Evaluation of the influence of Hayden White on the theory of history is made difficult by his preference for the essay form, valued for its experimental character, and by the need to find comparable data. A quantitative study of citations of his work in English and foreign-language journals, 1973–1993, reveals that although historians were prominent among early readers of Metahistory, few historical journals reviewed White's two subsequent collections of essays and few historians-except in Germany-cited them. Those historians who (...) did tended still to cite Metahistory and often the parts of it devoted specifically to nineteenth-century historians.Literary critics, on the other hand, were relatively late to discover White, but during the "narrative turn" of the 1970s and 1980s his work was important for students of the novel and the theater. Recognition of it was especially marked in Spanish-speaking countries and in Germany.As a result, salient themes of White's later work-the ideological and political import of narrativization, the "historical sublime," and writing in the "middle voice"-have largely gone unremarked by historians and philosophers. Both these groups have tended to be irritated by White's bracketing of questions of historical epistemology; some have accused him of effacing the line between fiction and history, while White's numerous literary readers have generally applauded his tendencies in this direction. White however has consistently maintained that there is a difference, although not the one conventionally postulated. His exploration of writing in the "middle voice" brings his work full circle, in that it promises a "modernist" realism appropriate for representing the "sublime" events of our century. (shrink)

This volume contains all of the presidential addresses given before the American Society for Value Inquiry since its first meeting in 1970. Contributions are by Richard Brandt*, Virgil Aldrich*, John W. Davis*, the late Robert S. Hartman*, James B. Wilbur*, the late William H. Werkmeister, Robert E. Carter, the late William T. Blackstone, Gene James, Eva Hauel Cadwallader, Richard T. Hull, Norman Bowie*, Stephen White*, Burton Leiser+, Abraham Edel, Sidney Axinn, Robert Ginsberg, Patricia Werhane, Lisa M. Newton, (...) Thomas Magnell, Sander Lee, John M. Abbarno, Ruth Miller Lucier, and Tom Regan*. Autobiographical sketches* by all of the living contributors and one recently deceased, biographical statements of the remainder, together with photographic portraits of all the contributors*, make this volume a unique record of value inquiry during the past quarter century. __. (shrink)

The development of Louis Mink's philosophy of history is traced beginning with his classic essay "The Autonomy of Historical Understanding" and culminating in "Narrative Form as a Cognitive Instrument". Mink's thoughts on history during this period were marked by an everdeepening interest in the textuality and intertextuality of historical accounts, in the modes of representation which historians adopt and use to produce their "reality effects," and in the effort to mediate between what he was to call the New Rhetorical Relativism (...) and the claim that histories are in some sense true. Mink's response to Hempel's "The Function of General Laws in History," the beginning of Mink's consideration of narrative in "The Autonomy of Historical Understanding" and later in "History and Fiction as Modes of Comprehension," his association with Hayden White, his critique of a paper by Arno Mayer, and the beginning of Mink's final thoughts in "History and Narrative" and "Narrative Form as a Cognitive Instrument" are considered in elaborating the development of Mink's philosophy of history. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:390 HUME'S DIALOGUES AND THE COMEDY OF RELIGION Laughter is the key to Hume's Dialogues Concerning Natural Religion. Indeed, I would suggest that if the Dialogues have not made one laugh, and if one has not experienced the sheer delight of Hume's rhetorical excesses and gaiety, then one hasn't really understood this work at all. From this perspective, the usual questions are irrelevant — Is Hume Cleanthes or Philo? (...) Is Philo a mitigated sceptic or a Pyrrhonian? Such debates are sterile and miss the point, for however consistent or inconsistent the characters may be, the actual drama of the text has an intention and a direction all of its own, destroying the religious hypothesis not so much by 'serious' calculated argument as by ridicule and excess. Hume's Dialogues Concerning Natural Religion are the expression of a healthy and cheerful malice which strives at every turn to intensify the sense of the absurdity of religion. Hence their flavour is primarily rhetorical, and it would be a mistake to consider them as merely a collection of paraphraseable proofs directed against the possibility of rational theology. This is not to say, however, that Hume did not take religion seriously; on the contrary, he uses all of the devices of comedy in order to overwhelm it — rather as Nietzsche was to argue: "Not by wrath does one kill but by laughter. ml In this paper, I will consider the rhetorical aspect of Hume's Dialogues to show how the literary mode — the elaboration and contrast of characters, the use of parody and sudden turns in the plot, etc. — enables Hume to make a far more compelling assault on the religious hypothesis than the plain recital of 391 'reasonable' objections would ever achieve. I will focus my discussion on three central themes: First, the professed acceptance of God by all of the participants, and the consequent need for an oblique attack upon religion; second, Hume's comic perspectives on the argument from Design; and third, Hume's development of an 'antinomies of religion,' whereby the various religious arguments are used to undermine each other. 1. The Belief in God No man; no man, at least of common sense, I am persuaded, ever entertained a serious doubt with regard to a truth so certain and self-evident. The question is not concerning the being but the nature of God. Ostensibly, the one thing that is never questioned in the Dialogues, the one thing that all the participants remain agreed upon, is that God exists. Indeed, it seems that however limited the scope of natural theology may turn out to be, the actual being of God can never be in dispute, for in the Dialogues, belief in God is often presented as if it were an unchallengeable 'given' of human experience. Cleanthes, for example, apparently follows Locke in arguing for the reasonableness of theism; and yet, when he is pressed he defends the Design hypothesis in terms of its psychological irresistibility, appealing to a natural sentiment of belief rather than the claim of any argument: Consider, anatomize the eye: Survey its structure and contrivance; and tell me, from your own feeling, if the idea of a contriver does not immediately flow in upon you with a force like that of sensation.... it requires time, reflection and study, to summon up those frivolous, though 392 abstruse, objections, which can support infidelity (D 154). According to Cleanthes, the Design hypothesis is so self-evident that it really does not need any philosophical justification at all. It is simply the articulation of what we all already knew to be true: The comparison of the universe to a machine of human contrivance is so obvious and natural, and is justified by so many instances of order and design in nature, that it must immediately strike all unprejudiced apprehensions, and procure universal approbation (D 216). Demea also denies that religion is based upon argument. He claims that each man is brought to feel the truth of religion within himself through the consciousness of his own complete ignorance and misery. And in this respect, 'reason' can only hamper religious belief. Finally, at the end of the Dialogues, even Philo... (shrink)

