) is already captured by the generality problem. (shrink)

The paper is concerned with the existence and asymptotic character of the nonlinear boundary value problemdG/dt=F ¦ –¦dF/dt=gG =k 1,G=k 2 as ¦– ¦ o+ The discussion is related to the problem of particle-number fluctuations in the theory of cosmic radiation andG andF denote respectively the probability generating functions for the electron distribution in an electron-initiated and a photon-initiated shower.A solution of the system satisfying the boundary conditions is constructed so that specified limiting conditions are fulfilled.

Understanding the spread of national public policies to increase the percentage of women on boards is often presented using different types of institutional theory logic. However, the importance of the political games influencing these decisions has not received the same attention. In this article, we look beyond the institutional setting by focusing on the role of actors. We explore processes that include who the critical actors that drive and determine these policies are, and what motivates them to push for change. (...) We employ a processual design approach using a longitudinal country-comparative case study exploring the case of Norway, England, Germany and Italy. We map the political games, both inside and outside legislative areas, including the micro-politics among various actors and groups of actors in the selected countries. Data are collected through participation observations, interviews and text analyses. The study contributes by filling important gaps in the literature by embedding the discussion about women on boards in politicking and national public policies and by introducing dynamic perspectives. Finally, by using a processual design approach, we capture the reality of the women on board debates at different points of time and in different actor and motivational contexts. The study has consequences for how policy-makers and businesses may follow up and act, based on the debates. (shrink)

In this article, Paul's use of the Old Testament in 1 Corinthians 10:1-4 comes under scrutiny. In contrast with the theory of some modern scholars that Paul uses, 'fanciful analogies', 'startling figurative claims' and metaphors that 'should not he pressed', in reaching his conclusion that 'the rock was Christ', in 1 Corinthians 10:4c, it is indicated that Paul is indeed taking the original text, the Old Testament's interpretation of the text, and the Jewish tradition of the interpretation of the text, (...) seriously, in the light of the Christ-event. To prove this claim, research of the text, that Paul uses in 1 Corinthians 10:1-4, is followed by research of the 'world in front of that text'.CONTRIBUTION: The conclusion that is reached indicates that Paul established within the context of contemporary Jewish practices, a true dialogical relationship between an intertextual handling of the text, and his interpretation thereof in the light of the relevance of the Christ-event for the conflict in the Church of Corinth. (shrink)

In this paper we present two types of logics and \ ) where certain p-adic functions are associated to propositional formulas. Logics of the former type are p-adic valued probability logics. In each of these logics we use probability formulas K r,ρ α and D ρ α,β which enable us to make sentences of the form “the probability of α belongs to the p-adic ball with the center r and the radius ρ”, and “the p-adic distance between the probabilities of (...) α and β is less than or equal to ρ”, respectively. Logics of the later type formalize processes of thinking where information are coded by p-adic numbers. We use the same operators as above, but in this formalism K r,ρ α means “the p-adic code of the information α belongs to the p-adic ball with the center r and the radius ρ”, while D ρ α,β means “the p-adic distance between codes of α and β are less than or equal to ρ”. The corresponding strongly complete axiom systems are presented and decidability of the satisfiability problem for each logic is proved. (shrink)

