In this paper we argue that there is a large class of expressions, typified by ‘plastic flower’, ‘stuffed animal’ and ‘kosher bacon’, that have a unique semantics combining compositional, idiomatic and decompositional interpretation. These expressions are compositional because their constituents contribute their meanings to the meanings of the wholes; they are idiomatic because their interpretation involves assigning dictionary entries to non-terminal elements in their syntactic structure; and they are decompositional because their meanings have proper parts that are not the meanings (...) of any of their syntactic constituents. We argue that extensionalist semantics, on which the meaning of an expression is a function from domains to extensions in those domains, cannot provide an adequate account of the semantics of these expressions, and that supplementation with a theory of pragmatic interpretation does not improve the situation. We show how our account explains the intensionality and the productivity of these expressions. (shrink)

First published in 1999. Routledge is an imprint of Taylor & Francis, an informa company.

Significant disagreement remains in ethics about the duties we have towards wild animals. This paper aims to mediate those disagreements by exploring how they are supported by, or diverge from, the common-sense ethical principles of non-maleficence, beneficence, autonomy and justice popular in medical ethics. We argue that these principles do not clearly justify traditional conservation or a ‘hands-off ’ approach to wild-animal welfare; instead, they support natural negative duties to reduce the harms that we cause as well as natural positive (...) duties to promote the welfare of wild animals. (shrink)

This paper examines the impact of a week-long philosophy summer camp on middle and high school-age youth with specific attention paid to the development of intellectual humility in the campers. In June 2016 a university in Texas hosted its first philosophy summer camp for youth who had just completed sixth through twelfth grades. Basing our camp on the pedagogical model of the Philosophy for Children program, our aim was specifically to develop a community of inquiry among the campers, providing them (...) with a safe intellectual space to be introduced to philosophy and philosophical discussion. In 2017 we launched a formal longitudinal study to determine what impact a week-long philosophy summer camp would have on teens and tweens. Examining quantitative and qualitative data collected from 2016–2020, we found that the camp has had a significant impact on the teenagers who have attended. In particular, we found that intellectual humility increased over the duration of their camp experience and that this increase correlates with an increased affinity for philosophy and philosophical discussion. (shrink)

For at least the past 15 years, food safety stakeholders across all levels of government have recognized the critical role that state and local agencies play in our nation's food safety system. State and local agencies are the first responders to foodborne outbreaks and have primary responsibility for keeping their residents safe from foodborne disease through effective surveillance and rapid response to outbreaks. They also conduct the vast majority of food safety inspections across the nation's restaurants, grocery stores, and other (...) food service and food retail establishments.Recent efforts among industry and government officials alike have focused on creating a more integrated, prevention-oriented food safety system. The Food Safety Modernization Act, the first major overhaul of the nation's food safety laws since the 1930s, now mandates that most sectors of the food industry put preventive controls in place, changing the emphasis of what the FDA does from response to prevention. (shrink)

Worldwide, the COVID-19 pandemic has forced people to adapt quickly, and to reexamine interactions and responsibilities toward communities in creative ways. This paper presents a qualitative media analysis of 50 online news articles published between March 17th and August 6th, 2020 using the key-words “creativity” and “COVID-19.” Informed by a definition of creativity as actions that are considered both “new” and “appropriate”, articles describing a “creative action” were kept for analysis. These articles highlight creative responses to the COVID-19 quarantine in (...) various domains including architecture, fashion, and faith. In this paper, we discuss the themes derived during this analysis- “renewal and continuity” and “the multidimensionality of creativity” which elaborate and contextualize a perspective of socio-cultural creativity theory and propose two implications of this study. The first implication posits that creativity was an observable, cultural response to the COVID-19 pandemic. The second implication offers a broader concept of how cultural resources function as dynamic constraints or “affordances” within the Five A’s model of creativity. Discussion of further research through the lens of socio-cultural creativity is discussed. (shrink)

