Despite their importance in public discourse, numbers in the range of 1 million to 1 trillion are notoriously difficult to understand. We examine magnitude estimation by adult Americans when placing large numbers on a number line and when qualitatively evaluating descriptions of imaginary geopolitical scenarios. Prior theoretical conceptions predict a log-to-linear shift: People will either place numbers linearly or will place numbers according to a compressive logarithmic or power-shaped function (Barth & Paladino, ; Siegler & Opfer, ). While about half (...) of people did estimate numbers linearly over this range, nearly all the remaining participants placed 1 million approximately halfway between 1 thousand and 1 billion, but placed numbers linearly across each half, as though they believed that the number words “thousand, million, billion, trillion” constitute a uniformly spaced count list. Participants in this group also tended to be optimistic in evaluations of largely ineffective political strategies, relative to linear number-line placers. The results indicate that the surface structure of number words can heavily influence processes for dealing with numbers in this range, and it can amplify the possibility that analogous surface regularities are partially responsible for parallel phenomena in children. In addition, these results have direct implications for lawmakers and scientists hoping to communicate effectively with the public. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:St. John Henry Newman's Theory of Doctrinal Development and the Synodal Process:A Survey and Concrete ApplicationWilliam B. GoldinGood afternoon, Your Excellencies, Most Reverend bishops, and my brother priests. Firstly, please permit me to say that, while it is certainly an honor to have been invited to speak to you, for which I would like to express my gratitude to my own bishop and our host for this reunion, His (...) Excellency, Bishop Kevin W. Vann, it is also not a little bit daunting. To speak to such an erudite group of clerics, all of whom have a connection to our common alma mater and to the various celebrated universities in the Eternal City, brings back fond memories of my three years at the Casa Santa Maria. During that time, while I would occasionally have the opportunity to preach at Sunday Masses at the Casa, I was always keenly aware that I was not nearly as qualified to do so as many of my listeners. As such, I beg your pardon if I should fail to explain adequately any aspect of this lecture, and I would be grateful for any questions and/or corrections, theological or otherwise, that you may have afterwards.Let us begin with a prayer:In the Name of the Father, and of the Son, and of the Holy Spirit. Amen. [End Page 21]Come, Holy Spirit, fill the hearts of thy faithful, and enkindle in them the fire of thy love. Send forth thy Spirit and they shall be created, and thou shalt renew the face of the earth.Let us pray.O God, who didst inspire thy faithful by the light of thy Holy Spirit, grant that, in the same Spirit we may be truly wise and ever more rejoice in His holy consolation.Through Christ our Lord.Amen.Vergine Immacolata... Aiutateci.Introduction: The Synod on Synodality and Speculation on Doctrinal ChangeIn the late autumn of 2021, Bishop Vann appointed me and my colleague, Mrs. Katie Dawson, our diocesan director of parish faith formation, as the coordinators for the Synod on Synodality in the Diocese of Orange. In this role, we were tasked with bringing to fruition the diocesan phase of the synodal consultation of the faithful here in Orange County. Since last autumn, we have labored to carry out the bishop's synodal plan for this diocese, and I must say that I have been pleasantly surprised with the manner in which the consultation took place, and in its results, notwithstanding my initial reservations both as to the scope of this particular synod and as to the potential risks inherent in such a universal survey. As we all know from diocesan and parochial life, "listening sessions" have a tendency to become "shouting sessions"; and as a thoroughgoing introvert myself, such sessions do not exactly bring joy to my heart. Thankfully, though, my fears were not realized, and the actual experience of our synodal process was almost altogether pleasant.Perhaps surprisingly, one of the fruits of our consultation, which we heard from the majority of the faithful, is their clear desire for doctrinal clarity in their faith journeys. The majority of the People of God in Orange County whom we surveyed do not want to see any doctrinal changes emerge from this synod that could be critiqued for being in serious discontinuity with the [End Page 22] solemnly defined magisterial teaching of the past. Regularly, they expressed to us that, if our "journeying together" is to be authentic and credible, then the continuity of our doctrinal teaching is a matter of no small importance. Indeed, the ability of many to take the Church's faith seriously depends on whether the doctrinal content of that faith seems solid and unshakeable. If the content of our faith can shift substantially in ways that mirror modern shifts in secular thinking, then people can easily critique our faith as being blown about by the winds of change, with no certitude whatsoever. If something taught by the Catholic Church can be true today and false tomorrow, then why is the Catholic Church's message worth listening to at all? What we heard from the overwhelming majority of... (shrink)