Recent work on the acquisition of number words has emphasized the importance of integrating linguistic and developmental perspectives [Musolino, J. (2004). The semantics and acquisition of number words: Integrating linguistic and developmental perspectives. Cognition93, 1-41; Papafragou, A., Musolino, J. (2003). Scalar implicatures: Scalar implicatures: Experiments at the semantics-pragmatics interface. Cognition, 86, 253-282; Hurewitz, F., Papafragou, A., Gleitman, L., Gelman, R. (2006). Asymmetries in the acquisition of numbers and quantifiers. Language Learning and Development, 2, 76-97; Huang, Y. T., Snedeker, (...) J., Spelke, L. (submitted for publication). What exactly do numbers mean?]. Specifically, these studies have shown that data from experimental investigations of child language can be used to illuminate core theoretical issues in the semantic and pragmatic analysis of number terms. In this article, I extend this approach to the logico-syntactic properties of number words, focusing on the way numerals interact with each other (e.g. Three boys are holding two balloons) as well as with other quantified expressions (e.g. Three boys are holding each balloon). On the basis of their intuitions, linguists have claimed that such sentences give rise to at least four different interpretations, reflecting the complexity of the linguistic structure and syntactic operations involved. Using psycholinguistic experimentation with preschoolers (n=32) and adult speakers of English (n=32), I show that (a) for adults, the intuitions of linguists can be verified experimentally, (b) by the age of 5, children have knowledge of the core aspects of the logical syntax of number words, (c) in spite of this knowledge, children nevertheless differ from adults in systematic ways, (d) the differences observed between children and adults can be accounted for on the basis of an independently motivated, linguistically-based processing model [Geurts, B. (2003). Quantifying kids. Language Acquisition, 11(4), 197-218]. In doing so, this work ties together research on the acquisition of the number vocabulary with a growing body of work on the development of quantification and sentence processing abilities in young children [Geurts, 2003; Lidz, J., Musolino, J. (2002). Children's command of quantification. Cognition, 84, 113-154; Musolino, J., Lidz, J. (2003). The scope of isomorphism: Turning adults into children. Language Acquisition, 11(4), 277-291; Trueswell, J., Sekerina, I., Hilland, N., Logrip, M. (1999). The kindergarten-path effect: Studying on-line sentence processing in young children. Cognition, 73, 89-134; Noveck, I. (2001). When children are more logical than adults: Experimental investigations of scalar implicature. Cognition, 78, 165-188; Noveck, I., Guelminger, R., Georgieff, N., & Labruyere, N. (2007). What autism can tell us about every. . . not sentences. Journal of Semantics,24(1), 73-90. On a more general level, this work confirms the importance of integrating formal and developmental perspectives [Musolino, 2004], this time by highlighting the explanatory power of linguistically-based models of language acquisition and by showing that the complex structure postulated by linguists has important implications for developmental accounts of the number vocabulary. (shrink)

Given the replication crisis in cognitive science, it is important to consider what researchers need to do in order to report results that are reliable. We consider three changes in current practice that have the potential to deliver more realistic and robust claims. First, the planned experiment should be divided into two stages, an exploratory stage and a confirmatory stage. This clear separation allows the researcher to check whether any results found in the exploratory stage are robust. The second change (...) is to carry out adequately powered studies. We show that this is imperative if we want to obtain realistic estimates of effects in psycholinguistics. The third change is to use Bayesian data-analytic methods rather than frequentist ones; the Bayesian framework allows us to focus on the best estimates we can obtain of the effect, rather than rejecting a strawman null. As a case study, we investigate number interference effects in German. Number feature interference is predicted by cue-based retrieval models of sentence processing, but it has shown inconsistent results. We show that by implementing the three changes mentioned, suggestive evidence emerges that is consistent with the predicted number interference effects. (shrink)

Cognitive Science, Volume 46, Issue 7, July 2022.

In this article, Paul's use of the Old Testament in 1 Corinthians 10:1-4 comes under scrutiny. In contrast with the theory of some modern scholars that Paul uses, 'fanciful analogies', 'startling figurative claims' and metaphors that 'should not he pressed', in reaching his conclusion that 'the rock was Christ', in 1 Corinthians 10:4c, it is indicated that Paul is indeed taking the original text, the Old Testament's interpretation of the text, and the Jewish tradition of the interpretation of the text, (...) seriously, in the light of the Christ-event. To prove this claim, research of the text, that Paul uses in 1 Corinthians 10:1-4, is followed by research of the 'world in front of that text'.CONTRIBUTION: The conclusion that is reached indicates that Paul established within the context of contemporary Jewish practices, a true dialogical relationship between an intertextual handling of the text, and his interpretation thereof in the light of the relevance of the Christ-event for the conflict in the Church of Corinth. (shrink)