We upgrade [3] to a complete proof of the conjecture NP = PSPACE that is known as one of the fundamental open problems in the mathematical theory of computational complexity; this proof is based on [2]. Since minimal propositional logic is known to be PSPACE complete, while PSPACE to include NP, it suffices to show that every valid purely implicational formula ρ has a proof whose weight and time complexity of the provability involved are both polynomial in the weight of (...) ρ. As is [3], we use proof theoretic approach. Recall that in [3] we considered any valid ρ in question that had a “short” tree-like proof π in the Hudelmaier-style cutfree sequent calculus for minimal logic. The “shortness” means that the height of π and the total weight of different formulas occurring in it are both polynomial in the weight of ρ. However, the size, and hence also the weight, of π could be exponential in that of ρ. To overcome this trouble we embedded π into Prawitz’s proof system of natural deductions containing single formulas, instead of sequents. As in π, the height and the total weight of different formulas of the resulting tree-like natural deduction ∂1 were polynomial, although the size of ∂1 still could be exponential, in the weight of ρ. In our next, crucial move, ∂1 was deterministically compressed into a “small”, although multipremise, dag-like deduction ∂ whose horizontal levels contained only mutually different formulas, which made the whole weight polynomial in that of ρ. However, ∂ required a more complicated verification of the underlying provability of ρ. In this paper we present a nondeterministic compression of ∂ into a desired standard dag-like deduction ∂0 that deterministically proves ρ in time and space polynomial in the weight of ρ.2 Together with [3] this completes the proof of NP = PSPACE.Natural deductions are essential for our proof. Tree-to-dag horizontal compression of π merging equal sequents, instead of formulas, is not sufficient, since the total number of different sequents in π might be exponential in the weight of ρ – even assuming that all formulas occurring in sequents are subformulas of ρ. On the other hand, we need Hudelmaier’s cutfree sequent calculus in order to control both the height and total weight of different formulas of the initial tree-like proof π, since standard Prawitz’s normalization although providing natural deductions with the subformula property does not preserve polynomial heights. It is not clear yet if we can omit references to π even in the proof of the weaker result NP = coNP. (shrink)

In our previous work we proved the conjecture NP = PSPACE by advanced proof theoretic methods that combined Hudelmaier’s cut-free sequent calculus for minimal logic with the horizontal compressing in the corresponding minimal Prawitz-style natural deduction. In this Addendum we show how to prove a weaker result NP = coNP without referring to HSC. The underlying idea is to omit full minimal logic and compress only “naive” normal tree-like ND refutations of the existence of Hamiltonian cycles in given non-Hamiltonian graphs, (...) since the Hamiltonian graph problem in NPcomplete. Thus, loosely speaking, the proof of NP = coNP can be obtained by HSC-elimination from our proof of NP = PSPACE. (shrink)

Abstract‘Raising aspirations’ for education among young people in low socioeconomic regions has become a widespread policy prescription for increasing human capital investment and economic competitiveness in so-called ‘knowledge economies’. However, policy tends not to address difficult social, cultural, economic and political conditions for aspiring, based in structural changes associated with globalization. Drawing conceptually on the works of Pierre Bourdieu, Raymond Williams, Arjun Appadurai and authors in the Funds of Knowledge tradition, this article theorizes two logics for aspiring that are recognizable (...) in research with young people and families: a doxic logic, grounded in populist–ideological mediations; and a habituated logic, grounded in biographic–historical legacies and embodied as habitus. A less tangible third ‘logic’ is also theorized: emergent senses of future potential, grounded in lived cultures, which hold possibility for imagining and pursuing alternative futures. The article offers a sociological framework for understanding aspirations as complex social–cultural phenomena, and for capacitating emergent and hopeful aspirations through school- and community-based research and dialogue. (shrink)

Children like Baby G, born with complex chronic medical conditions that compromise function in the long term, are an increasing presence in tertiary-level neonatal intensive care units. The parents and health-care providers of these children are faced with profoundly difficult decisions. Whether severe congenital anomalies with poor prognosis are diagnosed antenatally or are discovered at the time of birth, the issues are vexing, and the impact decisions will have on everyone in the family is profound. What should such decisions be (...) based upon? What values and principles might guide the decision-making process? What moral justifications allow for pursuing.. (shrink)