This book presents the foundations of classical Chinese aesthetic discourse--roughly from the Bronze Age to the early Middle Ages--with the following animating questions: What is art? Why do we produce it? How do we judge it? The arts that garnered the most theoretical attention during this time period were music, poetry, calligraphy, and painting, and the book considers the reasons why these four were privileged. Whereas modern artists most likely consider themselves musicians or poets or calligraphers or painters or sculptors (...) or architects, the pre-modern authors who produced the literature that established Chinese aesthetics prided themselves on being wenren, "cultured people," conversant with all forms of art and learning. Other comparisons with Western theories and works of art are presented at due junctures. Key Features Addresses Chinese aesthetic discourse on its own terms Provides comparisons of key concepts and theories with examples from Western sources Includes more coverage of primary sources than any other English-language book on the subject Each chapter opens with a helpful summary, highlighting the chapter's key themes. (shrink)

'The Fathers According to Rabbi Nathan' gives insight into the folklore of Palestine, the character of Rabbinic thought in New Testament times, and the views of the Pharisees and their successors on man's relationships with himself, his fellow man, the universe, and God.

Analogy researchers do not often examine gesture, and gesture researchers do not often borrow ideas from the study of analogy. One borrowable idea from the world of analogy is the importance of distinguishing between attributes and relations. Gentner observed that some metaphors highlight attributes and others highlight relations, and called the latter analogies. Mirroring this logic, we observe that some metaphoric gestures represent attributes and others represent relations, and propose to call the latter analogical gestures. We provide examples of such (...) analogical gestures and show how they relate to the categories of iconic and metaphoric gestures described previously. Analogical gestures represent different types of relations and different degrees of relational complexity, and sometimes cohere into larger analogical models. Treating analogical gestures as a distinct phenomenon prompts new questions and predictions, and illustrates one way that the study of gesture and the study of analogy can be mutually informative. (shrink)

Previous work has found that guiding problem-solvers' movements can have an immediate effect on their ability to solve a problem. Here we explore these processes in a learning paradigm. We ask whether guiding a learner's movements can have a delayed effect on learning, setting the stage for change that comes about only after instruction. Children were taught movements that were either relevant or irrelevant to solving mathematical equivalence problems and were told to produce the movements on a series of problems (...) before they received instruction in mathematical equivalence. Children in the relevant movement condition improved after instruction significantly more than children in the irrelevant movement condition, despite the fact that the children showed no improvement in their understanding of mathematical equivalence on a ratings task or on a paper-and-pencil test taken immediately after the movements but before instruction. Movements of the body can thus be used to sow the seeds of conceptual change. But those seeds do not necessarily come to fruition until after the learner has received explicit instruction in the concept, suggesting a “sleeper effect” of gesture on learning. (shrink)

How does sign language compare with gesture, on the one hand, and spoken language on the other? Sign was once viewed as nothing more than a system of pictorial gestures without linguistic structure. More recently, researchers have argued that sign is no different from spoken language, with all of the same linguistic structures. The pendulum is currently swinging back toward the view that sign is gestural, or at least has gestural components. The goal of this review is to elucidate the (...) relationships among sign language, gesture, and spoken language. We do so by taking a close look not only at how sign has been studied over the past 50 years, but also at how the spontaneous gestures that accompany speech have been studied. We conclude that signers gesture just as speakers do. Both produce imagistic gestures along with more categorical signs or words. Because at present it is difficult to tell where sign stops and gesture begins, we suggest that sign should not be compared with speech alone but should be compared with speech-plus-gesture. Although it might be easier (and, in some cases, preferable) to blur the distinction between sign and gesture, we argue that distinguishing between sign (or speech) and gesture is essential to predict certain types of learning and allows us to understand the conditions under which gesture takes on properties of sign, and speech takes on properties of gesture. We end by calling for new technology that may help us better calibrate the borders between sign and gesture. (shrink)

Developmental psychologists have long recognized the extraordinary influence of action on learning (Held & Hein, 1963; Piaget, 1952). Action experiences begin to shape our perception of the world during infancy (e.g., as infants gain an understanding of others’ goal-directed actions; Woodward, 2009) and these effects persist into adulthood (e.g., as adults learn about complex concepts in the physical sciences; Kontra, Lyons, Fischer, & Beilock, 2012). Theories of embodied cognition provide a structure within which we can investigate the mechanisms underlying action’s (...) impact on thinking and reasoning. We argue that theories of embodiment can shed light on the role of action experience in early learning contexts, and further that these theories hold promise for using action to scaffold learning in more formal educational settings later in development. (shrink)

