In his Metrica, Hero provides four procedures for finding the area of a circular segment (with b the base of the segment and h its height): an Ancient method for when the segment is smaller than a semicircle, $$(b + h)/2 \, \cdot \, h$$ ( b + h ) / 2 · h ; a Revision, $$(b + h)/2 \, \cdot \, h + (b/2)^{2} /14$$ ( b + h ) / 2 · h + ( b / 2 (...) ) 2 / 14 ; a quasi-Archimedean method (said to be inspired by the quadrature of the parabola) for cases where b is more than triple h, $${\raise0.5ex\hbox{$\scriptstyle 4$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 3$}}(h \, \cdot \, b/2)$$ 4 / 3 ( h · b / 2 ) ; and a method of Subtraction using the Revised method, for when it is larger than a semicircle. He gives superficial arguments that the Ancient method presumes $$\pi = 3$$ π = 3 and the Revision, $$\pi = {\raise0.5ex\hbox{$\scriptstyle {22}$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 7$}}$$ π = 22 / 7. We are left with many questions. How ancient is the Ancient? Why did anyone think it worked? Why would anyone revise it in just this way? In addition, why did Hero think the Revised method did not work when $$b > 3\;h$$ b > 3 h? I show that a fifth century BCE Uruk tablet employs the Ancient method, but possibly with very strange consequences, and that a Ptolemaic Egyptian papyrus that checks this method by comparing the area of a circle calculated from the sum of a regular inscribed polygon and the areas of the segments on its sides as determined by the Ancient method with the area of the circle as calculated from its diameter correctly sees that the calculations do not quite gel in the case of a triangle but do in the case of a square. Both traditions probably could also calculate the area of a segment on an inscribed regular polygon by subtracting the area of the polygon from the area of the circle and dividing by the number of sides of the polygon. I then derive two theorems about pairs of segments, that the reviser of the Ancient method should have known, that explain each method, why they work when they do and do not when they do not, and which lead to a curious generalization of the Revised method. Hero’s comment is right, but not for the reasons he gives. I conclude with an exploration of Hero’s restrictions of the Revised method and Hero’s two alternative methods. (shrink)

The discussion of mathematical knowledge and its relation to the construction of an appropriate diagram in Aristotle's Metaphysics Θ 9. 1051 a21—33 is an important, if compressed, account of Aristotle's most mature thoughts on mathematical knowledge. The discussion of what sort of previous knowledge one must have for understanding a theorem recalls the discussion at An. Post. A 1. 71 a 17–21, where the epistemological point is similar and the examples the same. The first example, that the interior angles of (...) a triangle equal two right angles, appears no less than thirty times in the corpus . The example of the angle inscribed in a semicircle being a right angle also occurs at An. Post. B 11. 94a 27–34, but in a very different context from its two companions. Illustrations of both theorems provided clear stock examples for Aristotle. (shrink)

Tout au long de sa longue carrière, Henri Lecoq a eu une réputation contrastée dans la communauté scientifique. Son oeuvre est citée par Mendel et par Darwin; cependant certains de ses compatriotes, tels qu'Adolphe Brongniart lui ont dénié originalité et profondeur. Dans une certaine mesure, Lecoq a subi le destin de beaucoup de naturalistes provinciaux dont les efforts n'étaient pas vraiment reconnus par les maîtres de la discipline. Mais une explication plus spécifique se trouve peut-être dans l'habitude qu'avait Lecoq d'utiliser (...) dans le même texte différents styles considérés comme incompatibles. Son travail sur l'hybridation végétale est à cet égard significatif: des bribes de vulgarisation hautes en couleurs y côtoient des conseils pratiques pour les horticulteurs, et les descriptions pittoresques s'y mêlent aux réflexions théoriques. Au terme de cette étude, Lecoq apparaît comme un homme de science qui combine un sens aigu de l'observation avec les caractéristiques d'un auteur romantique. (shrink)

