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)

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)

In Century of Genius: European Thought 1600-1700, Richard T. Vann links selections from the writings of such thinkers as Galileo, Bacon, Hobbes, Pascal, and Newton with interpretative commentary to show how seventeenth-century discoveries in science and mathematics not only changed the way in which men viewed the sun and the fall of apples from a tree, but also influenced forever afterward men's view of themselves. In Vann's interpretation, the spirit of the age was one of confidence and quest, given (...) perhaps its most eloquent expression in Milton's serene assurance that "though all the winds of doctrine were let loose to play upon the earth, so Truth be in the field ... let her and falsehood grapple; who ever knew Truth put to the worse in a free and open encounter?". In Century of Genius: European Thought 1600-1700, Richard T. Vann links selections from the writings of such thinkers as Galileo, Bacon, Hobbes, Pascal, and Newton with interpretative commentary to show how seventeenth-century discoveries in science and mathematics not only changed the way in which men viewed the sun and the fall of apples from a tree, but also influenced forever afterward men's view of themselves. In Vann's interpretation, the spirit of the age was one of confidence and quest, given perhaps its most eloquent expression in Milton's serene assurance that "though all the winds of doctrine were let loose to play upon the earth, so Truth be in the field ... let her and falsehood grapple; who ever knew Truth put to the worse in a free and open encounter?". (shrink)

In this age of interdisciplinary interaction, we probably owe one another disclosures of our qualifications for commenting on each other’s profession. And you might well wonder why a philosopher would be asked to address this distinguished society of professiona l geologists. So, let me give what information I can about my qualifications to talk this evening about, of all things, the ethics of water geology.

Debates over postmodernism, analyses of knowledge and power, and the recurring issue of Heidegger's Nazism have all deepened questions about the relation between philosophy and the social roles of intellectuals. Against such postmodernist rejections of philosophical theory as mounted by Rorty and Lyotard, Richard Peterson argues that precisely reflection on rationality, in appropriate social terms, is needed to confront urgent political issues about intellectuals. After presenting a conception of intellectual mediation set within the modern division of labor, he offers (...) an account of postmodern politics within which postmodern arguments against critical reflection are themselves treated socially and politically. Engaging thinkers as diverse as Kant, Hegel, Marx, Habermas, Foucault, and Bahktin, Peterson argues that a democratic conception and practice of philosophy is inseparable from democracy generally. His arguments about modern philosophy are tied to claims about the relation between liberalism and epistemology, and these in turn inform an account of impasses confronting contemporary politics. Historical arguments about the connections between postmodernist thought and practice are illustrated by discussions of the postmodernist dimensions of recent politics. (shrink)

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)

Philosophers have constituted business ethics as a field by providing a systematic overview that interrelates its problems and concepts and that supplies the basis for building on attained results. Is there a properly theological task in business ethics? The religious/theological literature on business ethics falls into four classes: (1) the application of religious morality to business practices; (2) the use of encyclical teachings about capitalism; (3) the interpretation of business relations in agapa-istic terms; and (4) the critique of business from (...) a liberation theological point of view. Theologians have not adequately addressed the questions of whether there are particular theological tasks in the field as they define it, and whether, if they define it, the theological definition is different from the philosophical. (shrink)

Mario Bunge wrote his classic Causality and Modern Science more than 60 years ago, and a third revised edition was published by Dover in 1979. With its impressive scope and historical perspective it was a long way ahead of its time. But many of its insights still have not been sufficiently appreciated by physicists and philosophers alike. These include Bunge’s distinction between causation and other types of determination, his critique of the still-dominant Humean accounts of causality as leaving out the (...) productive aspect of determination, his critique of the conflation of determination with predictability, his insistence on the fictional character of isolated causal chains, and his demonstration that “causal connectability” depends only on the principle of retarded action, not causation. It will be argued that there is a degree of agreement between his views on determinism and causality and those of Leibniz, and a comparison between the two thinkers’ views is used to throw further light on these matters. (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)

