Animals and War: Confronting the Military-Animal Industrial Complex is the first book to examine how nonhuman animals are used in war and the military. Animals and War contributes significantly to the fields of social justice, animal rights, and anti-war/peace activist communities. This book also will be read by peace, conflict, social justice, and critical animal studies scholars, students, and practitioners.
The opening argument in the Metaphysics M.2 series targeting separate mathematical objects has been dismissed as flawed and half-hearted. Yet it makes a strong case for a point that is central to Aristotle’s broader critique of Platonist views: if we posit distinct substances to explain the properties of sensible objects, we become committed to an embarrassingly prodigious ontology. There is also something to be learned from the argument about Aristotle’s own criteria for a theory of mathematical objects. I hope to (...) persuade readers of Metaphysics M.2 that Aristotle is a more thoughtful critic than he is often taken to be. (shrink)
Books M and N of Aristotle's Metaphysics receive relatively little careful attention. Even scholars who give detailed analyses of the arguments in M-N dismiss many of them as hopelessly flawed and biased, and find Aristotle's critique to be riddled with mistakes and question-begging. This assessment of the quality of Aristotle's critique of his predecessors (and of the Platonists in particular), is widespread. The series of arguments in M 2 (1077a14-b11) that targets separate mathematical objects is the subject of particularly strong (...) criticism by Annas and Ross. Two related arguments in this series (1077a14-20 and 1077a24-31) will serve as cases in point. The principal charges made against these arguments (that Aristotle misunderstands or misrepresents his opponents' views, and that he engages in question-begging because he presupposes his own metaphysical views) are frequently made against Aristotle's critique of Platonist positions more generally. If, as I argue, these charges are false for our two test case arguments, then there is good reason to think that they might also be false when they are leveled against the other arguments in this M 2 series. And, although presenting an argument for this is beyond the scope of this paper, this suggests that these two charges are more often than not false when applied to Aristotle's critique of Platonist mathematical views in M-N and beyond. (shrink)
Ethical self-management; an introduction to systematic personality psychology, by M. C. Katz.--Four axiological proofs of the infinite value of man, by R. S. Hartman.--Some thoughts regarding the current philosophy of the behavioral sciences, by C. R. Rogers.--Autonomy and community, by D. Lee.--Synergy in the society and in the individual, by A. H. Maslow.--Human nature: its cause and effect; a theoretical framework for understanding human motivation, by M. C. Katz.--Mental health; a generic attitude, by G. W. Allport.--Love feelings in (...) courtship couples; an analysis, by R. P. Hattis.--Economic policies and human well-being, by W. A. Weisskopf.--The great transformation, by H. F. W. Perk.--Contingencies of reinforcement in the design of a culture, by B. F. Skinner.--For further reading. (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)
Did Leibniz exploit infinitesimals and infinities à la rigueur or only as shorthand for quantified propositions that refer to ordinary Archimedean magnitudes? Hidé Ishiguro defends the latter position, which she reformulates in terms of Russellian logical fictions. Ishiguro does not explain how to reconcile this interpretation with Leibniz’s repeated assertions that infinitesimals violate the Archimedean property (i.e., Euclid’s Elements, V.4). We present textual evidence from Leibniz, as well as historical evidence from the early decades of the calculus, to undermine Ishiguro’s (...) interpretation. Leibniz frequently writes that his infinitesimals are useful fictions, and we agree, but we show that it is best not to understand them as logical fictions; instead, they are better understood as pure fictions. (shrink)
Felix Klein and Abraham Fraenkel each formulated a criterion for a theory of infinitesimals to be successful, in terms of the feasibility of implementation of the Mean Value Theorem. We explore the evolution of the idea over the past century, and the role of Abraham Robinson's framework therein.
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)
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)
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.
Microscopy has revealed tremendous diversity of bacterial and eukaryotic forms. Recent molecular analyses show discordance in estimates of biodiversity between morphological and molecular analyses. Moreover, phylogenetic analyses of the diversity of microbial forms reveal evidence of convergence at scales as deep as interdomain: morphologies shared between bacteria and eukaryotes. Here, we highlight examples of such discordance, focusing on exemplary lineages such as testate amoebae, ciliates, and cyanobacteria. These have long histories of morphological study, enabling deeper analyses on both the molecular (...) and morphological sides. We discuss examples in two main categories: (i) morphologically identical (or highly similar) individuals that are genetically distinct and (ii) morphologically distinct individuals that are genetically the same. We argue that hypotheses about discordance can be tested using the concept of neutral morphologies, or more broadly neutral phenotypes, as a null hypothesis. -/- . (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)
The inaugural collection in an exciting new exchange between philosophers and geographers, this volume provides interdisciplinary approaches to the environment as space, place, and idea. Never before have philosophers and geographers approached each other's subjects in such a strong spirit of mutual understanding. The result is a concrete exploration of the human-nature relationship that embraces strong normative approaches to environmental problems.
In the first, sweeping volume of The Venture of Islam, the late Marshall Hodgson recalls the Riddah Wars, fought in the 7th century between the brethren over the right to transmit the true legacy of the Prophet. Herbert Marcuse is as far from Mohammed as the deserts of America are from those of Arabia, but since his death in 1979, the familiar archetype has been playing itself out. At the head of the legions of the faithful rides the indomitable Douglas (...) Kellner, who for years has waged a single-minded campaign to clear the field of competition. Kellner has always concluded his polemics with a promise: the damage these pretenders have wrought is not yet irreversible, consequently, “Marcuse's legacy still awaits comprehensive and systematic treatment,” “an adequate appraisal of Marcuse's thought and legacy remains to be done.”. (shrink)