Background There is continued need for enhanced medical ethics education across the United States. In an effort to guide medical ethics education reform, we report the first interprofessional survey of a cohort of graduate medical, nursing and allied health professional students that examined perceived student need for more formalized medical ethics education and assessed preferences for teaching methods in a graduate level medical ethics curriculum. Methods In January 2018, following the successful implementation of a peer-led, grassroots medical ethics curriculum, student (...) leaders under faculty guidance conducted a cross-sectional survey with 562 of 1357 responses received among students enrolled in the School of Medicine, College of Nursing, Doctor of Physical Therapy and BS/ MD Professional Scholars programs at The Medical College of Georgia at Augusta University. An in person or web-based questionnaire was designed to measure perceived need for a more in-depth medical ethics curriculum. Results The majority of respondents were female, white and mid-20s in age. Almost half of respondents reported no prior medical ethics exposure or training in their previous educational experience, while 60% of students across all degree programs reported an interest in more medical ethics education and 92% noted that an understanding of medical ethics was important to their future career. Over a quarter of students were interested in pursuing graduate-level training in medical ethics, with case-based discussions, small group peer settings and ethics guest lectures being the most desired teaching methods. Conclusions The future physician, nursing and physical therapist workforce in our medical community demonstrated an unmet need and strong interest for more formal medical ethics education within their current coursework. Grassroots student-driven curricular development and leadership in medical ethics can positively impact medical education. Subsequent integration of interprofessional training in medical ethics may serve as a vital curricular approach to improving the training of ethically competent healthcare professionals and overcoming the current hierarchical clinical silos. (shrink)

The language of “participant-driven research,” “crowdsourcing” and “citizen science” is increasingly being used to encourage the public to become involved in research ventures as both subjects and scientists. Originally, these labels were invoked by volunteer research efforts propelled by amateurs outside of traditional research institutions and aimed at appealing to those looking for more “democratic,” “patient-centric,” or “lay” alternatives to the professional science establishment. As mainstream translational biomedical research requires increasingly larger participant pools, however, corporate, academic and governmental research programs (...) are embracing this populist rhetoric to encourage wider public participation. We examine the ethical and social implications of this recruitment strategy. We begin by surveying examples of “citizen science” outside of biomedicine, as paradigmatic of the aspirations this democratizing rhetoric was originally meant to embody. Next, we discuss the ways these aspirations become articulated in the biomedical context, with a view to drawing out the multiple and potentially conflicting meanings of “public engagement” when citizens are also the subjects of the science. We then illustrate two uses of public engagement rhetoric to gain public support for national biomedical research efforts: its post-hoc use in the “care.data” project of the National Health Service in England, and its proactive uses in the “Precision Medicine Initiative” of the United States White House. These examples will serve as the basis for a normative analysis, discussing the potential ethical and social ramifications of this rhetoric. We pay particular attention to the implications of government strategies that cultivate the idea that members of the public have a civic duty to participate in government-sponsored research initiatives. We argue that such initiatives should draw from policy frameworks that support normative analysis of the role of citizenry. And, we conclude it is imperative to make visible and clear the full spectrum of meanings of “citizen science,” the contexts in which it is used, and its demands with respect to participation, engagement, and governance. (shrink)