Hunting and gathering is, evolutionarily, the defining subsistence strategy of our species. Studying how children learn foraging skills can, therefore, provide us with key data to test theories about the evolution of human life history, cognition, and social behavior. Modern foragers, with their vast cultural and environmental diversity, have mostly been studied individually. However, cross-cultural studies allow us to extrapolate forager-wide trends in how, when, and from whom hunter-gatherer children learn their subsistence skills. We perform a meta-ethnography, which allows us (...) to systematically extract, summarize, and compare both quantitative and qualitative literature. We found 58 publications focusing on learning subsistence skills. Learning begins early in infancy, when parents take children on foraging expeditions and give them toy versions of tools. In early and middle childhood, children transition into the multi-age playgroup, where they learn skills through play, observation, and participation. By the end of middle childhood, most children are proficient food collectors. However, it is not until adolescence that adults (not necessarily parents) begin directly teaching children complex skills such as hunting and complex tool manufacture. Adolescents seek to learn innovations from adults, but they themselves do not innovate. These findings support predictive models that find social learning should occur before individual learning. Furthermore, these results show that teaching does indeed exist in hunter-gatherer societies. And, finally, though children are competent foragers by late childhood, learning to extract more complex resources, such as hunting large game, takes a lifetime. (shrink)

At the beginning of the third millennium we are entering a new era. I call it "The Integration/Disintegration Era" because the Integration/ Disintegration Problem is one of the basic problems our world is facing today. Philosophy attempts to work out an integrated view of the universe, of human nature, and of society. The specific philosophical science which has concerned itself with integration/ disintegration, is Integratism. This is the common denominator of different particular problems in the integration /disintegration of the universe, (...) society and personality; and it supplies a possible philosophical solution to the general problem of disintegration. The main concept of integratism is integration [Lat. integer, complete]. My theoretical and empirical study of various aspects of integration/ disintegration problems in modern science and education has led to the formulation of a new, rather systematic and, I believe, quite useful conception of contemporary integratism that contributes not only to the attempt to develop a theory of integration/disintegration processes in various biological and social systems but also to practical problems of developing contemporary integrated educational systems. Further concepts of contemporary integratism are: integrative level, IDon, adaptive disintegration, ADon, disadaptive disintegration, adaptive reintegration, sanosphere, pathosphere, etc. The philosophy of integratism might provide a possible philosophical solution to the general problem of disintegration and in this way assign priority to certain particular problems concerning the disintegration of the world. (shrink)

At the beginning of the third millennium we are entering a new era. I call it "The Integration/Disintegration Era" because the Integration/ Disintegration Problem is one of the basic problems our world is facing today. Philosophy attempts to work out an integrated view of the universe, of human nature, and of society. The specific philosophical science which has concerned itself with integration/ disintegration, is Integratism. This is the common denominator of different particular problems in the integration /disintegration of the universe, (...) society and personality; and it supplies a possible philosophical solution to the general problem of disintegration. The main concept of integratism is integration [Lat. integer, complete]. My theoretical and empirical study of various aspects of integration/ disintegration problems in modern science and education has led to the formulation of a new, rather systematic and, I believe, quite useful conception of contemporary integratism that contributes not only to the attempt to develop a theory of integration/disintegration processes in various biological and social systems but also to practical problems of developing contemporary integrated educational systems. Further concepts of contemporary integratism are: integrative level, IDon, adaptive disintegration, ADon, disadaptive disintegration, adaptive reintegration, sanosphere, pathosphere, etc. The philosophy of integratism might provide a possible philosophical solution to the general problem of disintegration and in this way assign priority to certain particular problems concerning the disintegration of the world. (shrink)

Infants have been described as 'statistical learners' capable of extracting structure (such as words) from patterned input (such as language). Here, we investigated whether prior knowledge influences how infants track transitional probabilities in word segmentation tasks. Are infants biased by prior experience when engaging in sequential statistical learning? In a laboratory simulation of learning across time, we exposed 9- and 10-month-old infants to a list of either disyllabic or trisyllabic nonsense words, followed by a pause-free speech stream composed of a (...) different set of disyllabic or trisyllabic nonsense words. Listening times revealed successful segmentation of words from fluent speech only when words were uniformly disyllabic or trisyllabic throughout both phases of the experiment. Hearing trisyllabic words during the pre-exposure phase derailed infants' abilities to segment speech into disyllabic words, and vice versa. We conclude that prior knowledge about word length equips infants with perceptual expectations that facilitate efficient processing of subsequent language input. (shrink)