Foundations of Science recently published a rebuttal to a portion of our essay it published 2 years ago. The author, G. Schubring, argues that our 2013 text treated unfairly his 2005 book, Conflicts between generalization, rigor, and intuition. He further argues that our attempt to show that Cauchy is part of a long infinitesimalist tradition confuses text with context and thereby misunderstands the significance of Cauchy’s use of infinitesimals. Here we defend our original analysis of various misconceptions and misinterpretations concerning (...) the history of infinitesimals and, in particular, the role of infinitesimals in Cauchy’s mathematics. We show that Schubring misinterprets Proclus, Leibniz, and Klein on non-Archimedean issues, ignores the Jesuit context of Moigno’s flawed critique of infinitesimals, and misrepresents, to the point of caricature, the pioneering Cauchy scholarship of D. Laugwitz. (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)

The widespread idea that infinitesimals were “eliminated” by the “great triumvirate” of Cantor, Dedekind, and Weierstrass is refuted by an uninterrupted chain of work on infinitesimal-enriched number systems. The elimination claim is an oversimplification created by triumvirate followers, who tend to view the history of analysis as a pre-ordained march toward the radiant future of Weierstrassian epsilontics. In the present text, we document distortions of the history of analysis stemming from the triumvirate ideology of ontological minimalism, which identified the continuum (...) with a single number system. Such anachronistic distortions characterize the received interpretation of Stevin, Leibniz, d’Alembert, Cauchy, and others. (shrink)

First Published in 1999. Routledge is an imprint of Taylor & Francis, an informa company.

To explore the extent of embeddability of Leibnizian infinitesimal calculus in first-order logic (FOL) and modern frameworks, we propose to set aside ontological issues and focus on pro- cedural questions. This would enable an account of Leibnizian procedures in a framework limited to FOL with a small number of additional ingredients such as the relation of infinite proximity. If, as we argue here, first order logic is indeed suitable for developing modern proxies for the inferential moves found in Leibnizian infinitesimal (...) calculus, then modern infinitesimal frameworks are more appropriate to interpreting Leibnizian infinitesimal calculus than modern Weierstrassian ones. (shrink)

First Published in 1999. Routledge is an imprint of Taylor & Francis, an informa company.

The first half of the 17th century was a time of intellectual ferment when wars of natural philosophy were echoes of religious wars, as we illustrate by a case study of an apparently innocuous mathematical technique called adequality pioneered by the honorable judge Pierre de Fermat, its relation to indivisibles, as well as to other hocus-pocus. André Weil noted that simple applications of adequality involving polynomials can be treated purely algebraically but more general problems like the cycloid curve cannot be (...) so treated and involve additional tools–leading the mathematician Fermat potentially into troubled waters. Breger attacks Tannery for tampering with Fermat’s manuscript but it is Breger who tampers with Fermat’s procedure by moving all terms to the left-hand side so as to accord better with Breger’s own interpretation emphasizing the double root idea. We provide modern proxies for Fermat’s procedures in terms of relations of infinite proximity as well as the standard part function. (shrink)

Adequality, or παρισóτης (parisotēs) in the original Greek of Diophantus 1 , is a crucial step in Fermat’s method of finding maxima, minima, tangents, and solving other problems that a modern mathematician would solve using infinitesimal calculus. The method is presented in a series of short articles in Fermat’s collected works (1891, pp. 133–172). The first article, Methodus ad Disquirendam Maximam et Minimam 2 , opens with a summary of an algorithm for finding the maximum or minimum value of an (...) algebraic expression in a variable A. For convenience, we will write such an expression in modern functional notation as f (a). 3 The algorithm can be broken up into six steps in the following way:Introduce an auxiliary .. (shrink)