Recent studies in social endocrinology have explored the effects of social relationships on female reproductive steroid hormones—estradiol and progesterone—investigating whether they are suppressed in partnered and parous women. Results have been mixed for these hormones although evidence is more consistent that partnered women and women with young children have lower levels of testosterone. These studies were sequential to earlier research on men, based on Wingfield’s Challenge Hypothesis, which showed that men in committed relationships, or with young children, have lower levels (...) of testosterone than unpartnered men or men with older or no children. The study described here explored associations between estradiol and progesterone with partnership and parity among women from two different ethnicities: South Asian and white British. We hypothesized that both steroid hormones would be lower among partnered and/or parous women with children ≤3 years old, regardless of ethnicity. In this study we analyzed data from 320 Bangladeshi and British women of European origin aged 18 to 50 who participated in two previous studies of reproductive ecology and health. Levels of estradiol and progesterone were assayed using saliva and/or serum samples and the body mass index calculated from anthropometric data. Questionnaires provided other covariates. Multiple linear regressions were used to analyze the data. The hypotheses were not supported. We argue here that, unlike links between testosterone and male social relationships, theoretical foundations for such relationships with female reproductive steroid hormones are lacking, especially given the primary role of these steroids in regulating female reproductive function. Further longitudinal studies are needed to explore the bases of independent relationships between social factors and female reproductive steroid hormones. (shrink)

Written by leading experts in the field, Stellar Spectral Classification is the only book to comprehensively discuss both the foundations and most up-to-date techniques of MK and other spectral classification systems. Definitive and encyclopedic, the book introduces the astrophysics of spectroscopy, reviews the entire field of stellar astronomy, and shows how the well-tested methods of spectral classification are a powerful discovery tool for graduate students and researchers working in astronomy and astrophysics. The book begins with a historical survey, followed by (...) chapters discussing the entire range of stellar phenomena, from brown dwarfs to supernovae. The authors account for advances in the field, including the addition of the L and T dwarf classes; the revision of the carbon star, Wolf-Rayet, and white dwarf classification schemes; and the application of neural nets to spectral classification. Copious figures illustrate the morphology of stellar spectra, and the book incorporates recent discoveries from earth-based and satellite data. Many examples of spectra are given in the red, ultraviolet, and infrared regions, as well as in the traditional blue-violet optical region, all of which are useful for researchers identifying stellar and galactic spectra. This essential reference includes a glossary, handy appendixes and tables, an index, and a Web-based resource of spectra. In addition to the authors, the contributors are Adam J. Burgasser, Margaret M. Hanson, J. Davy Kirkpatrick, and Nolan R. Walborn. (shrink)

With his clear and accessible prose, impeccable scholarship, and balanced Judgment, Roland Teske, SJ, has been an influential and important voice in Medieval philosophy for more than thirty years. This volume, in his honour, brings together more than a dozen essays on central metaphysical and theological themes in Augustine and other medieval thinkers. The authors, listed below, are noted scholars who draw upon Teskes work, reflect on it, go beyond it, and at times even disagree with it, but always in (...) a spirit of respectful co-operation, and always with the aim of getting at the truth. Essays on Augustine contributed by Gerald Bonner, Charles Brittain, Joseph Koterski, SJ, Joseph T. Lienhard, SJ, David Vincent Meconi, SJ, Ann A. Pang-White, Frederick Van Fleteren, Dorothea Weber, and James Wetzel. Essays on Bernard of Clairvaux, William of Auvergne, and other medieval themes contributed by John P. Doyle, William Harmless, SJ, John A. Laumakis, Edward P. Mahoney, and Philipp W. Rosemann. (shrink)

