We articulate a holistic understanding of hope, going beyond the common conceptualization of hope in terms of positive affect and cognition by considering what hope means for the underprivileged. In the recognition that hope is always situated in a particular place, we explore the perspective of the privileged and the underprivileged, clarifying how spatial contexts shape their goals for the future and their agency toward attaining these goals. Where some people experience precarity due to their disability, race, gender, sexuality, and (...) social class, others enjoy enhanced agency due to their privilege. In our analysis, this loss of agency does not mean the underprivileged are hopeless; instead, it suggests that hope can incorporate negative affect and cognition. In our view, a spatial understanding acknowledges the power of hope in discouraging situations, and it points to practical measures through which hope can be cultivated by marginalized communities. (shrink)

George S. Counts was a_ _major figure in American education for almost fifty years. Republication of this early work draws special attention to Counts’s role as a social and political activist. Three particular themes make the book noteworthy because of their importance in Counts’s plan for change as well as for their continuing contem­porary importance: _ _Counts’s crit­icism of child-centered progressives; _ _the role Counts assigns to teachers in achieving educational and social re­form; and Counts’s idea for the re­form of (...) the American economy. (shrink)

The article is an attempt to make sense of the different interdisciplinary perspectives associated with people’s attachment to places with a view to construct a holistic template for understanding people-place relationships and experiences. The author took note of the theoretical contributions of Jorgensen & Stedman, Scannell & Gifford, and Seamon to construct an integrative framework for understanding emotional links to places and people’s perception and experience of places. This was done with the intention of illuminating the meaning of place and (...) the different “places” people get attached to. The paper concludes by incorporating different place frameworks with the intention of establishing a holistic model for understanding the various attributes and perceptions of people-place relationships and experiences. (shrink)

The expression of attachment to the divine in certain places among different groups has been documented by anthropologists and sociologists for decades. However, the psychological processes by which this happens are not yet fully understood. This article focuses on the concept of ‘place spirituality’ as a psychological mechanism, which allows the religious believer or non-believer to achieve an organised attachment strategy, involving the interplay of place and spiritual attachment. First, place spirituality is considered as an experience that satisfies the attachment (...) relationship criteria in that geographic places and divine entities can be perceived as ‘objects’ of attachment. Second, it is proposed that the maturational aspects of the attachment repertoire in adults make the place spirituality experience possible since adults’ cognitive abilities are much wider than those of children and can include relationships to geographical spaces and invisible divine entities. Finally, the theme of place spirituality is explored to further position the concept as a relational paradigm for understanding the relationship between place experiences and spiritual attachment. (shrink)

This rejoinder acknowledges the empirical gaps and theoretical/theological disharmony highlighted in the three selected commentaries on Place Spirituality, but we defend our central argument about the developmental pathways of PS. First, we provide an overview of recent studies on PS, highlighting what has been done so far in the field. Second, we draw from the commentaries to advance the understanding of PS in relation to three world religions: Islam, Christianity and Hinduism. Third, we evaluate the normative aspects of PS as (...) a transactional versus transitional phenomenon. Finally, we defend the two contested developmental pathways to PS, involving the compensation and correspondence working models of attachment, while complementing these models using the motivational systems framework. We maintain that these models are relevant for understanding the relationship between religious attachment and place attachment among religious and non-religious people. Recommendations for further studies are made in relation to the broader implications of PS. (shrink)