The philosophy of deep ecology originated in the 1970s with the Norwegian philosopher Arne Naess and has since spread around the world. Its basic premises are a belief in the intrinsic value of nonhuman nature, a belief that ecological principles should dictate human actions and moral evaluations, an emphasis on noninterference into natural processes, and a critique of materialism and technological progress.This book approaches deep ecology as a philosophy, not as a political, social, or environmental movement. In part I, the (...) authors compare deep ecology's philosophical ideas with other positions and debates in environmental philosophy and to other schools of thought such as social ecology, ecofeminism, and moral pluralism. In part II, they investigate the connections between deep ecology and other contemporary world views, such as continental philosophy, postmodernism, and non-Western philosophical traditions. The first anthology on deep ecology that is not primarily the work of the movement's followers, Beneath the Surface offers a rigorous assessment of deep ecology's strengths and weaknesses as a philosophical position.Contributors : John Clark, Deane Curtin, Arran Gare, William Grey, Mathew Humphrey, Knut Jacobsen, Eric Katz, Andrew Light, Jonathan Maskit, Val Plumwood, David Rothenberg, Ariel Salleh, Bron Taylor, Michael Zimmerman. (shrink)

The Dirac δ function has solid roots in nineteenth century work in Fourier analysis and singular integrals by Cauchy and others, anticipating Dirac’s discovery by over a century, and illuminating the nature of Cauchy’s infinitesimals and his infinitesimal definition of δ.

I develop and defend a hedonistic view of the constitution of human subjectivity, agency and value, while disassociating it from utilitarian accounts of morality and from the view that only pleasure is desired. Chapter One motivates the general question, "What really is of value in human living?", and introduces evaluative hedonism as an answer to this question. Chapter Two argues against preference satisfaction accounts of pleasure and of welfare, and begins the explication and defense of the hedonist's conception of pleasure (...) as immediate experiencing liked for its own sake in its experiential moment, and which obtains or not in an experiential moment regardless of what obtains at other times. Chapter Three begins the task of finding a motivational theory that will support, or at least cohere with, evaluative hedonism. I here work toward my own position by discussing, criticizing and distinguishing some aspects of the views of earlier hedonistic writers, both ancient and modern. Chapter Four further explains the hedonist's conception of pleasure, and treats some contextualist objections to its tenability suggested by Plato, Moore and Anscombe. In the course of answering these objections, the view of consciousness belonging to the hedonist's view of mind is contrasted with that which the objections presuppose. Chapter Five first outlines the general kind of hedonistic view resulting from the work of the earlier sections, and then develops a specific view of this kind, drawing on contemporary work in philosophy, psychology and psychobiology. The result is an account of action, and of the kind of attention and consciousness connected with it, in which pleasure has a central organizing role. Such an account, if sustained and filled out by ongoing scientific work, would further motivate, and cohere with, evaluative hedonism and the related contention that the dimension of subjectivity in which human value consists is in the lives of human beings and other higher vertebrates much the same. (shrink)

Despite their diversity and ecological importance, many areas of the SAR—Stramenopila, Alveolata, and Rhizaria—clade are poorly understood as the majority of SAR species lack molecular data and only 5% of species are from well-sampled families. Here, we review and summarize the state of knowledge about the three major clades of SAR, describing the diversity within each clade and identifying synapomorphies when possible. We also assess the “dark area” of SAR: the morphologically described species that are missing molecular data. The majority (...) of molecular data for SAR lineages are characterized from marine samples and vertebrate hosts, highlighting the need for additional research effort in areas such as freshwater and terrestrial habitats and “non-vertebrate” hosts. We also describe the paucity of data on the biogeography of SAR species, and point to opportunities to illuminate diversity in this major eukaryotic clade. See also the video abstract here: https://youtu.be/_VUXqaX19Rw. Despite their diversity, abundance, and importance, fewer than 10% of the species within the SAR—Stramenopila, Alveolata, and Rhizaria—clade have been assessed using molecular tools. Only a small percentage of the molecular records contain information on ecology or have associate location data, indicating a tremendous dark area. (shrink)

We argue in favour of the general proposition that the nature of reasoning is best understood within a context of its origins and development. A major dimension of what develops in the years from childhood to adulthood, we propose, is increasing meta-level monitoring and management of cognition. Two domains are examined in presenting support for these claims—multivariable causal reasoning and argumentive reasoning.

