This book is about "diamond", a logic of paradox. In diamond, a statement can be true yet false; an "imaginary" state, midway between being and non-being.

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)

The moral of Buridan's Ass is that it can sometimes be rational to perform one action rather than another even though one lacks stronger reason to do so. Yet it is also commonly believed that it cannot ever be rational to believe one proposition rather than another if one lacks stronger reason to do so. This asymmetry has been taken to indicate a deep difference between epistemic and practical rationality. According to the view articulated here, the asymmetry should instead be (...) explained by the difference between rational intentions and rational actions. Thus, it turns out, Buridan's Ass-style cases do not indicate an asymmetry between epistemic and practical rationality as such. (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 conducts a mixed-method content analysis of Chinese and American news media coverage of Google DeepMind’s Go playing computer program, AlphaGo. Drawing on humanistic approaches to artificial intelligence, combined with an empirically rigorous content analysis, it examines the differences and overlap in coverage by the Chinese and American press in their accounts of AlphaGo, and its historic match with Korea’s Lee Sedol in March, 2016. The event was not only followed intensely in China, but also made the front page (...) of The New York Times. This article finds that the Chinese press was more likely than the American press to frame AlphaGo as non-threatening, which the authors attribute to cultural differences and the two countries' different understandings of Go. In addition to quantitatively identifying similarities and differences in the framing of AlphaGo, this paper also investigates the underlying and evolving contestations over what constitutes the “human” and the “machine.” It concludes by discussing the implications of the study’s findings as well as outlining avenues for further research. (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)

Identifying the determinants of reproductive success in small-scale societies is critical for understanding how natural selection has shaped human evolution and behavior. The available evidence suggests that status-accruing behaviors such as hunting and prosociality are pathways to reproductive success, but social egalitarianism may diminish this pathway. Here we introduce a mixed longitudinal/cross-sectional dataset based on 45 years of research with the Batek, a population of egalitarian rain forest hunter-gatherers in Peninsular Malaysia, and use it to test the effects of four (...) predictors of lifetime reproductive success: foraging return rate, sharing proclivity, cooperative foraging tendency, and kin presence. We found that none of these factors can explain variation in lifetime reproduction among males or females. We suggest that social egalitarianism, combined with strikingly low infant and juvenile mortality rates, can mediate the pathway between foraging, status-accruing behavior, and reproductive success. Our approach advocates for greater theoretical and empirical attention to quantitative social network measures, female foraging, and fitness outcomes. (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.

Alan Moore and Dave Gibbons’ Watchmen may be the most acclaimed graphic novel of the twentieth century. This chapter examines how it explores two metaphysical questions: What is the nature of time? Does free will exist? Moore and Gibbons explore these questions together, illuminating connections between time and free will through connections between the graphic novel’s form and content. The chapter introduces three views of the nature of time: presentism, the view that only the present exists; growing-universe theory, the view (...) that only the present and past exist; and eternalism, the view that past, present, and future exist. Because of Moore and Gibbons’ distinct use of images and words within the visual structure and their depiction of a character who is simultaneously aware of past, present, and future events, the chapter deduces that the operative view in Watchmen is eternalism. After discussing three views of the existence of free will, the chapter then argues that eternalism entails that people could not have acted otherwise than they actually acted. Hence the operative view in Watchmen is either determinism, according to which no one has free will because no one could have done otherwise, or compatibilism, according to which people can have free will because having it merely requires having acted. The chapter concludes that the operative view is compatibilism. Finally it responds to the objection that compatibilism is mistaken. If no one could have done otherwise, then determinism must be true. (shrink)

A revised version of Nathaniel Chipman's Sketches of the Principles of Government (1793), this early treatise on the underlying principles of American government addresses civil laws and obligations, the social state, rights of property, sovereignty and political power. An important early contribution to American constitutional law, it is also interesting for its Federalist perspective on the evolutions of political institutions from Washington to Jackson.Nathaniel Chipman [1752-1843] was a leading Vermont Federalist who was instrumental in that state's admission to (...) the Union. He became Vermont's chief Justice and went on to represent Vermont in the U.S. Senate. He was also one of America's first significant legal writers.One of his books, the Reports and Dissertations (1793) is included in Warren's list of "the four general works on the Common Law... [of] permanent value in American Legal Literature.": Warren, A History of the American Bar 335-336. See Cohen, Bibliography of Early American Law 5752, Sabin, A Dictionary of Books Relating to America 12824, Dictionary of American Biography II:73-74. (shrink)