BackgroundChildhood adversity is linked to adverse health in adulthood. One posited mechanistic pathway is through physiological responses to acute stress. Childhood adversity has been previously related to both exaggerated and blunted physiological responses to acute stress, however, less is known about the psychological mechanisms which may contribute to patterns of physiological reactivity linked to childhood adversity.ObjectiveIn the current work, we investigated the role of challenge and threat stress appraisals in explaining relationships between childhood adversity and cortisol reactivity in response to (...) an acute stressor.MethodsUndergraduate students completed an online survey that included general demographic information and the Risky Families Questionnaire 24 h before a scheduled lab visit. In the lab, a research assistant collected a baseline salivary cortisol sample. Following the baseline period, participants were read instructions for the Trier Social Stress Test, a validated psychological lab stressor. Next, they completed a challenge vs. threat task appraisal questionnaire and completed the speech and math portion of the TSST. Twenty minutes following the start of the TSST, a second salivary sample was collected to measure changes in salivary cortisol following the TSST.ResultsLinear regression analyses adjusted for age, sex, childhood socioeconomic status, and baseline cortisol levels, showed childhood adversity associated with changes in cortisol levels [B = –0.29 t = –2.35, p = 0.02, R2=0.07]. Linear regression analyses controlling for age, sex, and childhood SES showed childhood adversity associated with both challenge [B = –0.52 t = –5.04, p < 0.001, R2=0.24] and threat [B = 0.55 t = 5.40, p < 0.001, R2=0.27] appraisals. Significant indirect effects of childhood trauma on cortisol reactivity were observed through challenge appraisals [B = –0.01 ], and threat appraisals [B = –0.01 ].ConclusionChildhood adversity may contribute to blunted cortisol reactivity, a pattern of response which is linked to obesity, addiction, and other behavior-related diseases. Our findings suggest that this relationship is in part a product of stress appraisals. (shrink)

The problem for many troubled youths seeking help within a Christian context is that their need for meaningful connections and spiritual growth is attached to relationships with their significant others. When needs of attachment are not adequately met due to the effect of an insecure attachment working model in a relationship with God, the teen may end up leaving the faith community seeking a new caregiver or regress into spiritual struggles, depression, anxiety, self-doubt and other negative emotions. This paper responds (...) to the issues associated with youth attachment behaviour towards God using a caregiving theology that draws on the 'power of two' through incarnational creativity and pneumatological ecclesiology. This proposed theology first supplements the work of the pastoral counsellor to create a transformative container through which young people, already within a redemptive Christian community, can grow spiritually and deepen their relationship with God. Secondly, pastoral juxtaposition targeting the spiritual needs of hurting youths serves to create a magnet space within the church community that models incarnational love, pastoral care and support for young people by entering their world order to reframe their personal stories of grief, abandonment and insecurity through creative means. Finally, we theologise that pastoral juxtaposition also integrates the power of the Holy Spirit, as the ultimate caregiver in times of conflict, into each youth's unique journey of faith and healing. Implications of this pastoral theology are discussed and applied to everyday life. (shrink)

The purpose of this article is to analyze how the concept of African Christian diaspora religion and/or spirituality, as a missionary-based model, is currently being used and defined within African transnational research and diaspora religion. I conducted a review using a citation search strategy to retrieve peer-reviewed articles that explore the extent to which the seminal paper of Steven Vertovec on “Diaspora Religion” has informed the conceptualization and analysis of the concept of African Christian diaspora religion and/or spirituality. The search (...) generated empirical articles which met the inclusion criteria and were included for concept analysis. This concept analysis identified five emerging attributes of ACDRS as a network of support, a transnational dynamic, a platform for civic engagement and activism, the basis for developing place bonds and diaspora identity, and as an experiential religion. These defining attributes position ACDRS as a multidimensional concept encompassing noninstitutionalized religious expressions and activities, albeit with limited empirical data. I also discussed some study limitations and conceptual issues related to the attributes, antecedents, consequences, and cases of ACDRS. (shrink)