In this paper I offer a fresh interpretation of Leibniz’s theory of space, in which I explain the connection of his relational theory to both his mathematical theory of analysis situs and his theory of substance. I argue that the elements of his mature theory are not bare bodies (as on a standard relationalist view) nor bare points (as on an absolutist view), but situations. Regarded as an accident of an individual body, a situation is the complex of its angles (...) and distances to other co-existing bodies, founded in the representation or state of the substance or substances contained in the body. The complex of all such mutually compatible situations of co-existing bodies constitutes an order of situations, or instantaneous space. Because these relations of situation change from one instant to another, space is an accidental whole that is continuously changing and becoming something different, and therefore a phenomenon. As Leibniz explains to Clarke, it can be represented mathematically by supposing some set of existents hypothetically (and counterfactually) to remain in a fixed mutual relation of situation, and gauging all subsequent situations in terms of transformations with respect to this initial set. Space conceived in terms of such allowable transformations is the subject of Analysis Situs. Finally, insofar as space is conceived in abstraction from any bodies that might individuate the situations, it encompasses all possible relations of situation. This abstract space, the order of all possible situations, is an abstract entity, and therefore ideal. (shrink)

In the May, 1960, issue of the American Bar Association Journal (vol. 499), Morton Birnbaum, a lawyer and physician, argued for a legal right to psychiatric treatment of the involuntarily committed mentally ill person. In the 18 years since his article appeared,, there have been several key court cases in which this concept of a right to psychiatric treatment has figured prominently and decisively. It is important to note that the language of the decisions have had at least an indirect (...) effect in the recently enacted mental Hygiene Law of the State of New York. While I shall not seek to establish the historical thesis that Birnbaum’s article has been efficacious in bringing about both these court decisions and changes in statutory laws, I do want to examine Birnbaum’s article and some of the opinions for three cases: Wyatt v. Stickney (1972), Wyatt v. Aderholt (1974), and O’Connor v. Donaldson (422 US 563, 1975), in an effort to understand both the significance of these changes in our laws and the underlying philosophical and ethical notions of which they are an expression. Birnbaum observed that the notable feature of the legal situation at the time was that there had not been recognized a constitutional requirement that one who had been institutionalized for mental illness according to due process must receive treatment. Birnbaum argued that the effects of an omission of such a requirement to treat were that mental institutions typically offered only custodial care, that patients who were held only under custodial care typically did not improve, and that the result was that involuntary incarceration in a mental institution was, at least from the point of view of the patient, functionally no different than would be imprisonment for an unspecified period of time. Birnbaum argued for a recognition and enforcement in the courts of the right to treatment “...as a necessary and overdue development of our present concept of due process of law,” i.e., as required by the 14th Amendment to the U.S.. (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)

Normal narcissistic functioning has to do with the regulation of a coherent set of metarepresentations of the acting agent. That set of meta-representations has its own interior architecture and dynamics. Normal narcissistic functioning is an adaptive form of interpsychic processing which can be given a general account by integrating views of it drawn from the clinical traditions of psychoanalysis, empirical psychology, and contemporary cognitive and neurosciences. This is not to be confused with any form of organized psychopathology, though pathological forms (...) of narcissism are relevant to understanding normal narcissism. Neural correlates of normal narcissism, as also the characteristic emotions and pleasures/displeasures that accompany its operations, are also explored. It is proposed that this allostatic regulatory system plays a prominent role in a wide range of human behaviors. It also closes the gap between social norms governing such behaviors and the minds of the agents performing them. This integrative interpretation of the scientific material is offered as an exercise in “philosophy in cognitive science” and belongs to the tradition of naturalistic philosophical accounts of the human mind. (shrink)

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)

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)

Business ethics, which grew out of religion's interest in ethics in business and management education's concern with social issues, has become an interdisciplinary academic field. Thus far it has centered on teaching undergraduates. The easy work has now been done and the field has reached a plateau. To develop further it requires development on the MBA level, high quality research on new questions, positive models, better interdisciplinary integration, and attention to international business. Ultimately the field will stand or fall on (...) the quality of research those in it produce. (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.