The "two-envelopes" problem has stimulated much discussion on probabilistic reasoning, but relatively little experimentation. The problem specifies two identical envelopes, one of which contains twice as much money as the other. You are given one of the envelopes and the option of keeping it or trading for the other envelope. Variables of interest include the possible amounts of money involved, what is known about the process by which the amounts of money were assigned to the envelopes, and whether you are (...) allowed to know how much money is in the envelope in hand before deciding whether to keep or trade. In an earlier study, Butler and Nickerson found that when participants were allowed to know how much was in the envelope in hand, they generally elected to trade if that amount was small relative to the range of possibilities and to keep otherwise. The present experiments showed that this propensity was independent of the amount of money in the envelopes. Participants made decisions with a strong bias for avoiding the risk of losing by trading, particularly when the amount in hand was known and large relative to the range of possible amounts, regardless of the absolute value of the gamble. The results illustrate the dependence of thinking on the context in which it occurs, and demonstrate a tendency to treat quantities that are large or small relative to a particular context in which they are encountered as though they were large or small in a more general sense. (shrink)

BackgroundThe terminal illness of late-stage Alzheimer’s and related dementias is progressively cruel, burdensome, and can last years if caregivers assist oral feeding and hydrating. Options to avoid prolonged dying are limited since advanced dementia patients cannot qualify for Medical Aid in Dying. Physicians and judges can insist on clear and convincing evidence that the patient wants to die—which many advance directives cannot provide. Proxies/agents’ substituted judgment may not be concordant with patients’ requests. While advance directives can be patients’ last resort (...) to attain a peaceful and timely dying consistent with their lifelong values, success depends on their being effective and acceptable. A single flaw can provide opponents justification to refuse the directive’s requests to cease assisted feeding.AimThis article considers 24 common advance directive flaws in four categories. Process flaws focus on how patients express their end-of-life wishes. Content flaws reflect drafters’ selection of conditions and interventions, and how they are described. Inherent flaws can make advance directives unacceptable to authorities concerned about premature dying. Strategies are needed to compel physicians to write needed orders and to prevent third parties from sabotaging these orders after they are implemented. The article includes excerpts from “dementia-specific” directives or supplements that exemplify each flaw—mostly from the US and Europe. No directive critiqued here included an effective strategy to resolve this long-debated bioethical conflict: the past directive requests “Cease assisted feeding” but the incapacitated patient apparently expresses the desire to “Continue assisted feeding.” Some opponents to the controversial request, cease assisted feeding, use this conflict as a conceptual wedge to practice hard paternalism. This article proposes a protocol to prevent this conflict from emerging. These strategies may prevent authorities from requiring patients to fulfill authorities’ additional clinical criteria as a prerequisite to honor the requests in patients directives.ConclusionThis critique of flaws may serve as a guide to drafting and to selecting effective and acceptable advance directives for dementia. It also poses several bioethical and clinical questions to those in authority: Does your paternalistic refusal to honor patients’ wishes respect their self-determination? Protect vulnerable patients from harm? Force patients to endure prolonged suffering? Violate the principles of bioethics? Violate the very foundation of patient-centered care? (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)

Yes, Roya, a 2016 graphic novel written by C. Spike Trotman and illustrated by Emilee Denich, depicts Roya, a woman of color who writes and illustrates a comic strip; Joe, a white man who gave up his career after meeting Roya, who now publishes under his name; and Wylie, a young white man starting in the profession. Roya completely dominates Joe’s career, making it hers. She also partly dominates Wylie’s, acting as his mentor. Roya dominates Joe and Wylie personally too. (...) She is their sexual dominant, and they are her submissives. Professionally and personally, moreover, Joe and Wylie each submit to Roya consensually. Further, though Roya both writes and illustrates her comic strip, often writer and illustrator differ. The former, creating the story, dominates the latter, illustrating the story after the fact – as Trotman and Denich themselves did consensually via a contract when creating their graphic novel. Hence Yes, Roya highlights domination and submission in comics creation and in sex. More than that, the graphic novel also presents both kinds of domination and submission as ethical. Because Aristotle, Kant, and Mill are the most influential ethicists in the Western tradition, this chapter investigates how each could accommodate such professional and personal dominant/submissive relationships in their philosophy. (shrink)