With his clear and accessible prose, impeccable scholarship, and balanced Judgment, Roland Teske, SJ, has been an influential and important voice in Medieval philosophy for more than thirty years. This volume, in his honour, brings together more than a dozen essays on central metaphysical and theological themes in Augustine and other medieval thinkers. The authors, listed below, are noted scholars who draw upon Teskes work, reflect on it, go beyond it, and at times even disagree with it, but always in (...) a spirit of respectful co-operation, and always with the aim of getting at the truth. Essays on Augustine contributed by Gerald Bonner, Charles Brittain, Joseph Koterski, SJ, Joseph T. Lienhard, SJ, David Vincent Meconi, SJ, Ann A. Pang-White, Frederick Van Fleteren, Dorothea Weber, and James Wetzel. Essays on Bernard of Clairvaux, William of Auvergne, and other medieval themes contributed by John P. Doyle, William Harmless, SJ, John A. Laumakis, Edward P. Mahoney, and Philipp W. Rosemann. (shrink)

In this chapter I problematize Beauvoir's analogical analyses in The Second Sex, arguing that her utilization of the race/gender analogy omits the experiences and oppressions of Black women. Furthermore, taking into account select secondary literature that emphasizes these issues, I argue that several of Beauvoir's white feminist defenders and critics share in common their non‐engagement with Black feminist literature on Beauvoir. Put another way, Black feminists who explicitly take up Beauvoir in their writings have remained largely unacknowledged in the (...) secondary literature on Beauvoir by white feminists. As a corrective to this erasure, I highlight the scholarly contributions of Black feminists including Loraine Hansberry, Chikwenye Ogunyemi, Deborah King, Oyeronke Oyewumi, and bell hooks. (shrink)

In Minkowski spacetime, because of the relativity of simultaneity to the inertial frame chosen, there is no unique world-at-an-instant. Thus the classical view that there is a unique set of events existing now in a three dimensional space cannot be sustained. The two solutions most often advanced are that the four-dimensional structure of events and processes is alone real, and that becoming present is not an objective part of reality; and that present existence is not an absolute notion, but is (...) relative to inertial frame; the world-at-an-instant is a three dimensional, but relative, reality. According to a third view, advanced by Robb, Capek and Stein, what is present at a given spacetime point is, strictly speaking, constituted by that point alone. I argue here against the first of these views that the four-dimensional universe cannot be said to exist now, already, or indeed at any time at all; so that talk of its existence or reality as if that precludes the existence or reality of the present is a non sequitur. The second view assumes that in relativistic physics time lapse is measured by the time co-ordinate function; against this I maintain that it is in fact measured by the proper time, as I argue by reference to the Twin Paradox. The third view, although formally correct, is tarnished by its unrealistic assumption of point-events. This makes it susceptible to paradox, and also sets it at variance with our normal intuitions of the present. I argue that a defensible concept of the present is nonetheless obtainable when account is taken of the non-instantaneity of events, including that of conscious awareness, as that region of spacetime comprised between the forward lightcone of the beginning of a small interval of proper time t and the backward lightcone of the end of that interval. This gives a serviceable notion of what is present to a given event of short duration, as well as saving our intuition of the “reality” or robustness of present events. (shrink)

This book gathers together for the first time an important body of texts written between 1672 and 1686 by the great German philosopher and polymath Gottfried Leibniz. These writings, most of them previously untranslated, represent Leibniz's sustained attempt on a problem whose solution was crucial to the development of his thought, that of the composition of the continuum. The volume begins with excerpts from Leibniz's Paris writings, in which he tackles such problems as whether the infinite division of matter entails (...) perfect points, whether matter and space can be regarded as true wholes, whether motion is truly continuous, and the nature of body and substance. Comprising the second section is Pacidius Philalethi, Leibniz's brilliant dialogue of late 1676 on the problem of the continuity of motion. In the selections of the final section, from his Hanover writings of 1677-1686, Leibniz abandons his earlier transcreationism and atomism in favor of the theory of corporeal substance, where the reality of body and motion is founded in substantial form or force.Leibniz's texts (one in French, the rest in Latin) are presented with facing-page English translations, together with an introduction, notes, appendixes containing related excerpts from earlier works by Leibniz and his predecessors, and a valuable glossary detailing important terms and their translations. (shrink)

"This is an excellent textbook on Neoplatonism which gives the reader a very concise and lucid overview of the basic doctrines and leading thinkers of the last great philosophy to emerge before the Christianization of the Roman Empire. I’ve no doubt that my students next semester will benefit from the analyses contained in the book. The contents of the chapters are very informative and adequately place developments in their socio-cultural context." --Michael B. Simmons, Auburn University at Montgomery.

