Definition of the problem The umbrella term “explicability” refers to the reduction of opacity of artificial intelligence (AI) systems. These efforts are challenging for medical AI applications because higher accuracy often comes at the cost of increased opacity. This entails ethical tensions because physicians and patients desire to trace how results are produced without compromising the performance of AI systems. The centrality of explicability within the informed consent process for medical AI systems compels an ethical reflection on the trade-offs. Which (...) levels of explicability are needed to obtain informed consent when utilizing medical AI? Arguments We proceed in five steps: First, we map the terms commonly associated with explicability as described in the ethics and computer science literature, i.e., disclosure, intelligibility, interpretability, and explainability. Second, we conduct a conceptual analysis of the ethical requirements for explicability when it comes to informed consent. Third, we distinguish hurdles for explicability in terms of epistemic and explanatory opacity. Fourth, this then allows to conclude the level of explicability physicians must reach and what patients can expect. In a final step, we show how the identified levels of explicability can technically be met from the perspective of computer science. Throughout our work, we take diagnostic AI systems in radiology as an example. Conclusion We determined four levels of explicability that need to be distinguished for ethically defensible informed consent processes and showed how developers of medical AI can technically meet these requirements. (shrink)

Diese Untersuchung behandelt die Auseinandersetzung aus systematisch-theologischer Perspektive mit einem «unsystematischen» Denker, Emil Cioran. Sie versucht im Sinne einer dialogischen Kulturtheologie einen Dialog zwischen der christlichen Theologie orthodoxer Prägung und Cioran zu führen. Dieser Versuch soll von Toleranz als Anerkennung der Legitimität des Anderen und dem Respekt des Fremden als Fremden geprägt sein. Methodologisch untersucht die Arbeit drei Hauptcharakteristika von Ciorans Denken: den Dualismus, die Skepsis und die Mystik. Sie versucht diese mit Hilfe von zwei Strukturierungsprinzipien - dem hermeneutische Dreieck (...) Gott-Mensch-Welt und den sieben Leitebenen zu systematisieren. (shrink)

This functional Magnetic Resonance Imaging study investigated high and low suggestible people responding to two visual hallucination suggestions with and without a hypnotic induction. Participants in the study were asked to see color while looking at a grey image, and to see shades of grey while looking at a color image. High suggestible participants reported successful alterations in color perception in both tasks, both in and out of hypnosis, and showed a small benefit if hypnosis was induced. Low suggestible people (...) could not perform the tasks successfully with or without the hypnotic induction. The fMRI results supported the self report data, and changes in brain activity were found in a number of visual areas. The results indicate that a hypnotic induction, although having the potential to enhance the ability of high suggestible people, is not necessary for the effective alteration of color perception by suggestion. (shrink)

Recent work has demonstrated that the sense of agency is not only determined by efference-copy-based internal predictions and internal comparator mechanisms, but by a large variety of different internal and external cues. The study by Moore and colleagues [Moore, J. W., Wegner, D. M., & Haggard, P. . Modulating the sense of agency with external cues. Conscious and Cognition] aimed to provide further evidence for this view by demonstrating that external agency cues might outweigh or even substitute efferent signals to (...) install a basic registration of self-agency. Although the study contains some critical points that, so we argue, are central to a proper interpretation of the data, it hints at a new perspective on agency: optimal cue integration seems to be the key to a robust sense of agency. We here argue that this framework could allow integrating the findings of Moore and colleagues and other recent agency studies into a comprehensive picture of the sense of agency and its pathological disruptions. (shrink)

This paper presents the metaphysics of the Vietnamese Buddhist Zen monk Thich Nhat Hanh. He interprets the Buddhist principle of interdependent arising in terms of interbeing, the idea that everything depends for its existence on everything else. On his view, everything “inter-is” with everything else, or “to be is to inter-be.” His interpretation is particularly interesting in light of the contemporary debate on fundamentality in western metaphysics. By embracing the idea of interbeing, he opposes the view that there are fundamental (...) entities which do not depend for their existence on anything else. I give an outline of Thich Nhat Hanh’s views, answer an objection, and explain his reasons for adopting his standpoint. My aim is not to offer a full defense of his views, but only to show that the often neglected position of metaphysical coherentism, which Thich Nhat Hanh adopts, deserves further consideration. (shrink)