Teaching allows human culture to exist and to develop. Despite its significance, it has not been studied in depth by the cognitive neurosciences. Here we propose two hypotheses to boost the claim that teaching is a human instinct, and to expand our understanding of how teaching occurs as a dynamic bi-directional relation within the teacher-learner dyad. First, we explore how children naturally use ostensive communication when teaching; allowing them to be set in the emitter side of natural pedagogy. Then, we (...) hypothesize that the capacity to teach may precede to even have a mature metacognition and, we argue that a teacher will benefit from the interaction with her student, improving her understanding on both contents of knowledge: her own and her student’s. Thus, we propose that teaching may be the driving force of metacognitive development and may be occurring as an instinct from very early ages. (shrink)

We examined the effects of three different training conditions, all of which involve the motor system, on kindergarteners’ mental transformation skill. We focused on three main questions. First, we asked whether training that involves making a motor movement that is relevant to the mental transformation—either concretely through action or more abstractly through gestural movements that represent the action —resulted in greater gains than training using motor movements irrelevant to the mental transformation. We tested children prior to training, immediately after training, (...) and 1 week after training, and we found greater improvement in mental transformation skill in both the action and move-gesture training conditions than in the point-gesture condition, at both posttest and retest. Second, we asked whether the total gain made by retest differed depending on the abstractness of the movement-relevant training, and we found that it did not. Finally, we asked whether the time course of improvement differed for the two movement-relevant conditions, and we found that it did—gains in the action condition were realized immediately at posttest, with no further gains at retest; gains in the move-gesture condition were realized throughout, with comparable gains from pretest-to-posttest and from posttest-to-retest. Training that involves movement, whether concrete or abstract, can thus benefit children's mental transformation skill. However, the benefits unfold differently over time—the benefits of concrete training unfold immediately after training ; the benefits of more abstract training unfold in equal steps immediately after training and during the intervening week with no additional training. These findings have implications for the kinds of instruction that can best support spatial learning. (shrink)

When asked to explain their solutions to a problem, both adults and children gesture as they talk. These gestures at times convey information that is not conveyed in speech and thus reveal thoughts that are distinct from those revealed in speech. In this study, we use the classic Tower of Hanoi puzzle to validate the claim that gesture and speech taken together can reflect the activation of two cognitive strategies within a single response. The Tower of Hanoi is a well‐studied (...) puzzle, known to be most efficiently solved by activating subroutines at theoretically defined choice points. When asked to explain how they solved the Tower of Hanoi puzzle, both adults and children produced significantly more gesture‐speech mismatches—explanations in which speech conveyed one path and gesture another—at these theoretically defined choice points than they produced at non‐choice points. Even when the participants did not solve the problem efficiently, gesture could be used to indicate where the participants were deciding between alternative paths. Gesture can, thus, serve as a useful adjunct to speech when attempting to discover cognitive processes in problem‐solving. (shrink)

Goldin thus begins the book by asking the basic question "What are we reading?" while also considering why it has been so rarely asked. Yet far from denigrating Chinese philosophy, he argues that liberating these texts from the mythic idea that they are the product of a single great mind only improves our understanding and appreciation. By no means does a text require single and undisputed authorship to be meaningful; nor is historicism the only legitimate interpretive stance. The first (...) chapter takes up a hallmark of Chinese philosophy that demands a Western reader's cognizance: its preference for non-deductive argumentation. Chinese philosophy is an art he demonstrates, more than it is a rigorous logical method. Then comes the core of the book, eight chapters devoted to the eight philosophical texts divided into three parts: Philosophy of Heaven, Philosophy of the Way, and Two Titans at the End of an Age.. (shrink)

In Explaining an Eclipse, Owen Goldin provides a book-length treatment of the first ten chapters of book 2 of the Posterior Analytics. Goldin’s aim is to answer one question: how can an Aristotelian demonstration show anything of scientific interest if all the premises are definitions? To this question Goldin gives his undivided attention.

The first study of this ancient text in over 70 years, Rituals of the Way explores how the Xunzi influenced Confucianism and other Chinese philosophies through its emphasis on "the Way.".