It is commonly held that there is no place for the 'now’ in physics, and also that the passing of time is something subjective, having to do with the way reality is experienced but not with the way reality is. Indeed, the majority of modern theoretical physicists and philosophers of physics contend that the passing of time is incompatible with modern physical theory, and excluded in a fundamental description of physical reality. This book provides a forceful rebuttal of such claims. (...) In successive chapters the author explains the historical precedents of the modern opposition to time flow, giving careful expositions of matters relevant to becoming in classical physics, the special and general theories of relativity, and quantum theory, without presupposing prior expertise in these subjects. Analysing the arguments of thinkers ranging from Aristotle, Russell, and Bergson to the proponents of quantum gravity, he contends that the passage of time, understood as a local becoming of events out of those in their past at varying rates, is not only compatible with the theories of modern physics, but implicit in them. (shrink)

This article responds to a common criticism of Aristotelian naturalism known as the Pollyanna Problem, the objection that Aristotelian naturalism, when combined with recent empirical research, generates morally unacceptable conclusions. In developing a reply to this objection, I draw upon the conception of human nature developed by the ancient Chinese philosopher Mencius, and build up an account of ethical naturalism that provides a satisfying response to the Pollyanna Problem while also preserving what is most attractive about Aristotelian naturalism.

It is well known that Leibniz advocated the actual infinite, but that he did not admit infinite collections or infinite numbers. But his assimilation of this account to the scholastic notion of the syncategorematic infinite has given rise to controversy. A common interpretation is that in mathematics Leibniz’s syncategorematic infinite is identical with the Aristotelian potential infinite, so that it applies only to ideal entities, and is therefore distinct from the actual infinite that applies to the actual world. Against this, (...) I argue in this paper that Leibniz’s actual infinite, understood syncategorematically, applies to any entities that are actually infinite in multitude, whether numbers, actual parts of matter, or monads. It signifies that there are more of them than can be assigned a number, but that there is no infinite number or collection of them, which notion involves a contradiction. Similarly, to say that a magnitude is actually infinitely small in the syncategorematic sense is to say that no matter how small a magnitude one takes, there is a smaller, but there are no actual infinitesimals. In geometry one may calculate with expressions apparently denoting such entities, on the understanding that they are fictions, standing for variable magnitudes that can be made arbitrarily small, so as to produce demonstrations that there is no error in the resulting expressions. (shrink)

This paper consists in a study of Leibniz’s argument for the infinite plurality of substances, versions of which recur throughout his mature corpus. It goes roughly as follows: since every body is actually divided into further bodies, it is therefore not a unity but an infinite aggregate; the reality of an aggregate, however, reduces to the reality of the unities it presupposes; the reality of body, therefore, entails an actual infinity of constituent unities everywhere in it. I argue that this (...) depends on a generalized notion of aggregation, according to which a thing may be an aggregate of its constituents if every one of its actual parts presupposes such constituents, but is not composed from them. One of the premises of this argument is the reality of bodies. If this premise is denied, Leibniz’s argument for the infinitude of substances, and even of their plurality, cannot go through. (shrink)

In the transition to Einstein’s theory of Special Relativity (SR), certain concepts that had previously been thought to be univocal or absolute properties of systems turn out not to be. For instance, mass bifurcates into (i) the relativistically invariant proper mass m0, and (ii) the mass relative to an inertial frame in which it is moving at a speed v = βc, its relative mass m, whose quantity is a factor γ = (1 – β2) -1/2 times the proper mass, (...) m = γm0. (shrink)

In this interview, C. P. Goodman invites British Polanyi scholar Richard T. Allen to reflect on his interest in Polanyi’s philosophical ideas and share what he believes is valuable in his thought.

