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)
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.
Professor Grünbaum's much-discussed refutation of Zeno's metrical paradox turns out to be ad hoc upon close examination of the relevant portion of measure theory. Although the modern theory of measure is able to defuse Zeno's reasoning, it is not capable of refuting Zeno in the sense of showing his error. I explain why the paradox is not refutable and argue that it is consequently more than a mere sophism.
F. A. Hayek is uniquely responsible for his fellow economists grasping the importance of the decentralization of knowledge: as Hayek shows in his pathbreaking “The Use of Knowledge in Society,” knowledge nowhere exists as a coherent whole and to pretend otherwise is a most serious error. Hayek also shares responsibility for the popularity of a strong form of the methodological individualist research program which asserts that since collectives as such have no impact on the choices of individuals, investigators ought to (...) purge any reliance on collectives from our analysis. (shrink)
Democracy is not naturally plausible. Why turn such important matters over to masses of people who have no expertise? Many theories of democracy answer by appealing to the intrinsic value of democratic procedure, leaving aside whether it makes good decisions. In Democratic Authority, David Estlund offers a groundbreaking alternative based on the idea that democratic authority and legitimacy must depend partly on democracy's tendency to make good decisions.Just as with verdicts in jury trials, Estlund argues, the authority and legitimacy (...) of a political decision does not depend on the particular decision being good or correct. But the "epistemic value" of the procedure--the degree to which it can generally be accepted as tending toward a good decision--is nevertheless crucial. Yet if good decisions were all that mattered, one might wonder why those who know best shouldn't simply rule.Estlund's theory--which he calls "epistemic proceduralism"--avoids epistocracy, or the rule of those who know. He argues that while some few people probably do know best, this can be used in political justification only if their expertise is acceptable from all reasonable points of view. If we seek the best epistemic arrangement in this respect, it will be recognizably democratic--with laws and policies actually authorized by the people subject to them. (shrink)
Consciousness and Mind presents David Rosenthal's influential work on the nature of consciousness. Central to that work is Rosenthal's higher-order-thought theory of consciousness, according to which a sensation, thought, or other mental state is conscious if one has a higher-order thought that one is in that state. The first four essays develop various aspects of that theory. The next three essays present Rosenthal's homomorphism theory of mental qualities and qualitative consciousness, and show how that theory fits with and helps (...) sustain the HOT theory. A crucial feature of homomorphism theory is that it individuates and taxonomizes mental qualities independently of the way we're conscious of them, and indeed independently of our being conscious of them at all. So the theory accommodates the qualitative character not only of conscious sensations and perceptions, but also of those which fall outside our stream of consciousness. Rosenthal argues that, because this account of mental qualities makes no appeal to consciousness, it enables us to dispel such traditional quandaries as the alleged conceivability of undetectable quality inversion, and to disarm various apparent obstacles to explaining qualitative consciousness and understanding its nature. Six further essays build on the HOT theory to explain various important features of consciousness, among them the complex connections that hold in humans between consciousness and speech, the self-interpretative aspect of consciousness, and the compelling sense we have that consciousness is unified. Two of the essays, one an extended treatment of homomorphism theory, appear here for the first time. There is also a substantive introduction, which draws out the connections between the essays and highlights their implications. (shrink)
No mental phenomenon is more central than consciousness to an adequate understanding of the mind. Nor does any mental phenomenon seem more stubbornly to resist theoretical treatment. Consciousness is so basic to the way we think about the mind that it can be tempting to suppose that no mental states exist that are not conscious states. Indeed, it may even seem mysterious what sort of thing a mental state might be if it is not a conscious state. On this way (...) of looking at things, if any mental states do lack consciousness, they are exceptional cases that call for special explanation or qualification. Perhaps dispositional or cognitive states exist that are not conscious, but nonetheless count as mental states. (shrink)
Reasoned disagreement is a pervasive feature of public life, and the persistence of disagreement is sometimes troublesome, reflecting the need to make difficult decisions. Fogelin suggests that parties to a deep disagreement should abandon reason and switch to non-rational persuasion. But how are the parties to know when to make such a switch? I argue that Fogelin's analysis doesn't clearly address this question, and that disputes arising in areas like medical decision making are such that the parties to them have (...) reasons to act as if they can be rationally resolved even if they are deep. Fogelin's analysis is thus of limited value as regards the practical moral demand of addressing concrete moral dilemmas. (shrink)
This long-awaited book sets out the implications of Habermas's theory of communicative action for moral theory. "Discourse ethics" attempts to reconstruct a moral point of view from which normative claims can be impartially judged. The theory of justice it develops replaces Kant's categorical imperative with a procedure of justification based on reasoned agreement among participants in practical discourse.Habermas connects communicative ethics to the theory of social action via an examination of research in the social psychology of moral and interpersonal development. (...) He aims to show that our basic moral intuitions spring from something deeper and more universal than contingent features of our tradition, namely from normative presuppositions of social interaction that belong to the repertoire of competent agents in any society. JÃ¼rgen Habermas is Professor of Philosophy at the University of Frankfurt. (shrink)
This text addresses the profound human questions of love and work. Beginning with a historical introduction, the author progresses through adaptive problems that humans face, and concludes by showing how evolutionary psychology encompasses all branches of psychology.