The aim of the study was to illustrate the impact of teachers’ implementation of differentiation and individualization on students’ perception of their inclusion regarding their social inclusion, emotional wellbeing and academic self-concept. The study sample comprised 824 third-to-eighth-grade students [255 males and 569 females ]. Around 10% of the sample had special educational needs. Students’ perceived inclusion levels and academic self-concept were examined with the Arabic version of the Perceptions of Inclusion Questionnaire. Students’ ratings of inclusive practices in their classroom (...) were examined using the Arabic version of the Inclusive Teaching Practices Scale. SEN students expressed lower perceived social inclusion, emotional inclusion, and academic self-concept in comparison with non-SEN students. Moreover, high levels of inclusive teaching practices strongly predicted students’ perceived emotional inclusion, social inclusion, and academic self-concept. The results of the study supported the importance of school-level inclusive teaching practices and their relation to students’ school experiences. It also highlighted the need for schools and teachers to work towards improved school-level inclusion experiences for SEN students. (shrink)

Concerted, timely action for mitigating climate change is of uttermost importance to keep global warming as close to 1.5°C as possible. Air traffic already plays a strong role in driving climate change and is projected to grow—with only limited technical potential for decarbonizing this means of transport. Therefore, it is desirable to minimize the expansion of air traffic or even facilitate a reduction in affluent countries. Effective policies and behavioral change, especially among frequent flyers, can help to lower greenhouse gas (...) emissions. For both, a positive evaluation and public support is indispensable. This study contributes to understanding air travel behavior and the perception of regulative policies. We examined the role of attitudes, perceived behavioral control, efficacy, global identity, and justice concerns for intentions to avoid flights and aviation-related environmental policy support. We conducted an online survey study with a quota sample of N = 2,530 participants in Germany. The strongest positive predictors of intentions to refrain from flying and policy support were perceived behavioral control to travel without flying, efficacy beliefs that avoiding air travel contributes to climate change mitigation, and intergenerational justice concerns; pro-travel attitude was a negative predictor. Moreover, we tested whether the provision of additional information on climate impact, global and intranational inequalities as well as subsidies affected the intention to avoid air travel and policy support. We found no effects of the different types of information. Nor did we find an interaction between the type of information provided and global or national identity. Our results highlight the need for a shift within the mobility sector that facilitates attractive and accessible transport alternatives in order to strengthen people’s behavioral control to choose other means than planes and their efficacy perceptions. Moreover, raising awareness of the impacts of climate change on future generations and developing strategies to promote people’s concern for intergenerational justice might motivate people to reduce air travel and thereby contribute to a livable future for new generations. (shrink)

Background: Although performance on the category fluency test is influenced by many cognitive functions, item-level scoring methods of CFT performance might be a promising way to capture aspects of semantic memory that are less influenced by intervenient abilities. One such approach is based on the calculation of correlation coefficients that quantify the association between item-level features and the serial order with which words are recalled.Methods: We explored the neural underpinnings of 10 of these correlational indices in a sample of 40 (...) healthy adults who completed a classic 1-min CFT and an MRI protocol inclusive of T1-weighted and resting-state fMRI sequences for the evaluation of the default-mode network. Two sets of linear models were defined to test the association between neural maps and each correlational index: a first set in which major demographic and clinical descriptors were controlled for and a second set in which, additionally, all other 9 correlational indices were regressed out.Results: In the analysis of the DMN, ‘SRO-frequency’, ‘SRO-dominance’ and ‘SRO-body-object interaction’ correlational indices were all negatively associated with the anterior portion of the right temporoparietal junction. The ‘SRO-frequency’ correlational index was also negatively associated with the right dorsal anterior cingulate and the ‘SRO-dominance’ correlational index with the right lateral prefrontal cortex. From the second set of models, the ‘SRO-typicality’ correlational index was positively associated with the left entorhinal cortex. No association was found in relation to grey matter maps.Conclusion: The ability to retrieve more difficult words during CFT performance as measured by the correlational indices between SRO and item-level descriptors is associated with DMN expression in regions deputed to attentional reorienting and processing of salience of infrequent stimuli and dominance status. Of all item-level features, typicality appears to be that most closely linked with entorhinal functioning and may thus play a relevant role in assessing its value in testing procedures for early detection of subtle cognitive difficulties in people with suspected Alzheimer’s degeneration. Although exploratory, these findings warrant further investigations in larger cohorts. (shrink)

