This chapter contains sections titled: I The Nature of Philosophy of Education and Conceptual Analysis II Peters' Conception of Education and some of its Normative Implications III Peters' Indeterminacy of Educational Aims and the Need for Sustained Dialogue References.

Abraham Robinson’s framework for modern infinitesimals was developed half a century ago. It enables a re-evaluation of the procedures of the pioneers of mathematical analysis. Their procedures have been often viewed through the lens of the success of the Weierstrassian foundations. We propose a view without passing through the lens, by means of proxies for such procedures in the modern theory of infinitesimals. The real accomplishments of calculus and analysis had been based primarily on the elaboration of novel techniques for (...) solving problems rather than a quest for ultimate foundations. It may be hopeless to interpret historical foundations in terms of a punctiform continuum, but arguably it is possible to interpret historical techniques and procedures in terms of modern ones. Our proposed formalisations do not mean that Fermat, Gregory, Leibniz, Euler, and Cauchy were pre-Robinsonians, but rather indicate that Robinson’s framework is more helpful in understanding their procedures than a Weierstrassian framework. (shrink)

The Mathematical Intelligencer recently published a note by Y. Sergeyev that challenges both mathematics and intelligence. We examine Sergeyev’s claims concerning his purported Infinity computer. We compare his grossone system with the classical Levi-Civita fields and with the hyperreal framework of A. Robinson, and analyze the related algorithmic issues inevitably arising in any genuine computer implementation. We show that Sergeyev’s grossone system is unnecessary and vague, and that whatever consistent subsystem could be salvaged is subsumed entirely within a stronger and (...) clearer system. Lou Kauffman, who published an article on a grossone, places it squarely outside the historical panorama of ideas dealing with infinity and infinitesimals. (shrink)

This article aims to highlight why R. S. Peters' conceptual analysis of ‘education’ was such an important contribution to the normative field of philosophy of education. In the article, I do the following: 1) explicate Peters' conception of philosophy of education as a field of philosophy and explain his approach to the philosophical analysis of concepts; 2) emphasize several (normative) features of Peters' conception of education, while pointing to a couple of oversights; and 3) suggest how Peters' analysis might be (...) used to reinvigorate a conversation on one central educational aim—that of how we might educate citizens for the 21st century. (shrink)

This article aims to highlight why R. S. Peters' conceptual analysis of ‘education’ was such an important contribution to the normative field of philosophy of education. In the article, I do the following: 1) explicate Peters' conception of philosophy of education as a field of philosophy and explain his approach to the philosophical analysis of concepts; 2) emphasize several (normative) features of Peters' conception of education, while pointing to a couple of oversights; and 3) suggest how Peters' analysis might be (...) used to reinvigorate a conversation on one central educational aim—that of how we might educate citizens for the 21st century. (shrink)

Throughout his life, John Tyler Bonner contributed to major transformations in the fields of developmental and evolutionary biology. He pondered the evolution of complexity and the significance of randomness in evolution, and was instrumental in the formation of evolutionary developmental biology. His contributions were vast, ranging from highly technical scientific articles to numerous books written for a broad audience. This historical vignette gathers reflections by several prominent researchers on the greatness of John Bonner and the implications of his work.

Humanist sociologists are activists rooted in the reality of history and change and guided by a concern for the 'real life' problems of equality, peace, and social justice. They view people as active shapers of social life, capable of creating societies in which everyone's potential can unfold. Alfred McClung Lee introduces this volume with 'Sociology: Humanist and Scientific' and develops the theme that a sociology that is humanist is also scientific. The other nine selections are grouped into four parts: 'The (...) Individual and Social Life;' 'Social Institutions: Technology, Science, and Formal Organization;' 'Political Structures: Issues of Justice and Equality;' and 'Methodological Critiques and Counterproposals.'. (shrink)

Yochanan's Gamble investigates how the talmudic rabbis navigate their own ethical challenges - determining truth, upholding compromise, convincing others, keeping the peace, weighing sinning in hopes of promoting greater good - thereby forging a pragmatic Jewish path for resolving moral conundrums today.