When world’s most famous taxidermist, Carl Akeley, died in 1926, many obituaries cited his consummate skill and innovative technique, often arguing that he had elevated taxidermy from a craft to an art. Such claims notwithstanding, taxidermy tends still to be considered as a craft. While scholars have studied the various ways in which taxidermy has been deployed within art practices – to critique gender, colonialism and concepts of mortality – late nineteenth- and early twentieth-century attempts to classify it as a (...) fine art failed. This critical and historical asymmetry frames the following article, which explores what it tells us about how art is conceived today. I argue that taxidermy ‘failed’ as a form of art not because its procedures were distasteful, nor because its practice lacked the skill and vision an art might require. Rather, taxidermy remains outside of art due to a confluence of historical shifts in art practice and theory in the late nineteenth century, particularly those associated with the rise of instant photography and the advent of the snapshot. In this context, the making and display of taxidermied specimens entailed tensions – between ideal and real, type and example, multiple and singular, index and object – that were and remain central to photography and art. But, unlike photography, around which art historians have developed a sophisticated discourse, taxidermy lacks a critical vocabulary. Importantly, I argue, the taxidermied animal’s status involves no author-function, thus throwing into question methods of production and display. And, in light of this, I delineate taxidermy’s ‘failure’ in order to elucidate some of the tacit exclusions enacted by art history, particularly with regard to works that simultaneously reveal and negate their own manufacture. (shrink)

In a recent series of lectures delivered at the Institute of Fine Arts and the Frick Collection, Michael Ann Holly highlighted a moment in the 1950s when, she argues, art history made a pivotal choice, opting to follow Erwin Panofsky’s iconographic system of interpretation, based in a neo-Kantian historical distance, rather than Hans-Georg Gadamer’s theory of immediacy of experience.1 The dichotomy between visual experience and contextualization that Holly implicitly posits in her lecture suggests a long-standing tension in the historiography of (...) art history. Holly’s argument that Gadamer is a forgotten founder figure for the discipline of art history is a compelling one, not only for art history but, as I... (shrink)

In several articles, Mumma has presented a formal diagrammatic system Eu meant to give an account of one way in which Euclid's use of diagrams in the Elements could be formalized. However, largely because of the way in which it tries to limit case analysis, this system ends up being inconsistent, as shown here. Eu also suffers from several other problems: it is unable to prove several wide classes of correct geometric claims and contains a construction rule that is probably (...) computationally intractable and that may not even be decidable. (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.

Call the epistemological grounds on which we rationally should determine our ontological (or alethiological) commitments regarding an entity its arbiter of existence (or arbiter of truth). It is commonly thought that arbiters of existence and truth can be provided by our practices. This paper argues that such views have several implications: (1) the relation of arbiters to our metaphysical commitments consists in indispensability, (2) realist views about a kind of entity should take the kinds of practices providing that entity’s arbiters (...) to align with respect to their metaphysical dependencies, (3) if realists take a kind of practice to provide grounds on which to affirm the existence of a kind of entity, they should turn to those same grounds when seeking to provide an epistemology of the relevant domain. (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)

John Rawls’s 1980 Dewey Lectures are widely acknowledged to represent the locus classicus for contemporary discussions of moral constructivism. Nevertheless, few published works have engaged with the significant interpretive challenges one finds in these lectures, and those that have fail to offer a satisfactory reading of the view that Rawls presents there or the place the lectures occupy in the development of Rawls's thinking. Indeed, there is a surprising lack of consensus about how best to interpret the constructivism of these (...) lectures. In this paper, I argue that the constructivism presented in the Dewey Lectures is best understood as involving the view that moral truth is correspondence with procedurally-determined, stance-dependent facts. Employing Rawls’s discussion of rational intuitionism as a foil, I defend this reading against textual discrepancies from within the lectures, as well as those one finds across Rawls’s other works. In addition to settling interpretive disputes, I draw out the ways in which this understanding of Kantian constructivism fits within the broader comparative project in ‘moral theory’ that Rawls inherits from Sidgwick. (shrink)