The aim of psychology is to understand the human mind and behavior. In contemporary psychology, the method of choice to accomplish this incredibly complex endeavor is the experiment. This dominance has shaped the whole discipline from the self-concept as an empirical science and its very epistemological and theoretical foundations, via research practice and the scientific discourse to teaching. Experimental psychology is grounded in the scientific method and positivism, and these principles, which are characteristic for modern thinking, are still upheld. Despite (...) this apparently stalwart adherence to modern principles, experimental psychology exhibits a number of aspects which can best be described as facets of postmodern thinking although they are hardly acknowledged as such. Many psychologists take pride in being “real natural scientists” because they conduct experiments, but it is particularly difficult for psychologists to evade certain elements of postmodern thinking in view of the specific nature of their subject matter. Postmodernism as a philosophy emerged in the 20th century as a response to the perceived inadequacy of the modern approach and as a means to understand the complexities, ambiguities, and contradictions of the times. Therefore, postmodernism offers both valuable insights into the very nature of experimental psychology and fruitful ideas on improving experimental practice to better reflect the complexities and ambiguities of human mind and behavior. Analyzing experimental psychology along postmodern lines begins by discussing the implications of transferring the scientific method from fields with rather narrowly defined phenomena—the natural sciences—to a much broader and more heterogeneous class of complex phenomena, namely the human mind and behavior. This ostensibly modern experimental approach is, however, per se riddled with postmodern elements: creating phenomena in an experimental setting, including the hermeneutic processes of generating hypotheses and interpreting results, is no carbon copy of “reality” but rather an active construction which reflects irrevocably the pre-existing ideas of the investigator. These aspects, analyzed by using postmodern concepts like hyperreality and simulacra, did not seep in gradually but have been present since the very inception of experimental psychology, and they are necessarily inherent in its philosophy of science. We illustrate this theoretical analysis with the help of two examples, namely experiments on free will and visual working memory. The postmodern perspective reveals some pitfalls in the practice of experimental psychology. Furthermore, we suggest that accepting the inherently fuzzy nature of theoretical constructs in psychology and thinking more along postmodern lines would actually clarify many theoretical problems in experimental psychology. (shrink)

A challenge for theories of incomplete descriptions is to capture the consistency of ‘Sobel sequences’ and to account for an asymmetry in the acceptability of utterances of Sobel sequences and ‘reverse Sobel sequences’. David Lewis’s theory of incomplete descriptions answers, unlike many other theories, the challenge from Sobel sequences, but it does not answer the challenge from reverse Sobel sequences. This article presents another asymmetry in the availability of anaphoric readings of Sobel sequences and reverse Sobel sequences, and proposes an (...) explanation of the original asymmetry on its grounds. This provides an answer to the challenge for Lewis’s theory. (shrink)

The Diamond Sutra is one of the earliest and most treasured of the Perfection of Wisdom Sutras and had a wide influence on the development of Zen Buddhism. There has been, in recent years, great interest in one particular form of sentences that repeatedly occur in the sutra, sentences of the form “A is not A, therefore it is A”. These sentences display what has been called the “logic of not” or the “logic of affirmation-in-negation”. They are of special interest (...) since they do not only encapsulate one of the central insights of Zen Buddhism, that of nonduality, but at the same time seem to go against one of the most orthodox laws of logic in Western philosophy, the law of identity. This paper discusses the interpretation of these “diamond sentences” by the Vietnamese Zen monk Thich Nhat Hanh. I present Thich Nhat Hanh’s interpretation of the diamond sentences in terms of interbeing and go on to argue that and explain how, on his interpretation, the validity of the law of identity is indeed rejected. Finally, I spell out consequences for formulating a “logic of Zen” and for a related debate about the validity of the law of non-contradiction in Zen. (shrink)

Sumit Sarkar, one of the leading Indian historians of his generation, participated in the Indian-British Subaltern Studies Collective that established new standards in the historiography of colonialism in the 1980’s. In this Interview, Déborah Cohen and Urs Lindner ask him about the achievements and oversights of the Subaltern Studies project, the prospects of global history, Marx’s eurocentrism and the problem of religion.