This Student's Companion edition lays out, in nontechnical terms, the main ideas contained in Maimonides' famous work Guide of the Perplexed so it can be read by an ambitious beginner or an advanced high school student. It provides a general introduction to Maimonides' life, the plan and outline of the Guide, the required philosophical background, and a concise chapter-by-chapter overview and commentary.

This new translation of The Upanishads is at once delightfully simple and rigorously learned, providing today's readers with an accurate, accessible rendering of the core work of ancient Indian philosophy. The Upanishads are often considered the most important literature from ancient India. Yet many academic translators fail to capture the work's philosophical and spiritual subtlety, while others convey its poetry at the cost of literal meaning. This new translation by Vernon Katz and Thomas Egenes fills the need for an Upanishads (...) that is clear, simple, and insightful - yet remains faithful to the original Sanskrit. As Western Sanskrit scholars who have spent their lives immersed in meditative practice, Katz and Egenes offer a unique perspective in penetrating the depths of Eastern wisdom and expressing these insights in modern yet poetic language. Their historical introduction is suited to newcomers and experienced readers alike, providing the perfect entry to this unparalleled work. (shrink)

The purpose of this paper is to examine the role that trustworthiness plays in the ability of teachers to function as moral role models. Through exploration of Muriel Spark’s novel, The Prime of Miss Jean Brodie, I explain some of the central features of trustworthiness as a moral virtue and suggest how these features are critical to developing moral relationships between teachers and students. I show how and why the character of Miss Jean Brodie fails to embody trustworthiness, and how (...) moral philosophy and psychological insight are bound up with teachers’ efforts to treat students well and to behave in ways that morally warrant the trust most of us typically grant them. Finally, I propose some of the important implications this analysis has for teacher education. (shrink)

Comparative studies demonstrate that homologous neural structures differ in function and that neural mechanisms underlying behavior evolved independently. A neural structure does not serve a particular function so much as it executes an algorithm on its inputs though its dynamics. Neural dynamics are altered by a neuromodulation, and species-differences in neuromodulation can account for behavioral differences.

To improve the quality and efficiency of research, groups within the scientific community seek to exploit the value of data sharing. Funders, institutions, and specialist organizations are developing and implementing strategies to encourage or mandate data sharing within and across disciplines, with varying degrees of success. Academic journals in ecology and evolution have adopted several types of public data archiving policies requiring authors to make data underlying scholarly manuscripts freely available. The effort to increase data sharing in the sciences is (...) one part of a broader “data revolution” that has prompted discussion about a paradigm shift in scientific research. Yet anecdotes from the community and studies evaluating data availability suggest that these policies have not obtained the desired effects, both in terms of quantity and quality of available datasets. We conducted a qualitative, interview-based study with journal editorial staff and other stakeholders in the academic publishing process to examine how journals enforce data archiving policies. We specifically sought to establish who editors and other stakeholders perceive as responsible for ensuring data completeness and quality in the peer review process. Our analysis revealed little consensus with regard to how data archiving policies should be enforced and who should hold authors accountable for dataset submissions. Themes in interviewee responses included hopefulness that reviewers would take the initiative to review datasets and trust in authors to ensure the completeness and quality of their datasets. We highlight problematic aspects of these thematic responses and offer potential starting points for improvement of the public data archiving process. (shrink)