Work-themed play may allow children to learn complex skills, and ethno-typical and gender-typical behaviors. Thus, play may have made important contributions to the evolution of childhood through the development of embodied capital. Using data from Aka foragers and Ngandu farmer children from the Central African Republic, we ask whether children perform ethno- and gender-typical play and work activities, and whether play prepares children for complex work. Focal follows of 50 Aka and 48 Ngandu children were conducted with the aim of (...) recording children’s participation in 12 categories of work and work-themed play. Using these data, we test a set of hypotheses regarding how age, gender, ethnicity, and task complexity influence children’s activities. As hypothesized, we find performance of work-themed play is negatively correlated with age. Contrary to our hypothesis, children do not play more than they work at complex tasks, but they work more than they play at simple ones. Gender and ethnicity are associated with play and work at culturally salient activities, despite availability of other-gender and other-ethnicity social partners. Our findings show that ethnic and gender biases are apparent in the play and work behavior of Aka and Ngandu children. Moreover, our results show that play helps both forager and farmer children learn complex skills, consistent with play having an adaptive learning function. (shrink)

Aspects of human life history and cognition, such as our long childhoods and extensive use of teaching, theoretically evolved to facilitate the acquisition of complex tasks. The present paper empirically examines the relationship between subsistence task difficulty and age of acquisition, rates of teaching, and rates of oblique transmission among Hadza and BaYaka foragers from Tanzania and the Republic of Congo. We further examine cross-cultural variation in how and from whom learning occurred. Learning patterns and community perceptions of task difficulty (...) were assessed through interviews. We found no relationship between task difficulty, age of acquisition, and oblique transmission, and a weak but positive relationship between task difficulty and rates of teaching. While same-sex transmission was normative in both societies, tasks ranked as more difficult were more likely to be transmitted by men among the BaYaka, but not among the Hadza, potentially reflecting cross-cultural differences in the sexual division of subsistence and teaching labor. Further, the BaYaka were more likely to report learning via teaching, and less likely to report learning via observation, than the Hadza, possibly owing to differences in socialization practices. (shrink)

This paper provides a roadmap for engaging in cross-cultural, developmental research in practical, ethical, and community-engaged ways. To cultivate the flexibility necessary for conducting cross-cultural research, we structure our roadmap as a series of questions that each research program might consider prior to embarking on cross-cultural examinations in developmental science. Within each topic, we focus on the challenges and opportunities inherent to different types of study designs, fieldwork, and collaborations because our collective experience in conducting research in multiple cultural contexts (...) has taught us that there can be no single “best practice”. Here we identify the challenges that are unique to cross-cultural research as well as present a series of recommendations and guidelines. We also bring to the forefront ethical considerations which are rarely encountered in the laboratory context, but which researchers face daily while conducting research in a cultural context which one is not a member. As each research context requires unique solutions to these recurring challenges, we urge researchers to use this set of questions as a starting point, and to expand and tailor the questions and potential solutions with community members to support their own research design or cultural context. This will allow us to move the field towards more inclusive and ethical research practices. (shrink)

This paper analyses how the discursive construction, valuation and subjective experience of human capital is evolving in parallel with crises of capital as a world-system. Ideology critique provides tools for analysing policy ‘fictions’ that aim to sustain investment in human capital through education. Foucauldian analytical tools enable analysis of how human capital has become a project of self-appreciation and cultivation of positive psychological traits. We argue that the work of Lauren Berlant provides an important complement to these approaches and enables (...) us to analyse how crises of capital are being lived as the cruelling of optimism about social mobility through investment in oneself as human capital. The paper points to an educational politics and pedagogy for living through infrastructural breakdown in darkly uncertain historical times. (shrink)