Although embalming is traditionally considered an Egyptian custom, ancient sources suggest that in imperial Rome the practice was not employed by Egyptians or Egyptianized Romans alone. The mos Romanorum in funerary ritual encompassed both cremation and inhumation, yet embalming appears in Rome as early as the first century AD and evidence points to its limited use during the first three centuries AD. Within the social structure of Rome's dead these preserved corpses certainly occupied a distinct place. Yet who were they (...) and why were they embalmed? It is argued here that various factors allowed for the occasional use of embalming by Romans: an apparent shift in attitudes towards Egypt, the manipulation of death ritual for social distinction, and the flexibility of the traditional Roman funeral, which was able to incorporate deviations in methods of body disposal. Although embalming has been largely ignored as a significant aspect of Roman funerary history, its patrons come from the classes of highest status, including even the imperial household. This fact alone makes it worthwhile to examine this small corpus of evidence. For example, the emperor Nero embalmed his wife Poppaea; such a deviation from standard disposal methods reflects imperial fashion, but also requires us to re-evaluate Nero's reign and, especially, the societal constructs of Neronian Rome. This study attempts to contextualize embalming within Roman society and offer some likely causes and effects of its use. (shrink)

The Standards' ecumenical implications are critically assessed in view of the risks which their cross-denominational or cross-faith cooperation implications on the one hand, and, on the other hand, their secular commitments to mutual learning, non-proselytizing, professionalism, and efficiency assessment might carry for chaplains' properly spiritual orientation. The problem posed by the ambiguity of language is raised as a warning that concepts like human dignity have a profoundly different meaning in secular and Christian contexts. Invoking such concepts can be seriously misleading.

BackgroundChildhood abuse increases risk for high levels of distress in response to future stressors. Interpersonal social support is protective for health, particularly during stress, and may be particularly beneficial for individuals who experienced childhood abuse.ObjectiveInvestigate whether childhood abuse predicts levels of posttraumatic stress disorder (PTSD) symptoms related to the COVID-19 pandemic, and test whether the perceived availability of social companionship preceding the pandemic moderates this relationship.MethodsDuring Phase 1, adults (N= 120; AgeM[SD] = 19.4 [0.94]) completed a retrospective measure of childhood (...) adversity along with a measure of perceived availability of opportunities for social engagement immediately preceding the pandemic. Two weeks after the COVID-19 pandemic declaration, participants completed the Impact of Event Scale-Revised (IES-R) with respect to the pandemic. Hierarchical linear regression analyses examined the interaction between childhood abuse and the perceived availability of social companionship preceding the pandemic as a predictor of PTSD symptoms.ResultsAdjusting for covariates, the interaction between childhood abuse and perceived availability of others to engage with before the onset of the pandemic was a significant predictor of IES-hyperarousal (β = −0.19,t= −2.06,p= 0.04, ΔR2= 0.032, CI: [−0.31 to −0.01]).ConclusionLevels of perceived opportunities for social companionship before the pandemic associates with levels of hyperarousal related to the pandemic, particularly for individuals who experienced high levels of childhood abuse. More research is needed to understand how to mitigate the higher levels of distress related to the pandemic for these individuals in order to reduce risk for future psychiatric disorders. (shrink)

This article discusses the relationship between stress, physical health, and well-being in cultural context, offers examples of laws, policies, and programs to promote mental health and well-being, and examines how collective impact supports mental health and well-being.

Arthur E. Lean’s irreverent and con­troversial essays represent the distillation of many ideas about education—ideas developed during most of a lifetime spent in and about schools. In the second edition of this popular work, to which he has added eight new essays, he presents his latest observations on current ele­ments and programs in education—such as the grading system, academic rank, the teaching process, assessment of edu­cational progress—concluding that many of them are not only unnecessary but actually harmful to the very (...) process which they are supposed to serve. Covering a broad spectrum of current issues in its criticism of American edu­cation at all levels, _And Merely Teach _is a book to be read by veteran educator, beginning teacher, and lay citizen alike. Though critical of the teaching profes­sion, Arthur Lean also offers constructive suggestions in the form of practical solu­tions that are urgently needed to save our ailing educational system. (shrink)