This contribution to part 4 of the Common Knowledge symposium “Fuzzy Studies: On the Consequence of Blur” shows how the reputedly radical position that history is not about eternal truths but about the creative construction of a convincing narrative of past events is not an argument of recent vintage. In the days when postmodernism was a technical term used mainly by scholars of art and architecture—and indeed, decades before then—professional historians were grappling with the incapacity of facts to write themselves (...) into a universally satisfying, single version of history. Successive presidents of the American Historical Association such as Andrew Dickson White, Carl Becker, Charles Beard, and William McNeill admitted that writing history is a desperate attempt at pattern recognition in a fuzzy discipline. Pattern recognition is a tool, valuable as a stage in historical thinking, but destined ultimately to come undone. What remains, then, is fuzzy thinking. It can be a good thing, the article concludes, to let our thinking about history remain a blur or, at least, to bear in mind that any patterns we recognize in the past are liable to dissolve under a different light. (shrink)

The essays in this volume are a contribution to this process of reappraisal, focusing specifically on the phenomena of scepticism and millenarianism, especially ...

Once shunned, interdisciplinarity has now become fashionable-but badly in need of unpacking. The transfer of ideas from one field to another requires full understanding of the ways in which they are used and understood, where they come from and where they are going. This book calls attention to certain linguistic tools that served scholars in the past and that are still relevant today-if properly employed. It offers a roadmap that inter-relates problems within and between the sciences-human and natural. Throughout, the (...) book interpolates excerpts from scholarly texts that light the road. Spelling out how research may go beyond the mere assembly of facts, it invites the reader to join a sequence of steps that highlights the processes which problem solving entails. Ruth Katz (Ph.D. Columbia University) is one of the founding members of the Department of Musicology at the Hebrew University of Jerusalem. Upon receiving the prestigious Israel Prize in 2012, her work was cited for shedding light on such things as the interdisciplinary processes implicated in "the origin of opera, the history of Western notation, the relationship of stylistic change to the history of ideas, music's place in philosophy, and the role of musical aesthetics in cognition." She founded the Excellence Program at the University and co-founded the Laboratory for the study of music. Her most recent book, hailed as "magisterial," is entitled A Language of Its Own: Sense and Meaning in the Making of Western Art Music (University of Chicago Press, 2009). It is an analysis of the decisions that underlay the crafting and understanding of stylistic change. (shrink)

This book addresses the growing use of computerized systems to influence people’s decisions without their awareness, a significant but underappreciated sea-change in the way the world works. To assess these systems, this volume’s contributors explore the philosophical and ethical dimensions of algorithms that guide people’s behavior by nudging them toward choices preferred by systems architects. Particularly in an era of heightened awareness of bias and discrimination, these systems raise profound concerns about the morality of such activities. This volume brings together (...) a diverse array of thinkers to critically examine these nudging systems. Not only are high-level perspectives presented, but so too are of those who use them on a day-to-day basis. While algorithmic nudging can produce benefits for users there are also many less-obvious costs to using such systems, costs that require examination and deliberation. This book is a major step towards delineating these concerns and suggesting ways to provide a sounder basis for future policies for algorithms. It should be of interest to system designers, public policymakers, scholars, and those who wonder more deeply about the nudges they receive from various websites and on their phones. (shrink)

Chomsky's criticism of Bloomfieldian structuralism's conception of linguistic reality applies equally to his own conception of linguistic reality. There are too many sentences in a natural language for them to have either concrete acoustic reality or concrete psychological or neural reality. Sentences have to be types, which, by Peirce's generally accepted definition, means that they are abstract objects. Given that sentences are abstract objects, Chomsky's generativism as well as his psychologism have to be given up. Langendoen and Postal's argument in (...) The Vastness of Natural Languages to show that there are more than denumerably many sentences is flawed. But, with the view that sentences are abstract objects, the flaws can be corrected. Once psychologism and generativism are abandoned, the revolution against Bloomfieldian structuralism can be brought to completion and linguistics can be put on a sound philosophical basis. (shrink)