After Confucius is a collection of eight studies of Chinese philosophy from the time of Confucius to the formation of the empire in the second and third centuries B.C.E. As detailed in a masterful introduction, each essay serves as a concrete example of thick description - an approach invented by philosopher Gilbert Ryle - which aims to reveal the logic that informs an observable exchange among members of a community or society. To grasp the significance of such exchanges, it is (...) necessary to investigate the networks of meaning on which they rely. Paul R. Goldin argues that the character of ancient Chinese philosophy can be appreciated only if we recognize the cultural codes underlying the circulation of ideas in that world. Thick description is the best preliminary method to determine how Chinese thinkers conceived of their own enterprise. Who were the ancient Chinese philosophers? What was their intended audience? What were they arguing about? How did they respond to earlier thinkers, and to each other? Why did those in power wish to hear from them, and what did they claim to offer in return for patronage? Goldin addresses these questions as he looks at several topics, including. (shrink)

Aristotle’s account of epistēmē is foundationalist. In contrast, the web of dialectical argumentation that constitutes justification for scientific principles is coherentist. Aristotle’s account of explanation is structurally parallel to the argument for a foundationalist account of justification. He accepts the first argument but his coherentist accounts of justification indicate that he would not accept the second. Where is the disanalogy? For Aristotle, the intelligibility of a demonstrative premise is the cause of the intelligibility of a demonstrated conclusion and causation is (...) asymmetric. Within the Posterior Analytics itself, Aristotle does not account for this, but elsewhere he develops the resources for doing so: the cause is what acts on a substrate to actualize a potential in that substrate, resulting in the effect. On the other hand, it may well happen that two propositions entail each other, in which case one may as well justify the one on the basis of the other as vice versa. (shrink)

"Confucianism" presents the history and salient tenets of Confucian thought, and discusses its viability, from both a social and a philosophical point of view, in the modern world. Despite most of the major Confucian texts having been translated into English, there remains a surprising lack of straightforward textbooks on Confucian philosophy in any Western language. Those that do exist are often oriented from the point of view of Western philosophy - or, worse, a peculiar school of thought within Western philosophy (...) - and advance correspondingly skewed interpretations of Confucianism. This book seeks to rectify this situation. It guides readers through the philosophies of the three major classical Confucians: Confucius, Mencius and Xunzi, and concludes with an overview of later Confucian revivals and the standing of Confucianism today. (shrink)

_Ideology of Power and Power of Ideology in Early China_ explores Chinese political thought during the centuries surrounding the formation of the empire in 221 BCE, examining devices of legitimation, views of rulers and ministers, economic thought, and administrative practices.

Chapter 49 of the Han Feizi, entitled 'Wudu', includes one of the earliest discussions in Chinese history of the concepts of gong and si: Han Fei takes si to mean 'acting in one's own interest'. Gong is simply what opposes si. 'Acting in one's own interest' is not inherently reprehensible in Han Fei's view; but a ruler must remember why ministers propose their policies: they are concerned only with enriching themselves, and look upon the ruler as nothing more than a (...) resource to be exploited in their quest for material aggrandizement. The interests of the ministers and the ruler are diametrically opposed. Ministers hope for a comfortable career; a ruler must weed out the posers in his search for those rare and invaluable adjuvants who are genuinely capable of administering the state. In short, if si is the self-interest of the minister, gong is the self-interest of the ruler. (shrink)

"Confucianism" presents the history and salient tenets of Confucian thought, and discusses its viability, from both a social and a philosophical point of view, in the modern world. Despite most of the major Confucian texts having been translated into English, there remains a surprising lack of straightforward textbooks on Confucian philosophy in any Western language. Those that do exist are often oriented from the point of view of Western philosophy - or, worse, a peculiar school of thought within Western philosophy (...) - and advance correspondingly skewed interpretations of Confucianism. This book seeks to rectify this situation. It guides readers through the philosophies of the three major classical Confucians: Confucius , Mencius and Xunzi , and concludes with an overview of later Confucian revivals and the standing of Confucianism today. (shrink)