"My work has had nothing to do with gay liberation," Michel Foucault reportedly told an admirer in 1975. And indeed there is scarcely more than a passing mention of homosexuality in Foucault's scholarly writings. So why has Foucault, who died of AIDS in 1984, become a powerful source of both personal and political inspiration to an entire generation of gay activists? And why have his political philosophy and his personal life recently come under such withering, normalizing scrutiny by commentators as (...) diverse as Camille Paglia, Richard Mohr, Bruce Bawer, Roger Kimball, and biographer James Miller? David M. Halperin's Saint Foucault is an uncompromising and impassioned defense of the late French philosopher and historian as a galvanizing thinker whose career as a theorist and activist will continue to serve as a model for other gay intellectuals, activists, and scholars. A close reading of both Foucault and the increasing attacks on his life and work, it explains why straight liberals so often find in Foucault only counsels of despair on the subject of politics, whereas gay activists look to him not only for intellectual inspiration but also for a compelling example of political resistance. Halperin rescues Foucault from the endless nature-versus-nurture debate over the origins of homosexuality ("On this question I have absolutely nothing to say," Foucault himself once remarked) and argues that Foucault's decision to treat sexuality not as a biological or psychological drive but as an effect of discourse, as the product of modern systems of knowledge and power, represents a crucial political breakthrough for lesbians and gay men. Halperin explains how Foucault's radical vision of homosexuality as a strategic opportunity for self-transformation anticipated the new anti-assimilationist, anti-essentialist brand of sexual identity politics practiced by contemporary direct-action groups such as ACT UP. Halperin also offers the first synthetic account of Foucault's thinking about gay sex and the future of the lesbian and gay movement, as well as an up-to-the-minute summary of the most recent work in queer theory. "Where there is power, there is resistance," Michel Foucault wrote in The History of Sexuality, Volume I. Erudite, biting, and surprisingly moving, Saint Foucault represents Halperin's own resistance to what he views as the blatant and systematic misrepresentation of a crucial intellectual figure, a misrepresentation he sees as dramatic evidence of the continuing personal, professional, and scholarly vulnerability of all gay activists and intellectuals in the age of AIDS. (shrink)
Contemporary mate preferences can provide important clues to human reproductive history. Little is known about which characteristics people value in potential mates. Five predictions were made about sex differences in human mate preferences based on evolutionary conceptions of parental investment, sexual selection, human reproductive capacity, and sexual asymmetries regarding certainty of paternity versus maternity. The predictions centered on how each sex valued earning capacity, ambition— industriousness, youth, physical attractiveness, and chastity. Predictions were tested in data from 37 samples drawn from (...) 33 countries located on six continents and five islands. For 27 countries, demographic data on actual age at marriage provided a validity check on questionnaire data. Females were found to value cues toresource acquisitionin potential mates more highly than males. Characteristics signalingreproductive capacitywere valued more by males than by females. These sex differences may reflect different evolutionary selection pressures on human males and females; they provide powerful cross-cultural evidence of current sex differences in reproductive strategies. Discussion focuses on proximate mechanisms underlying mate preferences, consequences for human intrasexual competition, and the limitations of this study. (shrink)
In considering the nature of properties four controversial decisions must be made. (1) Are properties universals or tropes? (2) Are properties attributes of particulars, or are particulars just bundles of properties? (3) Are properties categorical (qualitative) in nature, or are they powers? (4) If a property attaches to a particular, is this predication contingent, or is it necessary? These choices seem to be in a great degree independent of each other. The author indicates his own choices.
One phenomenon pertains roughly to being awake. A person or other creature is conscious when it's awake and mentally responsive to sensory input; otherwise it's unconscious. This kind of consciousness figures most often in everyday discourse.
Abstract While agreeing that dynamical models play a major role in cognitive science, we reject Stepp, Chemero, and Turvey's contention that they constitute an alternative to mechanistic explanations. We review several problems dynamical models face as putative explanations when they are not grounded in mechanisms. Further, we argue that the opposition of dynamical models and mechanisms is a false one and that those dynamical models that characterize the operations of mechanisms overcome these problems. By briefly considering examples involving the generation (...) of action potentials and circadian rhythms, we show how decomposing a mechanism and modeling its dynamics are complementary endeavors. (shrink)
Drawing on theory and research on ethical leadership and ethical climate, we examine ethical climate as a mediator of the relationship between ethical leadership and employee misconduct. Using a sample of 1,525 employees and their supervisors in 300 units in different organizations, we find support for our hypothesized model. We discuss theoretical and practical implications of these findings.
The emphasis is always on the arguments used, and the way one position develops from another. By the end of the book the reader is afforded both a grasp of the state of the controversy, and how we got there.
This anthology brings together readings mainly from contemporary philosophers, but also from writers of the past two centuries, on the philosophy of mind. Some of the main questions addressed are: is a human being really a mind in relation to a body; if so, what exactly is this mind and how it is related to the body; and are there any grounds for supposing that the mind survives the disintegration of the body?
This book explores food from a philosophical perspective, bringing together sixteen leading philosophers to consider the most basic questions about food: What is it exactly? What should we eat? How do we know it is safe? How should food be distributed? What is good food? David M. Kaplan’s erudite and informative introduction grounds the discussion, showing how philosophers since Plato have taken up questions about food, diet, agriculture, and animals. However, until recently, few have considered food a standard subject (...) for serious philosophical debate. Each of the essays in this book brings in-depth analysis to many contemporary debates in food studies—Slow Food, sustainability, food safety, and politics—and addresses such issues as “happy meat,” aquaculture, veganism, and table manners. The result is an extraordinary resource that guides readers to think more clearly and responsibly about what we consume and how we provide for ourselves, and illuminates the reasons why we act as we do. (shrink)