The project 'Facing Forward' started with a collaboration between five institutions: the Stedelijk Museum Amsterdam, the Amsterdam School for Cultural Analysis at the University of Amsterdam, De Appel arts centre, W139, the Stedelijk Museum Bureau Amsterdam and the art magazine Metroplis M. Having previously organized the lecture series and publications 'Right About Now: Art & Theory in the 1990s' (2005/2006) and 'Now is the Time: Art & Theory in the 21st Century' (2008/2009), the organizing committee decided to take the final (...) step in this timeline and turn its attention to the far horizon. Informed by a shared interest in the role that history, speculation, and utopianism play in the field of contemporary art and design (as well as the larger context of global, socio-economic and political developments), a selection of seven themes emerged from the conversations of the initial organizers. These would eventually shape the seven lecture and discussions events - collected in this volume of essays - publicized under the banner Art & Theory From a Future Perspective. A great number of internationally renowned speakers were invited to reflect on the proposed themes during often sold-out events, which were presented at the Oude Lutherse Kerk in Amsterdam in 2011/2012. Yet, however compelling our desire as organizers to go beyond the framework of contemporary events and the current interest, well-nigh obsession, with history, it is obviously an illusion to think that we can escape the past by means of a turn towards the future."--Page 8. (shrink)

Since the publication of Nikolas Rose’s ‘The Politics of Life Itself’ there has been vivid discussion about how biopolitical governance has changed over the last decades. This article uses what Rose terms ‘molecular politics’, a new socio-technical grip on the human body, as a contrasting background to ask anew his question ‘What, then, of biopolitics today?’ – albeit focusing not on advances in genetics, microbiology, and pharmaceutics, as he does, but on the rapid proliferation of wearables and other sensor-software gadgets. (...) In both cases, new technologies providing information about the individual body are the common ground for governance and optimization, yet for the latter, the target is habits of moving, eating and drinking, sleeping, working and relaxing. The resulting profound differences are carved out along four lines: ‘somatic identities’ and a modified understanding of the body; the role of ‘expert knowledge’ compared to that of networks of peers and self-experimentation; the ‘types of intervention’ by which new technologies become effective in our everyday life; and the ‘post-discipline character’ of molecular biopolitics. It is argued that, taken together, these differences indicate a remarkable shift which could be termed aretaic: its focus is not ‘life itself’ but ‘life as it is lived’, and its modality are new everyday socio-technical entanglements and their more-than-human rationalities of governance. (shrink)

In this accessible integration of psychology and theology, Marjorie Lindner Gunnoe offers a comprehensive understanding of personhood from both perspectives, examining the intersection of biblical perspectives with established theories of social development as proposed by Erik Erikson, B. F. Skinner, Evoluntionary Psychology, and more.

To address the tension between demands for more transparent AI systems and the aim to develop and design robots with apparent agency for smooth and intuitive human-robot interaction (HRI), we present in this paper an argument for why explainability in HRI would benefit from being question-centered. First, we review how explainability has been discussed in AI and HRI respectively, to then present the challenge in HRI to accommodate the requirement of transparency while also keeping up the appearance of the robot (...) as a social agent. Based on the conceptualization of questions as information-seeking acts, our proposal for a question-centered approach to explainable HRI (xHRI) implies that to ensure transparency, robots shall provide explanations upon request in the form of questioning. We end this paper by laying out a preliminary taxonomy of xHRI-relevant questions that present the kinds of explanations a robot can or should be able to provide for successful and transparent HRI. (shrink)

Averageness is purportedly the result of stabilizing selection maintaining the population mean, whereas facial paedomorphosis is a product of directional selection driving the population mean towards an increasingly juvenile appearance. If selection is predominantly stabilizing, intermediate phenotypes reflect high genetic quality and mathematically average faces should be found attractive. If, on the other hand, directional selection is strong enough, extreme phenotypes reflect high genetic quality and juvenilized faces will be found attractive. To compare the effects of stabilizing and directional selection (...) on facial paedomorphosis (juvenilization), graphic morphing and editing techniques were used to alter the appearance of composite faces to make them appear more or less juvenile. Both facial models and judges of attractiveness were from the CSU-Long Beach campus. Although effect sizes for both preferences were large, the effect for averageness was nearly twice that found for juvenilization, an indication that stabilizing selection influences preferences for facial paedomorphosis more so than directional selection in contemporary humans. (shrink)