Unfounded—conspiracy and health—beliefs about COVID-19 have accompanied the pandemic worldwide. Here, we examined cross-nationally the structure and correlates of these beliefs with an 8-item scale, using a multigroup confirmatory factor analysis. We obtained a two-factor model of unfounded (conspiracy and health) beliefs with good internal structure (average CFI = 0.98, RMSEA = 0.05, SRMR = 0.04), but a high correlation between the two factors (average latent factor correlation = 0.57). This model was replicable across 50 countries (total N = 13,579), (...) as evidenced by metric invariance between countries (CFI = 0.96, RMSEA = 0.06, SRMS = 0.07) as well as scalar invariance across genders (CFI = 0.98, RMSEA = 0.04, SRMS = 0.03) and educational levels (CFI = 0.98, RMSEA = 0.04, SRMS = 0.03). Also, lower levels of education, more fear of COVID-19, and more cynicism were weakly associated with stronger conspiracy and health beliefs. The study contributes to knowledge about the structure of unfounded beliefs, and reveals the potential relevance of affective (i.e., fear of COVID-19) and cognitive (i.e., cynicism) factors along with demographics, in endorsing such beliefs. In summary, we obtained cross-cultural evidence for the distinctiveness of unfounded conspiracy and health beliefs about COVID-19 in terms of their structure and correlates. (shrink)

Unfounded—conspiracy and health—beliefs about COVID-19 have accompanied the pandemic worldwide. Here, we examined cross-nationally the structure and correlates of these beliefs with an 8-item scale, using a multigroup confirmatory factor analysis. We obtained a two-factor model of unfounded (conspiracy and health) beliefs with good internal structure (average CFI = 0.98, RMSEA = 0.05, SRMR = 0.04), but a high correlation between the two factors (average latent factor correlation = 0.57). This model was replicable across 50 countries (total N = 13,579), (...) as evidenced by metric invariance between countries (CFI = 0.96, RMSEA = 0.06, SRMS = 0.07) as well as scalar invariance across genders (CFI = 0.98, RMSEA = 0.04, SRMS = 0.03) and educational levels (CFI = 0.98, RMSEA = 0.04, SRMS = 0.03). Also, lower levels of education, more fear of COVID-19, and more cynicism were weakly associated with stronger conspiracy and health beliefs. The study contributes to knowledge about the structure of unfounded beliefs, and reveals the potential relevance of affective (i.e., fear of COVID-19) and cognitive (i.e., cynicism) factors along with demographics, in endorsing such beliefs. In summary, we obtained cross-cultural evidence for the distinctiveness of unfounded conspiracy and health beliefs about COVID-19 in terms of their structure and correlates. (shrink)

Frege, famously, held that there is a close connection between our concept of cardinal number and the notion of one-one correspondence, a connection enshrined in Hume's Principle. Husserl, and later Parsons, objected that there is no such close connection, that our most primitive conception of cardinality arises from our grasp of the practice of counting. Some empirical work on children's development of a concept of number has sometimes been thought to point in the same direction. I argue, however, that Frege (...) was close to right, that our concept of cardinal number is closely connected with a notion like that of one-one correspondence, a more primitive notion we might call just as many. (shrink)

This paper accounts for broad definitions of memory, which extend to paradigmatic memory phenomena, like episodic memory in humans, and phenomena in worms and sea snails. These definitions may seem too broad, suggesting that they extend to phenomena that don’t count as memory or illustrate that memory is not a natural kind. However, these responses fail to consider a definition as a hypothesis. As opposed to construing definitions as expressing memory’s properties, a definition as a hypothesis is the basis (...) to test inferences about phenomena. A definition as a hypothesis is valuable when the “kinding” of phenomena is ongoing. (shrink)

Anti-exceptionalism about logic is the Quinean view that logical theories have no special epistemological status, in particular, they are not self-evident or justified a priori. Instead, logical theories are continuous with scientific theories, and knowledge about logic is as hard-earned as knowledge of physics, economics, and chemistry. Once we reject apriorism about logic, however, we need an alternative account of how logical theories are justified and revised. A number of authors have recently argued that logical theories are justified by abductive (...) argument (e.g. Gillian Russell, Graham Priest, Timothy Williamson). This paper explores one crucial question about the abductive strategy: what counts as evidence for a logical theory? I develop three accounts of evidential confirmation that an anti-exceptionalist can accept: (1) intuitions about validity, (2) the Quine-Williamson account, and (3) indispensability arguments. I argue, against the received view, that none of the evidential sources support classical logic. (shrink)