This book brings together papers of the conference on 'Space, Geometry and the Imagination from Antiquity to the Modern Age' held in Berlin, Germany, 27-29 August 2012. Focusing on the interconnections between the history of geometry and the philosophy of space in the pre-Modern and Early Modern Age, the essays in this volume are particularly directed toward elucidating the complex epistemological revolution that transformed the classical geometry of figures into the modern geometry of space. Contributors: Graciela De Pierris Franco Farinelli (...) Michael Friedman Daniel Garber Jeremy Gray Gary Hatfield Andrew Janiak Douglas Jesseph Alexander Jones Henry Mendell David Rabouin. (shrink)

Contributors in the order of contributions: David Ebrey, Richard Kraut, T. H. Irwin, Leonard Brandwood, Eric Brown, Agnes Callard, Gail Fine, Suzanne Obdrzalek, Gábor Betegh, Elizabeth Asmis, Henry Mendell, Constance C. Meinwald, Michael Frede, Emily Fletcher, Verity Harte, Rachana Kamtekar, and Rachel Singpurwalla. -/- The first edition of the Cambridge Companion to Plato (1992), edited by Richard Kraut, shaped scholarly research and guided new students for thirty years. This new edition introduces students to fresh approaches to Platonic dialogues (...) while advancing the next generation of research. Of its seventeen chapters, nine are entirely new, written by a new generation of scholars. Six others have been thoroughly revised and updated by their original authors. The volume covers the full range of Plato's interests, including ethics, political philosophy, epistemology, metaphysics, aesthetics, religion, mathematics, and psychology. Plato's dialogues are approached as unified works and considered within their intellectual context, and the revised introduction suggests a way of reading the dialogues that attends to the differences between them while also tracing their interrelations. The result is a rich and wide-ranging volume which will be valuable for all students and scholars of Plato. (shrink)

This paper has two specific goals. The first is to demonstrate that the theorem in MetaphysicsΘ 9, 1051a24-27 is not equiva-lent to Euclid’s Proposition 32 of book I (which contradicts some Aristotelian commentators, such as W. D. Ross, J. L. Heiberg, and T. L. Heith). Agreeing with Henry Mendell’s analysis, I ar-gue that the two theorems are not equivalent, but I offer different reasons for such divergence: I propose a pedagogical-philosoph-ical reason for the Aristotelian theorem being shorter than (...) the Euclidean one (and the previous Aristotelian versions). Aristotle wants to emphasize the deductive procedure as a satisfactory method to discover scientific knowledge. The second objective, opposing some consensus about geometrical deductions/theo-rems in Aristotle, is to briefly propose that the theorem, exactly as we found it in Metaphysics and without any emendation to the text (therefore opposing Henry Mendell’s suggested amend-ments), allows the ancient philosopher to demonstrate that universal mathematical knowledge is in potence in geometrical figures. This tentatively proves that Aristotle emphasizes that geometrical deduction is sufficient to actualize mathematical knowledge. (shrink)

This paper presents an overview of the risks and benefits of Social AI, understood as conversational AI systems that cater to human social needs like romance, companionship, or entertainment. Section 1 of the paper provides a brief history of conversational AI systems and introduces conceptual distinctions to help distinguish varieties of Social AI and pathways to their deployment. Section 2 of the paper adds further context via a brief discussion of anthropomorphism and its relevance to assessment of human-chatbot relationships. Section (...) 3 of the paper provides a survey of potential and in some cases demonstrated harms associated with user interactions with Social AI systems. Finally, Section 4 discusses how the benefits and harms of Social AI can best be addressed, with a primary focus on how frameworks from AI ethics can inform their development. (shrink)

Researchers do not owe their subjects the same level of care that physicians owe patients, but they owe more than merely what the research protocol stipulates. In keeping with the dynamics of the relationship between researcher and subject, they have limited but substantive fiduciary obligations.