In their debate here Jacques Bidet, Gérard Duménil and Urs Lindner confront their interpretations of Marx’s Capital, discussing the usages to be made of it today. Questions addressed here include the place of the philosophy, economics, and social sciences, in the critique of political economy. They examine the points where Marx’s analysis has been reformulated or completed, to what extent it has been rendered obsolete by historical evolutions, and in what respect it still retains its pertinence. These are the (...) principal questions addressed in the discussion. (shrink)

Stereotype threat is a possible reason for difficulties faced by girls and women in the fields of science, technology, engineering, and mathematics. The threat experienced due to gender can cause elevated worry during performance situations. That is, if the stereotype that women are not as good as men in math becomes salient, this stereotype activation draws women’s attention to task-irrelevant worry caused by the fear of conforming to the negative stereotype. Increased worry can reduce cognitive resources, potentially leading to performance (...) decrements. We argue that such worry is more pronounced immediately after an unrelated self-control demand, which is assumed to temporarily decrease people’s self-control exertion over their attention and stream of thought. This prediction was examined in an experiment conducted with 102 participating university students enrolled in courses in which math plays a crucial role. After the manipulation of self-control capacity, stereotype threat was induced for the female students, but not the male students. Then, the students were asked to report their thoughts during a math performance situation three times. Multiple-group autoregressive path models revealed that when self-control capacity was relatively low, female compared with male students reported more intense worry in the initial two thought protocols. In contrast, in the relatively high self-control capacity condition, female and male students did not differ significantly in their reported worry at any time. These results expand on previous findings, suggesting that threat effects depend on definable situational self-control conditions. (shrink)

LS Penrose was the first to propose a measure of voting power (which later came to be known as ‘the [absolute] Banzhaf index’). His limit theorem – which is implicit in Penrose (1952) and for which he gave no rigorous proof – says that, in simple weighted voting games, if the number of voters increases indefinitely while the quota is pegged at half the total weight, then – under certain conditions – the ratio between the voting powers (as measured by (...) him) of any two voters converges to the ratio between their weights. We conjecture that the theorem holds, under rather general conditions, for large classes of variously defined weighted voting games, other values of the quota, and other measures of voting power. We provide proofs for some special cases. (shrink)

Previous research has found that funding disparities are driven by applications’ final impact scores and that only a portion of the black/white funding gap can be explained by bibliometrics and topic choice. Using National Institutes of Health R01 applications for council years 2014–2016, we examine assigned reviewers’ preliminary overall impact and criterion scores to evaluate whether racial disparities in impact scores can be explained by application and applicant characteristics. We hypothesize that differences in commensuration—the process of combining criterion scores into (...) overall impact scores—disadvantage black applicants. Using multilevel models and matching on key variables including career stage, gender, and area of science, we find little evidence for racial disparities emerging in the process of combining preliminary criterion scores into preliminary overall impact scores. Instead, preliminary criterion scores fully account for racial disparities—yet do not explain all of the variability—in preliminary overall impact scores. (shrink)

The ‘default mode’ network refers to cortical areas that are active in the absence of goal-directed activity. In previous studies, decreased activity in the ‘default mode’ has always been associated with increased activation in task-relevant areas. We show that the induction of hypnosis can reduce anterior default mode activity during rest without increasing activity in other cortical regions. We assessed brain activation patterns of high and low suggestible people while resting in the fMRI scanner and while engaged in visual tasks, (...) in and out of hypnosis. High suggestible participants in hypnosis showed decreased brain activity in the anterior parts of the default mode circuit. In low suggestible people, hypnotic induction produced no detectable changes in these regions, but instead deactivated areas involved in alertness. The findings indicate that hypnotic induction creates a distinctive and unique pattern of brain activation in highly suggestible subjects. (shrink)

The prior issue of Krisis (42:1) published Critical Naturalism: A Manifesto, with the aim to instigate a debate of the issues raised in this manifesto – the necessary re-thinking of the role (and the concept) of nature in critical theory in relation to questions of ecology, health, and inequality. Since Krisis considers itself a place for philosophical debates that take contemporary struggles as starting point, it issued an open call and solicited responses to the manifesto. This is one of the (...) sixteen selected responses, which augment, specify, or question the assumptions and arguments of the manifesto. (shrink)

