In this paper we criticize the commonly accepted theory of memory, and offer an alternative. According to the traditional view, memory is a stored mental representation of things past. We show, through an analysis of a single act of recognition, the logical oddities to which this view leads. Since, however, these are generally ignored, we also consider those characteristics of the traditional view which apparently make it attractive to those who hold it, namely its consonance with the commonly held conception (...) of time, its explanation for the fallibility of memory, and its way of making behavior predictable. We then present the alternative view, the direct realist theory. According to it, there is no such thing as a stored mental representation. The theory redefines memory as the perception of sequential structure, and in so doing successfully treats of the fallibility of memory and the necessity for making behavior predictable. Moreover, and perhaps most importantly, it does not lead to the logical difficulties of the traditional theory. (shrink)

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)

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.

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 analyzes the question of how the size of bribes should impact criminal sanctions. In contrast to the commonly held view that punishment should increase with the size of the bribe, we argue to the contrary: that the punishment of the bribee should decrease with the size of the bribe. Our conclusion is based both on a philosophical argument and an economic argument. We argue that all else being equal, as an agent’s reservation price for selling public interests decreases, (...) the culpability of the agent willing to receive a bribe increases. In addition, from an economic perspective, the expected social harm of an official acting with a low reservation price for bribes is much greater than one acting with a high reservation price: both the susceptibility of being bribed as well as the potential for social harm is much greater when the reservation price is low. (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)

For the past thirty years, Hal Foster has pushed the boundaries of cultural criticism, establishing a vantage point from which the seemingly disparate agendas of artists, patrons, and critics have a telling coherence. In The Anti-Aesthetic, preeminent critics such as Jean Baudrillard, Rosalind Krauss, Fredric Jameson, and Edward Said consider the full range of postmodern cultural production, from the writing of John Cage, to Cindy Sherman's film stills, to Barbara Kruger's collages. With a redesigned cover and a new afterword that (...) situates the book in relation to contemporary criticism, The Anti-Aesthetic provides a strong introduction for newcomers and a point of reference for those already engaged in discussions of postmodern art, culture, and criticism. Includes a new afterword by Hal Foster and 12 black and white photographs. (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)

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)

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.

The flaws in social psychological research pointed out by Cesario have societal costs. These include ignoring crucial base rates thereby degrading the effectiveness of policy decisions, generalizing the conclusions derived from experiments on non-professionals thereby distorting the public's view of professional law enforcement personnel, questionable accusations of racism, and mis-attributions of the causes of racial differences in behavior.

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)

Cauchy's sum theorem is a prototype of what is today a basic result on the convergence of a series of functions in undergraduate analysis. We seek to interpret Cauchy’s proof, and discuss the related epistemological questions involved in comparing distinct interpretive paradigms. Cauchy’s proof is often interpreted in the modern framework of a Weierstrassian paradigm. We analyze Cauchy’s proof closely and show that it finds closer proxies in a different modern framework.

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 ...

We examine Paul Halmos’ comments on category theory, Dedekind cuts, devil worship, logic, and Robinson’s infinitesimals. Halmos’ scepticism about category theory derives from his philosophical position of naive set-theoretic realism. In the words of an MAA biography, Halmos thought that mathematics is “certainty” and “architecture” yet 20th century logic teaches us is that mathematics is full of uncertainty or more precisely incompleteness. If the term architecture meant to imply that mathematics is one great solid castle, then modern logic tends to (...) teach us the opposite lesson, namely that the castle is floating in midair. Halmos’ realism tends to color his judgment of purely scientific aspects of logic and the way it is practiced and applied. He often expressed distaste for nonstandard models, and made a sustained effort to eliminate first-order logic, the logicians’ concept of interpretation, and the syntactic vs semantic distinction. He felt that these were vague, and sought to replace them all by his polyadic algebra. Halmos claimed that Robinson’s framework is “unnecessary” but Henson and Keisler argue that Robinson’s framework allows one to dig deeper into set-theoretic resources than is common in Archimedean mathematics. This can potentially prove theorems not accessible by standard methods, undermining Halmos’ criticisms. (shrink)

This essay is a review of Ronald Dworkin's recent essay on equality of resources. Many of the ideas discussed by Dworkin have also been examined by economists with, I believe, considerable insight. Unfortunately, economists tend to write for economists, not for philosophers, and their insights are seldom communicated properly to noneconomists. Of course, the same criticism can be levied on philosophers! But perhaps legal theorists are less subject to this criticism. One of the great contributions of Dworkin is that he (...) is very readable; and the quality of his exposition makes these ideas accessible to a wide audience of philosophers, lawyers, and social scientists in general. (shrink)