Ethical decision-making is a multi-faceted phenomenon, and our understanding of ethics rests on diverse perspectives. While considering how leaders ought to act, scholars have created integrated models of moral reasoning processes that encompass diverse influences on ethical choice. With this, there has been a call to continually develop an understanding of the micro-level factors that determine moral decisions. Both rationalist, such as moral processing, and non-rationalist factors, such as virtue and humanity, shape ethical decision-making. Focusing on the role of moral (...) judgement and moral intent in moral reasoning, this study asks what bearings a trait of mindfulness and a sense of moral responsibility may have on this process. A survey measuring mindfulness, moral responsibility and moral judgement completed by 171 respondents was used for four hypotheses on moral judgement and intent in relation to moral responsibility and mindfulness. The results indicate that mindfulness predict moral responsibility but not moral judgement. Moral responsibility does not predict moral judgement, but moral judgement predicts moral intent. The findings give further insight into the outcomes of mindfulness and expand insights into the models of ethical decision-making. We offer suggestions for further research on the role of mindfulness and moral responsibility in ethical decision-making. (shrink)

The philosopher and critic George Henry Lewes published this work in two volumes in 1845–6. This is a reissue of an 1892 printing, which brought the volumes into one book. Lewes wrote widely on literature, science and philosophy, and was also the long-term intimate companion of George Eliot. This book is a narrative history, rather than an encyclopedia, of key philosophers. It is, therefore, a partial and personal study instead of an exhaustive textbook. The first volume concentrates solely (...) on Greek philosophy, beginning with the Pre-Socratics and ending with the Neo-Platonists. The second volume jumps to Francis Bacon, concentrating on British, German and French philosophy, and addressing, among others, Spinoza, Locke, Hume and Kant, and ending with Auguste Comte. Containing both historical anecdotes and pithy analyses of ideas, this book reflects the expertise and intellectual sympathies of a Victorian polymath. (shrink)

In this article, we examine how the U.N. Convention on the Rights of the Child can be useful in pediatric bioethics. Adopted in 1989, the CRC reflects norms that have been deliberated upon for a long period of time and endorsed by most nations. The United States is now the only country that has not ratified the CRC.1 International human rights law shares many key moral concepts with clinical pediatric bioethics, and the CRC provides a considered language common to many (...) jurisdictions that can assist bioethicists in their daily practice and help health-care organizations in their policy development and international interactions. There may, however, be practical challenges with using the CRC in the practice of.. (shrink)

In this chapter we use methods of corpus linguistics to investigate the ways in which mathematicians describe their work as explanatory in their research papers. We analyse use of the words explain/explanation (and various related words and expressions) in a large corpus of texts containing research papers in mathematics and in physical sciences, comparing this with their use in corpora of general, day-to-day English. We find that although mathematicians do use this family of words, such use is considerably less prevalent (...) in mathematics papers than in physics papers or in general English. Furthermore, we find that the proportion with which mathematicians use expressions related to ‘explaining why’ and ‘explaining how’ is significantly different to the equivalent proportion in physics and in general English. We discuss possible accounts for these differences. (shrink)

Michael A. Petersa and Fazal Rizvib aBeijing Normal University, Beijing, PR China; bMelbourne University, Melbourne, Australia Our minds are still racing back and forth, longing for a return to ‘no...

The writers of these works make the transition from folk psychology, theological views on human nature and metaphysical speculation to a more empirical and scientific study of the human mind, giving an insight into how pyschology emerged.

Learning to use, make, and modify tools is key to our species’ success. Researchers have hypothesized that play with objects may have a foundational role in the ontogeny of tool use and, over evolutionary timescales, in cumulative technological innovation. Yet, there are few systematic studies investigating children’s interactions with objects outside the post-industrialized West. Here, we survey the ethnohistorical record to uncover cross-cultural trends regarding hunter-gatherer children’s use of objects during play and instrumental activities. Our dataset, consisting of 434 observations (...) of children’s toys and tools from 54 hunter-gatherer societies, reveals several salient trends: Most objects in our dataset are used in play. Children readily manufacture their own toys, such as dolls and shelters. Most of the objects that children interact with are constructed from multiple materials. Most of the objects in our dataset are full-sized or miniature versions of adult tools, reflecting learning for adult roles. Children also engage with objects related to child culture, primarily during play. Taken together, our findings show that hunter-gatherer children grow up playing, making, and learning with objects. (shrink)