Since the last ice age, when ice enveloped most of the northern continents, the earth has warmed by about five degrees. Within a century, it is likely to warm by another four or five. This revolution in our climate will have immense and mostly harmful effects on the lives of people not yet born. We are inflicting this harm on our descendants by dumping greenhouse gases into the atmosphere. We can mitigate the harm a little by taking measures to control (...) our emissions of these gases, and to adapt to the changes by, for instance, building sea walls around coastlines threatened by rising sea levels. But these measures will be very expensive, and the costs will be born by us, the present generation, whereas the benefits will come to future generations. How much should we sacrifice for the sake of the future? Economists and philosophers have independently worked on the question of our responsibility to future generations. This book brings their work together and applies it to global warming. It suggests a programme for future research on the economic and ethical issues. The book is intended for economists, and for philosophers and other social scientists who have a little knowledge of economic methods. (shrink)

After 50 years of debate, the ethics of aggregation has reached a curious stalemate, with both sides arguing that only their theory treats people as equals. I argue that, on the issue of equality, both sides are wrong. From the premise that “each counts for one,” we cannot derive the conclusion that “more count for more”—or its negation. The familiar arguments from equality to aggregation presuppose more than equality: the Kamm/Scanlon “Balancing Argument” rests on what social choice theorists call (...) “(Positive) Responsiveness,” Kamm’s “Aggregation Argument” assumes that “equal” lives are fungible, and Hsieh et al. have it that spreading goods broadly best approximates equality. In each case, the crucial premise is not equality itself but a further idea that Taurek, I argue, can safely reject. I conclude with a conjecture: there is no theory-neutral argument that settles the question of whether the numbers count. (shrink)

Very close analysis of Baruch Spinoza's wording in describing individuals rather than things. Individuals, but not collections such as a political state or club, each have their own specific conatus, or essence. Collectivities, like nations or institutions, fail to meet this necessary condition of individuation.

For most early Medieval and Scholastic philosophers working in the Aristotelian tradition, knowledge of any specific subject is knowledge of its causes and principles. Knowledge of individuals was no exception. As Jorge Gracia has written "To know individuality [for early Medieval and Scholastic philosophers] is to be able to determine the causes and principles that are responsible for it."1 The achievement of such ability is also known as the problem of individuation. This paper will be concerned with the solution to (...) the problem suggested by Leibniz’s writings and how it relates to the contemporary metaphysical debate. In the first section I introduce the problem of individuation along with the solution Leibniz proposed during the latter part of his life. The second section analyzes Leibniz’s solution in a contemporary perspective. I argue that, unlike during the Medieval and early Modern periods, today the epistemic side of the problem of individuation plays a major role in the debate. In this light, Leibniz’s proposal that humans cannot grasp what the individuality of an individual consists in seems problematic. I show, however, that Leibniz’s proposal can stand on its feet also nowadays, provided we are willing to give up the pretenses that there is a definitive count of individuals and that re-identifying individuals across time and space is part of the problem of individuation. (shrink)

In a recent article in this journal, Alan Thomas presents a novel defence of what I call ‘Rawlsian Institutionalism about Justice’ against G. A. Cohen’s well-known critique. In this response I aim to defend Cohen’s rejection of Institutionalism against Thomas’s arguments. In part this defence requires clarifying precisely what is at issue between Institutionalists and their opponents. My primary focus, however, is on Thomas’s critical discussion of Cohen’s endorsement of an ethical prerogative, as well as his appeal to the institutional (...) framework of a ‘property-owning democracy’ in his elaboration of the precise institutional requirements of Rawlsian Institutionalist justice, and his related claim that Cohen’s rejection of Institutionalism involves an objectionable ‘double counting’ of the demands of justice. I argue that once we are clear about both the kind of justification that can be given for a prerogative within a plausible ethical theory, and about the key points of departure between Institutionalist views and their rivals, Cohen’s rejection of Institutionalism appears well-motivated, and Thomas’s claim that his view is guilty of double counting the demands of justice can be seen to be mistaken. (shrink)