This book is both a critique of the concept of the rights-holding, free, autonomous individual and attendant ideology dominant in the contemporary West, and an account of an alternative view, that of the role-bearing, interrelated responsible person of classical Confucianism, suitably modified for addressing the manifold problems of today.

The advent of the post-Stalin "thaw," particularly the period after 1956, was marked by a spectacular expansion in the publishing of translated Western writing and also, on occasion, of editions in the original languages: the virtual ban on import of Western books was, as of 1975, never relaxed. The more permissive political atmosphere favored the publication of a vastly larger variety of Western authors and titles and provision for the Soviet public of much larger quantities of such books in the (...) country's bookstores and libraries. While the improvement was very impressive in itself, abundant data attest that it was far from adequate to satisfy reader demand.1 Among the beneficiaries, books by American authors stood out the more prominently since it was these that were most discriminated against during the years immediately preceding.2 Decades of neglect, to say nothing of politically inspired selectivity, resulted in such incongruities as the first Russian translation of Melville's Moby Dick in 1961—more than a century after the novel's appearance—and the first Soviet publication of any work by Henry James in 1973. It was not until the 1960's that Russians had an opportunity to read Faulkner—but then, the same was true of Kafka. However unevenly, the range of American literature, both old and new, now made available to Soviet readers is gradually expanding. · 1. The overall problem is discussed in detail in this writer's forthcoming book, A Decade of Euphoria: Western Literature in Post-Stalin Russia, 1954-64 . · 2. For a thorough and illuminating discussion of the fate of American literature in the U.S.S.R. from the Revolution until the early post-Stalin years, see Deming Brown, Soviet Attitudes toward American Writing . Interesting statistical data on the first post-Stalin years may also be found in Melville J. Ruggles, "American Books in Soviet Publishing," Slavic Review 20, n.3 : 419-35. A useful, very brief list of selected works of American writing published by 1968, though not entirely as complete as it purports to be, may be found in M.O. Mendel'son, A.N. Nikolyukin, R.M. Samarin, eds., Problemy literature S. Sh. A. XX. veka , pp. 391-517. Unfortunately, the Soviet bibliography contains no information on press runs of the books listed. Maurice Friedberg, head of the Department of Slavic Languages and Literatures at the University of Illinois, is the author of numerous essays and articles on Soviet literature. Professor Friedberg's most recent book, A Decade of Euphoria: Western Literature in Post-Stalin Russia, 1954-1964, will be published this year. (shrink)

Book reviewed in this article: Clinical Ethics: A Practical Approach to Ethical Decisions in Clinical Medicine. By Albert R. Jonsen, Mark Siegler, and William J. Winslade.

A picture of the world as chiefly one of discrete objects, distributed in space and time, has sometimes seemed compelling. It is however one of the main targets of Henry Laycock's book; for it is seriously incomplete. The picture, he argues, leaves no space for "stuff" like air and water. With discrete objects, we may always ask "how many?," but with stuff the question has to be "how much?" Laycock's fascinating exploration also addresses key logical and linguistic questions about (...) the way we categorize the many and the much. (shrink)

Martha Nussbaum has powerfully argued in Frontiers ofJustice and elsewhere that John Rawls’s sort of social-contract theory cannot usefully be deployed to deal with issues pertaining to justice for the disabled. To counter this claim, this article deploys Rawls’s sort of social-contract theory in order to deal with issues pertaining to justice for the disabled—or, since, as Nussbaum stresses, we all have some degree of disability—for the severely disabled. In this way, rather than questioning one by one Nussbaum’s interpretive claims (...) about Rawls’s view, one can simply see how the Rawlsian framework can work in application to this issue. Following Rawls’s lead, the paper utilizes the idealized “initial choice situation” as an analytic and comparative device for examining alternative principles of justice, developing three different interpretations of the initial choice situation that each correspond to a different set of principles that apply to people of all levels of disability. One of these sets of principles is a simple extension of Rawls’s, one is very close to what Nussbaum herself recommends, and the third is a kind of hybrid. In this way, it is shown not only that Rawls’s social-contract device can usefully be applied to these issues, but also that it is helpful for exploring the deep commitments underlying each of these competing sets of principles. (shrink)

Traces the decentered formulation of self at the heart of Paul Ricoeur's philosophy from his earliest works to his most recent.