The reappearance of the question of moral judgments by historians makes a reappraisal of the issues timely. Almost all that has been written on the subject addresses only the propriety of moral judgments in the written texts historians produce. However, historians have to make moral choices when selecting a subject upon which to write; and they make a tacit moral commitment to write and teach honestly. Historians usually dislike making explicit moral evaluations, and have little or no training in how (...) to do so. They can argue it’s not their job; they are only finders of fact. Historians holding a determinist view of actions do not think it appropriate to blame people for doing what they couldn’t help doing; for those believing there is an overall pattern to history, individual morality is beside the point. Finally, since earlier cultures had values different from ours, it seems unjust to hold them to contemporary standards. This essay modifies or rejects these arguments. Some historians have manifested ambivalence, acknowledging it is difficult or impossible to avoid making moral evaluations . Ordinary-language philosophers, noting that historiography has no specialized vocabulary, see it as saturated by the values inherent in everyday speech and thought. I argue that the historicist argument about the inevitably time-bound limitation of all values is exaggerated. Historians who believe in the religious grounding of values obviously disagree with it; but even on a secular level, morals are often confused with mores. If historians inevitably make moral evaluations, they should examine what philosophical ethicists—virtue ethicists, deontologists, and consequentialists—have said about how to make them; and even if they find no satisfactory grounding for their own moral attitudes, it is a brute fact that they have them. I end with an argument for “strong evaluations”—neither treating them as a troublesome residue in historiography nor, having despaired of finding a solid philosophical ground for moral evaluations, concluding that they are merely matters of taste. I believe historians should embrace the role of moral commentators, but that they should be aware that their evaluations are, like all historical judgments, subject to the criticisms of their colleagues and readers. Historians run little risk of being censorious and self-righteous; the far greater danger is acquiescing in or contributing to moral confusion and timidity. (shrink)

HellmanGeoffrey* * and ShapiroStewart.** ** Varieties of Continua—From Regions to Points and Back. Oxford University Press, 2018. ISBN: 978-0-19-871274-9. Pp. x + 208.

This set is a carefully balanced selection of writings representing some of the most important currents in the thought of city and regional planning during the period 1870-1940 when urban planning emerged as a serious disciplinary field. The set consists of eight key books from this period, handsomely illustrated and reproduced in their entirety, and a separate volume of fifteen seminal short selections - all by major figures of the time, such as Abercrombie, Geddes, and the Olmsteds. Soria y Mata's (...) writings on the linear city also appear in translation for the first time. In addition to seminal works on city planning, the set covers themes such as neighbourhood, Utopian and visionary planning; planning for parks; housing; transportation systems, and public health. A wide variety of cities feature including Paris, Vienna, Amsterdam, Berlin, London, Manchester, New York and San Francisco, showing a great diversity of cultural styles. Early Urban Planning 1870-1940 is of continued importance today, as it highlights ideals which remain strikingly relevant in development of the twentieth and twenty-first centuries. (shrink)

Russell’s most important source for his book on Leibniz was C. I. Gerhardt’s seven-volume Die philosophischen Schriften von Gottfried Wilhelm Leibniz. Russell heavily annotated his copy of this important edition of Leibniz’s works. The present paper records all Russell’s marginalia, with the exception of passages marked merely by vertical lines in the margin, and provides explanatory commentary.

In preparation for his lectures on Leibniz delivered in Cambridge in Lent Term 1899, Russell started in the summer of 1898 to keep notes on writings by and about Leibniz in a large notebook of the type he commonly used for notetaking at this time. This article prints, with annotation, all the material on Leibniz in that notebook.

In lively and readable prose, Arthur presents a new approach to the study of logic, one that seeks to integrate methods of argument analysis developed in modern “informal logic” with natural deduction techniques. The dry bones of logic are given flesh by unusual attention to the history of the subject, from Pythagoras, the Stoics, and Indian Buddhist logic, through Lewis Carroll, Venn, and Boole, to Russell, Frege, and Monty Python. A previous edition of this book appeared under the title _Natural (...) Deduction_. This new edition adds clarifications of the notions of explanation, validity and formal validity, a more detailed discussion of derivation strategies, and another rule of inference, Reiteration. (shrink)

In contrast with some recent theories of infinitesimals as non-Archimedean entities, Leibniz’s mature interpretation was fully in accord with the Archimedean Axiom: infinitesimals are fictions, whose treatment as entities incomparably smaller than finite quantities is justifiable wholly in terms of variable finite quantities that can be taken as small as desired, i.e. syncategorematically. In this paper I explain this syncategorematic interpretation, and how Leibniz used it to justify the calculus. I then compare it with the approach of Smooth Infinitesimal Analysis, (...) as propounded by John Bell. I find some salient differences, especially with regard to higher-order infinitesimals. I illustrate these differences by a consideration of how each approach might be applied to propositions of Newton’s Principia concerning the derivation of force laws for bodies orbiting in a circle and an ellipse. “If the Leibnizian calculus needs a rehabilitation because of too severe treatment by historians in the past half century, as Robinson suggests (1966, 250), I feel that the legitimate grounds for such a rehabilitation are to be found in the Leibnizian theory itself.”—(Bos 1974–1975, 82–83). (shrink)