Marx’s Eurocentrism : Postcolonial Studies and Marx Scholarship. This article takes as its starting-point the fourfold concept of Eurocentrism developed in postcolonial studies and global history. Against this backdrop, it traces the treatment of non-Western societies throughout Marx’s work. His 1853 articles on India are shown to be Eurocentric in every respect. They are partly based on a travel narrative written by François Bernier. Bernier’s text is analyzed in some detail as one of Marx’s sources. Marx’s treatment of the 1857-59 (...) Indian rebellions also displays Eurocentric traits. However his writings on British colonialism in Ireland begin to break with the Eurocentric mould. The Marxian critique of political economy is, in contrast, saturated with Orientalist motifs. The late work is however quite different in this respect. Both in the excerpts from his readings from 1879 on and in his discussions with the Russian Social Revolutionaries, it is evident that Marx breaks with Eurocentrism. The development of Marx’s thought thus shows that the somewhat hasty dismissal which he is frequently subjected to in postcolonial studies is, in many cases, inadequately thought out. The fact remains however that Marxists striving to apprehend global capitalism, historical progress and contingent development have something to learn from postcolonial studies. (shrink)

The text sets out from a fourfold concept of Eurocentrism developed in postcolonial studies and global history. Against this backdrop, it traces the treatment of non-Western societies throughout Marx's work. His 1853 articles on India are shown to be Eurocentric in every respect. They are partially based on a travel narrative by François Bernier. Bernier's text is analyzed in some detail as one of Marx's sources. Marx's treatment of the 1857-59 Indian rebellions also displays Eurocentric features. His writings on British (...) colonialism, in Ireland, however, begin to break with the Eurocentric mold. The Marxian critique of political economy, in contrast, teems with Orientalist motifs. Marx's late work is quite different in this respect: in the excerpts from his reading that he made from 1879 on, as well as in his discussions with the Russian Social Revolutionaries, he breaks with Eurocentrism. The development of Marx's thought shows that the hasty dismissal of him often observed in postcolonial studies is not carefully thought out. Yet the fact remains that Marxists who attempt to think global capitalism, historical progress and contingent development have something to learn from postcolonial studies. (shrink)

In general, analyses of voting power are performed through the notion of a simple voting game (SVG) in which every voter can choose between two options: ‘yes’ or ‘no’. Felsenthal and Machover [Felsenthal, D.S. and Machover, M. (1997), International Journal of Game Theory 26, 335–351.] introduced the concept of ternary voting games (TVGs) which recognizes abstention alongside. They derive appropriate generalizations of the Shapley–Shubik and Banzhaf indices in TVGs. Braham and Steffen [Braham, M. and Steffen, F. (2002), in Holler, et (...) al. (eds.), Power and Fairness, Jahrbuch für Neue Politische Ökonomie 20, Mohr Siebeck, pp. 333–348.] argued that the decision-making structure of a TVG may not be justified. They propose a sequential structure in which voters first decide between participation and abstention and then between ‘yes’ or ‘no’. The purpose of this paper is two-fold. First, we compare the two approaches and show how the probabilistic interpretation of power provides a unifying characterization of analogues of the Banzhaf (Bz) measure. Second, using the probabilistic approach we shall prove a special case of Penrose’s Limit Theorem (PLT). This theorem deals with an asymptotic property in weighted voting games with an increasing number of voters. It says that under certain conditions the ratio between the voting power of any two voters (according to various measures of voting power) approaches the ratio between their weights. We show that PLT holds in TVGs for analogues of Bz measures, irrespective of the particular nature of abstention. (shrink)

Numerical magnitude information is assumed to be spatially represented in the form of a mental number line defined with respect to a body-centred, egocentric frame of reference. In this context, spatial language skills such as mastery of verbal descriptions of spatial position have been proposed to be relevant for grasping spatial relations between numerical magnitudes on the mental number line. We examined 4- to 5-year-old’s spatial language skills in tasks that allow responses in egocentric and allocentric frames of reference, as (...) well as their relative understanding of numerical magnitude. In addition, we evaluated influences of children’s absolute understanding of numerical magnitude assessed by their number word comprehension and of their knowledge on numerical sequences. Results indicated that when considering responses that corresponded to the egocentric perspective, children’s spatial language was associated significantly with their relative numerical magnitude understanding, even after controlling for covariates, such as children’s SES, mental rotation skills, and also absolute magnitude understanding or knowledge on numerical sequences. This suggests that the use of egocentric reference frames in spatial language may facilitate spatial representation of numbers along a mental number line and thus seem important for preschoolers’ relative understanding of numerical magnitude. (shrink)