In relation to a thesis put forward by Marx Wartofsky, we seek to show that a historiography of mathematics requires an analysis of the ontology of the part of mathematics under scrutiny. Following Ian Hacking, we point out that in the history of mathematics the amount of contingency is larger than is usually thought. As a case study, we analyze the historians’ approach to interpreting James Gregory’s expression ultimate terms in his paper attempting to prove the irrationality of \. Here (...) Gregory referred to the last or ultimate terms of a series. More broadly, we analyze the following questions: which modern framework is more appropriate for interpreting the procedures at work in texts from the early history of infinitesimal analysis? As well as the related question: what is a logical theory that is close to something early modern mathematicians could have used when studying infinite series and quadrature problems? We argue that what has been routinely viewed from the viewpoint of classical analysis as an example of an “unrigorous” practice, in fact finds close procedural proxies in modern infinitesimal theories. We analyze a mix of social and religious reasons that had led to the suppression of both the religious order of Gregory’s teacher degli Angeli, and Gregory’s books at Venice, in the late 1660s. (shrink)

Our understanding of the nature and processing of figurative language is central to several important issues in cognitive science, including the relationship of language and thought, how we process language, and how we comprehend abstract meaning. Over the past fifteen years, traditional approaches to these issues have been challenged by experimental psychologists, linguists, and other cognitive scientists interested in the structures of the mind and the processes that operate on them. In Figurative Language and Thought, internationally recognized experts in the (...) field of figurative language, Albert Katz, Mark Turner, Raymond W. Gibbs Jr., and Cristina Cacciari, provide a coherent and focused debate on the subject. The book's authors discuss a variety of fundamental questions, including: What can figures of speech tell us about the structure of the conceptual system? If and how should we distinguish the literal from the nonliteral in our theories of language and thought? Are we primarily figurative thinkers and consequently figurative language users or the other way around? Why do we prefer to speak metaphorically in everyday conversation, when literal options may be available for use? Is metaphor the only vehicle through which we can understand abstract concepts? What role do cultural and social factors play in our comprehension of figurative language? These and related questions are raised and argued in an integrative look at the role of nonliteral language in cognition. This volume, a part of Counterpoints series, will be thought-provoking reading for a wide range of cognitive psychologists, linguists, and philosophers. (shrink)

We apply Benacerraf’s distinction between mathematical ontology and mathematical practice to examine contrasting interpretations of infinitesimal mathematics of the seventeenth and eighteenth century, in the work of Bos, Ferraro, Laugwitz, and others. We detect Weierstrass’s ghost behind some of the received historiography on Euler’s infinitesimal mathematics, as when Ferraro proposes to understand Euler in terms of a Weierstrassian notion of limit and Fraser declares classical analysis to be a “primary point of reference for understanding the eighteenth-century theories.” Meanwhile, scholars like (...) Bos and Laugwitz seek to explore Eulerian methodology, practice, and procedures in a way more faithful to Euler’s own. Euler’s use of infinite integers and the associated infinite products are analyzed in the context of his infinite product decomposition for the sine function. Euler’s principle of cancellation is compared to the Leibnizian transcendental law of homogeneity. The Leibnizian law of continuity similarly finds echoes in Euler. We argue that Ferraro’s assumption that Euler worked with a classical notion of quantity is symptomatic of a post-Weierstrassian placement of Euler in the Archimedean track for the development of analysis, as well as a blurring of the distinction between the dual tracks noted by Bos. Interpreting Euler in an Archimedean conceptual framework obscures important aspects of Euler’s work. Such a framework is profitably replaced by a syntactically more versatile modern infinitesimal framework that provides better proxies for his inferential moves. (shrink)

ABSTRACTA probability model is underdetermined when there is no rational reason to assign a particular infinitesimal value as the probability of single events. Pruss claims that hyperreal probabilities are underdetermined. The claim is based upon external hyperreal-valued measures. We show that internal hyperfinite measures are not underdetermined. The importance of internality stems from the fact that Robinson’s transfer principle only applies to internal entities. We also evaluate the claim that transferless ordered fields may have advantages over hyperreals in probabilistic modeling. (...) We show that probabilities developed over such fields are less expressive than hyperreal probabilities. (shrink)