All languages, both spoken and signed, make a formal distinction between two types of terms in a proposition – terms that identify what is to be talked about (nominals) and terms that say something about this topic (predicates). Here we explore conditions that could lead to this property by charting its development in a newly emerging language – Nicaraguan Sign Language (NSL). We examine how handshape is used in nominals vs. predicates in three Nicaraguan groups: (1) homesigners who are not (...) part of the Deaf com- munity and use their own gestures, called homesigns, to communicate; (2) NSL cohort 1 signers who fashioned the first stage of NSL; (3) NSL cohort 2 signers who learned NSL from cohort 1. We compare these three groups to a fourth: (4) native signers of American Sign Language (ASL), an established sign language. We focus on handshape in predicates that are part of a productive classifier system in ASL; handshape in these predicates varies sys- tematically across agent vs. no-agent contexts, unlike handshape in the nominals we study, which does not vary across these contexts. We found that all four groups, including home- signers, used handshape differently in nominals vs. predicates – they displayed variability in handshape form across agent vs. no-agent contexts in predicates, but not in nominals. Variability thus differed in predicates and nominals: (1) In predicates, the variability across grammatical contexts (agent vs. no-agent) was systematic in all four groups, suggesting that handshape functioned as a productive morphological marker on predicate signs, even in homesign. This grammatical use of handshape can thus appear in the earliest stages of an emerging language. (2) In nominals, there was no variability across grammatical con- texts (agent vs. no-agent), but there was variability within- and across-individuals in the handshape used in the nominal for a particular object. This variability was striking in homesigners (an individual homesigner did not necessarily use the same handshape in every nominal he produced for a particular object), but decreased in the first cohort of NSL and remained relatively constant in the second cohort. Stability in the lexical use of handshape in nominals thus does not seem to emerge unless there is pressure from a peer linguistic community. Taken together, our findings argue that a community of users is essential to arrive at a stable nominal lexicon, but not to establish a productive morpholog- ical marker in predicates. Examining the steps a manual communication system takes as it moves toward becoming a fully-fledged language offers a unique window onto factors that have made human language what it is. (shrink)

The classical view of computing positions computation as a closed-box transformation of inputs (rational numbers or finite strings) to outputs. According to the interactive view of computing, computation is an ongoing interactive process rather than a function-based transformation of an input to an output. Specifically, communication with the outside world happens during the computation, not before or after it. This approach radically changes our understanding of what is computation and how it is modeled. The acceptance of interaction as a new (...) paradigm is hindered by the Strong Church–Turing Thesis (SCT), the widespread belief that Turing Machines (TMs) capture all computation, so models of computation more expressive than TMs are impossible. In this paper, we show that SCT reinterprets the original Church–Turing Thesis (CTT) in a way that Turing never intended; its commonly assumed equivalence to the original is a myth. We identify and analyze the historical reasons for the widespread belief in SCT. Only by accepting that it is false can we begin to adopt interaction as an alternative paradigm of computation. We present Persistent Turing Machines (PTMs), that extend TMs to capture sequential interaction. PTMs allow us to formulate the Sequential Interaction Thesis, going beyond the expressiveness of TMs and of the CTT. The paradigm shift to interaction provides an alternative understanding of the nature of computing that better reflects the services provided by today’s computing technology. (shrink)

This chapter reviews the aspects of Mencius that did and did not interest Han-dynasty writers. With the help of digital concordances, it is easy to discover that many of the passages considered crucial today were rarely, if ever, cited in the Han. These include the parable of the infant about to fall into a well (2A.6), the debate with a Mohist named Yi Zhi 夷之 (3A.5), and the concept of liangzhi 良知 (7A.15), which, since Wang Yangming 王陽明 (1472–1528), has been (...) considered a cornerstone of Mencian ethics. The chapter discusses other key passages that are never mentioned in Han sources. Absence of evidence is not evidence of absence, and thus one cannot simply infer that these passages were unknown in the Han dynasty, but it remains significant that they were not regarded as essential to understanding Mencius’s philosophy. The conclusion will explore the differences between Mencius’s reception in the Han dynasty and his Neo-Confucianized reception today. (shrink)

Heng Xian is a previously unknown text reconstructed by Chinese scholars out of a group of more than 1,200 inscribed bamboo strips purchased by the Shanghai Museum on the Hong Kong antiquities market in 1994. The strips have all been assigned an approximate date of 300 B.C.E., and Heng Xian allegedly consists of thirteen of them, but each proposed arrangement of the strips is marred by unlikely textual transitions. The most plausible hypothesis is one that Chinese scholars do not appear (...) to take seriously: that we are missing one or more strips. The paper concludes with a discussion of the hazards of studying unprovenanced artifacts that have appeared during China’s recent looting spree. I believe the time has come for scholars to ask themselves whether their work indirectly abets this destruction of knowledge. (shrink)

Seventy-three children between 6 and 7 years of age were presented with a problem having ambiguous subgoal ordering. Performance in this task showed reliable fingerprints: a non-monotonic dependence of performance as a function of the distance between the beginning and the end-states of the problem, very high levels of performance when the first move was correct, and states in which accuracy of the first move was significantly below chance. These features are consistent with a non-Markov planning agent, with an inherently (...) inertial decision process, and that uses heuristics and partial problem knowledge to plan its actions. We applied a statistical framework to fit and test the quality of a proposed planning model. Our framework allows us to parse out independent contributions to problem-solving based on the construction of the value function and on general mechanisms of the search process in the tree of solutions. We show that the latter are correlated with children's performance on an independent measure of planning, while the former is highly domain specific. (shrink)