Rips et al. claim that the principles underlying the structure of natural numbers cannot be inferred from interactions with the physical world. However, in their target article they failed to consider an important source of interaction: finger counting. Here, we show that finger counting satisfies all the conditions required for allowing the concept of numbers to emerge from sensorimotor experience through a bottom-up process.

I endorse Composition as Identity, broadly and loosely understood as the thesis that a composite whole is nothing over and above its parts, and the parts nothing over and above the whole. Thus, given an object, x, composed of n proper parts, y1, ..., yn, I feel the tension between my Quinean heart and its Lewisian counterpart. I feel the tension between my obligation to countenance n+1 things, x and the y’s, each of which is a distinct portion of reality, (...) and my inclination to count just 1 thing, x, or just n things, the y’s, the former encompassing the same amount of reality as the latter. This paper is an attempt to reconstruct this tension and to explain it away without forgoing the intimate link between counting and countenancing. (shrink)

I here defend historical entitlement theories of property rights against a popular charge. This is the objection that such theories fail because no convincing account of original appropriation exists. I argue that this argument assumes a certain reading of historical entitlement theory and I spell out an alternative reading against which it misfires. On this reading, the role of acts of original appropriation is not to justify but to individuate people’s holdings. I argue that we can identify which acts (...) class='Hi'>count as original appropriation against the background of a general justification for a practice of property rights. On this view, what I will call ‘natural’ acts of original appropriation are acts by which a person begins to satisfy the general conditions for justified ownership. Finally, I offer an interpretation of John Locke's theory of appropriation along these lines and argue that it provides an attractive reading of his view. (shrink)

Number systems differ cross-culturally in characteristics like how high counting extends and which number is used as a productive base. Some of this variability can be linked to the way the hand is used in counting. The linkage shows that devices like the hand used as external representations of number have the potential to influence numerical structure and organization, as well as aspects of numerical language. These matters suggest that cross-cultural variability may be, at least in part, a matter of (...) whether devices are used in counting, which ones are used, and how they are used. (shrink)

Argle claimed that holes supervene on their material hosts, and that every truth about holes boils down to a truth about perforated things. This may well be right, assuming holes are perforations. But we still need an explicit theory of holes to do justice to the ordinary way of counting holes--or so says Cargle.

The central aim of this book is to answer two questions: Are alternatives for choice ever incomparable? and, In what ways can items be compared? The arguments offered suggest that alternatives for choice no matter how different are never incomparable, and that the ways in which items can be compared are richer and more varied than commonly supposed. This work is the first book length treatment of the topics of incomparability, value, and practical reason.

This article examines the relation between counting, counts and accountability. It does so by comparing the responses of the British government to deaths associated with Covid-19 in 2020 to its responses to deaths associated with the 2003 invasion of Iraq. Similarities and dissimilarities between the cases regarding what counted as data, what data were taken to count, what data counted for, and how data were counted provide the basis for considering how the bounds of democratic accountability are constituted. Based (...) on these two cases, the article sets out the metaphors of leaks and cascades as ways of characterising the data practices whereby counts, counting and accountability get configured. By situating deaths associated with Covid-19 against previous experience with deaths from war, the article also proposes how claims to truth and ignorance might figure in any future official inquiry into the handling of the pandemic. (shrink)