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)

Many historians of the calculus deny significant continuity between infinitesimal calculus of the seventeenth century and twentieth century developments such as Robinson’s theory. Robinson’s hyperreals, while providing a consistent theory of infinitesimals, require the resources of modern logic; thus many commentators are comfortable denying a historical continuity. A notable exception is Robinson himself, whose identification with the Leibnizian tradition inspired Lakatos, Laugwitz, and others to consider the history of the infinitesimal in a more favorable light. Inspite of his Leibnizian sympathies, (...) Robinson regards Berkeley’s criticisms of the infinitesimal calculus as aptly demonstrating the inconsistency of reasoning with historical infinitesimal magnitudes. We argue that Robinson, among others, overestimates the force of Berkeley’s criticisms, by underestimating the mathematical and philosophical resources available to Leibniz. Leibniz’s infinitesimals are fictions, not logical fictions, as Ishiguro proposed, but rather pure fictions, like imaginaries, which are not eliminable by some syncategorematic paraphrase. We argue that Leibniz’s defense of infinitesimals is more firmly grounded than Berkeley’s criticism thereof. We show, moreover, that Leibniz’s system for differential calculus was free of logical fallacies. Our argument strengthens the conception of modern infinitesimals as a development of Leibniz’s strategy of relating inassignable to assignable quantities by means of his transcendental law of homogeneity. (shrink)

In his 1676 text De Quadratura Arithmetica, Leibniz distinguished infinita terminata from infinita interminata. The text also deals with the notion, originating with Desargues, of the point of intersection at infinite distance for parallel lines. We examine contrasting interpretations of these notions in the context of Leibniz’s analysis of asymptotes for logarithmic curves and hyperbolas. We point out difficulties that arise due to conflating these notions of infinity. As noted by Rodríguez Hurtado et al., a significant difference exists between the (...) Cartesian model of magnitudes and Leibniz’s search for a qualitative model for studying perspective, including ideal points at infinity. We show how respecting the distinction between these notions enables a consistent interpretation thereof. (shrink)

The way Leibniz applied his philosophy to mathematics has been the subject of longstanding debates. A key piece of evidence is his letter to Masson on bodies. We offer an interpretation of this often misunderstood text, dealing with the status of infinite divisibility in nature, rather than in mathematics. In line with this distinction, we offer a reading of the fictionality of infinitesimals. The letter has been claimed to support a reading of infinitesimals according to which they are logical fictions, (...) contradictory in their definition, and thus absolutely impossible. The advocates of such a reading have lumped infinitesimals with infinite wholes, which are rejected by Leibniz as contradicting the part–whole principle. Far from supporting this reading, the letter is arguably consistent with the view that infinitesimals, as inassignable quantities, are mentis fictiones, i.e., (well-founded) fictions usable in mathematics, but possibly contrary to the Leibnizian principle of the harmony of things and not necessarily idealizing anything in rerum natura. Unlike infinite wholes, infinitesimals—as well as imaginary roots and other well-founded fictions—may involve accidental (as opposed to absolute) impossibilities, in accordance with the Leibnizian theories of knowledge and modality. (shrink)

A recent online article in the Journal of Medical Ethics, which received wide media coverage, raised the possibility that children are being ‘subjected to torture’ due to the ‘fervent or fundamentalist views’ of their parents. However, the quality of argument in that article was inadequate to sustain such a radical thesis. There was no engagement with the perspectives of different religious traditions about end-of-life care. Instead the authors invoked practices such as male infant circumcision which are wholly irrelevant to the (...) end-of-life theme. There were serious failings in relation to core principles of social and epidemiological research practice: the study based its conclusion on a sample of only six cases and failed to consider even the more obvious confounding features. Rather than demonizing the religious beliefs of parents there should be recognition of the need for mutual respect, dialogue based on an ‘expert–expert relationship’ and collaboration based on ‘shared understanding’. (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 ...

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)