In our day-to-day lives, we form responsibility judgements about one another – but we are imperfect beings, and our judgments can be mistaken. This paper suggests that we get things wrong not merely by chance, but predictably and systematically. In particular, these miscues are common when we are dealing with large gaps in social status and power. That is, when we form judgements about those who are much more or less socially powerful than ourselves, it is increasingly likely that “epistemic (...) distorters” will reliably disrupt our reasoning. In response to this situation, I argue for the introduction of a new norm concerning blame and social status: “Powerful Restraint.” This norm suggests that the socially powerful ought to blame the socially dispossessed less frequently, and that social pressure be applied to achieve that compliance. I argue that such a norm is justified given the pernicious down-stream moral effects of the up-stream epistemic distortion I describe. I defend it against objections that it suggests a normative solution to an epistemic problem, that it is paternalistic, and that it involves a kind of disrespect to the less socially powerful. (shrink)

The study examines the relative merits of a noncompatibility and a restructuring explanation of the recurrent empirical finding that a prominent attribute looms larger in choices than in judgments. Pairs of equally attractive options were presented to 72 undergraduates who were assigned to six conditions in which they performed (1) only preference judgments or choices, (2) preference judgments or choices preceded by judgments of attractiveness of attribute levels, or (3) preference judgments or choices accompanied by think-aloud reports. The results replicated (...) the prominence efTect for choices, but a prominence effect was also found for preference judgments. In accordance with the restructuring explanation, the think-aloud protocols indicated that options were more often restructured in choices than in preference judgments. However, restructuring could not explain the prominence effect observed for preference judgments. A modified compatibility hypothesis is offered as an alternative explanation. (shrink)

In the face of limited resources during the COVID-19 pandemic response, public health experts and ethicists have sought to apply guiding principles in determining how those resources, including vaccines, should be allocated.

Several studies have shown that preference is not necessarily synonymous with choice. In particular, the most preferred object from a set of objects presented in a non—choice context is not necessarily chosen when the same objects are options in a choice situation (Lichtenstein & Slovic, 1971, 1973; Tversky, Sattah, & Slovic, 1988) . Our research on the choice—preference discrepancy replicates these findings and thus bears some resemblance to the study by Tversky, Sattah, and Slovic (1988). Two competing explanations are tested.

In various contexts, it is thought to be important that we reason together. For instance, an attractive conception of democracy requires that citizens reach lawmaking decisions by reasoning with one another. Reasoning requires that reasoners survey the considerations that they take to be reasons, proceed by a coherent train of thought, and reach conclusions freely. De facto reliance on experts threatens the possibility of collective reasoning by making some reasons collectively unsurveyable, raising questions about the coherence of the resulting train (...) of thought. De jure reliance on experts threatens the possibility of collective reasoning by seeming to make some conclusions irreversible. The paper argues that collective reasoning that relies on experts would nonetheless be possible if the unsurveyable reasons "mesh," if the expert considerations are at least in principle publicly recoverable, and if de jure authority of expert decision is always subject to appeal. (shrink)

Direct-to-Consumer genomics has been a controversial topic for over a decade. Much work has been done on the legal issues it raises. This article asks a different question: What will DTC genomics and its legal issues look like in ten to twenty years? After discussing the five current uses of DTC genomics, it describes three current legal issues: medical uses, privacy of genomic information, and privacy in collection and analysis of human DNA. It then suggests that changes in human genomics (...) and how it is used will make the first of those DTC genomics legal issues less important in the future, but that the third will be increasingly significant. (shrink)

In her reply to Gershom Scholem’s criticism of Eichmann in Jerusalem: A Report on the Banality of Evil, Hannah Arendt writes.