We often speak as if there are merely possible people—for example, when we make such claims as that most possible people are never going to be born. Yet most metaphysicians deny that anything is both possibly a person and never born. Since our unreflective talk of merely possible people serves to draw non-trivial distinctions, these metaphysicians owe us some paraphrase by which we can draw those distinctions without committing ourselves to there being merely possible people. We show that such paraphrases (...) are unavailable if we limit ourselves to the expressive resources of even highly infinitary first-order modal languages. We then argue that such paraphrases are available in higher-order modal languages only given certain strong assumptions concerning the metaphysics of properties. We then consider alternative paraphrase strategies, and argue that none of them are tenable. If talk of merely possible people cannot be paraphrased, then it must be taken at face value, in which case it is necessary what individuals there are. Therefore, if it is contingent what individuals there are, then the demands of paraphrase place tight constraints on the metaphysics of properties: either (i) it is necessary what properties there are, or (ii) necessarily equivalent properties are identical, and having properties does not entail even possibly being anything at all. (shrink)

Categorical logic has shown that modern logic is essentially the logic of subsets (or "subobjects"). Partitions are dual to subsets so there is a dual logic of partitions where a "distinction" [an ordered pair of distinct elements (u,u′) from the universe U ] is dual to an "element". An element being in a subset is analogous to a partition π on U making a distinction, i.e., if u and u′ were in different blocks of π. Subset logic leads to finite (...) probability theory by taking the (Laplacian) probability as the normalized size of each subset-event of a finite universe. The analogous step in the logic of partitions is to assign to a partition the number of distinctions made by a partition normalized by the total number of ordered pairs |U|² from the finite universe. That yields a notion of "logical entropy" for partitions and a "logical information theory." The logical theory directly counts the (normalized) number of distinctions in a partition while Shannon's theory gives the average number of binary partitions needed to make those same distinctions. Thus the logical theory is seen as providing a conceptual underpinning for Shannon's theory based on the logical notion of "distinctions.". (shrink)

I would like to attack a certain view: The view that the concept of identity can fail to apply to some things although, for some positive integer n, we have n of them. The idea of entities without self-identity is seriously entertained in the philosophy of quantum mechanics. It is so pervasive that it has been labelled the Received View. I introduce the Received View in Section 1. In Section 2 I explain what I mean by entity, and I argue (...) that supporters of the Received View should agree with my characterization of the corresponding notion of entity. I also explain what I mean by identity, and I show that supporters of the Received View agree with my characterization of that notion. In Section 3 I argue that the concept of identity, so characterized, is one with the concept of oneness. Thus, it cannot but apply to what belongs to a collection with n elements, n being a positive integer. In Section 4 I add some considerations on the primitiveness of identity or unity and the status of the Identity of Indiscernibles. In Section 5 I address the problem of how reference to indiscernible objects with identity can be achieved. (shrink)

We show how to formalize approximate counting via hash functions in subsystems of bounded arithmetic, using variants of the weak pigeonhole principle. We discuss several applications, including a proof of the tournament principle, and an improvement on the known relationship of the collapse of the bounded arithmetic hierarchy to the collapse of the polynomial-time hierarchy.

By around the age of 5½, many children in the United States judge that numbers never end, and that it is always possible to add 1 to a set. These same children also generally perform well when asked to label the quantity of a set after one object is added (e.g., judging that a set labeled “five” should now be “six”). These findings suggest that children have implicit knowledge of the “successor function”: Every natural number, n, has a successor, n (...) + 1. Here, we explored how children discover this recursive function, and whether it might be related to discovering productive morphological rules that govern language‐specific counting routines (e.g., the rules in English that represent base‐10 structure). We tested 4‐ and 5‐year‐old children’s knowledge of counting with three tasks, which we then related to (a) children’s belief that 1 can always be added to any number (the successor function) and (b) their belief that numbers never end (infinity). Children who exhibited knowledge of a productive counting rule were significantly more likely to believe that numbers are infinite (i.e., there is no largest number), though such counting knowledge was not directly linked to knowledge of the successor function, per se. Also, our findings suggest that children as young as 4 years of age are able to implement rules defined over their verbal count list to generate number words beyond their spontaneous counting range, an insight which may support reasoning over their acquired verbal count sequence to infer that numbers never end. (shrink)