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)

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)

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)

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)

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.

"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.

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 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.

Ethical Studies is one of the most enlightening works of moral philosophy in English. This article surveys the principal structural theme running throughout it, but will concentrate on its more explicit development at the beginning and end of the book, Essays II and VI, and the “Concluding Remarks.” Essay II formulates the formal requirements of morality in terms of self-realization, and the remaining Essays survey possible contents, the valuable elements of which are brought together, with further materials, in Essays VI (...) and VII. But Bradley finds that morality involves a contradiction, and so, in order to resolve that contradiction, it issues into something more than morality, namely, religion. However, this article will show that Bradley’s resolution of this contradiction is not satisfactory and that, once morality is conceived as an ἐνέργεια and not a γένεσις, an activity and not a process, this contradiction vanishes. Yet morality does, nevertheless, on Bradley’s own principles, find its completion in religion when so conceived; and such an argument was developed in detail in the great work of one of Bradley’s pupils, A. E. Taylor’s Faith of a Moralist, Vol. I. (shrink)

In this paper I try to sort out a tangle of issues regarding time, inertia, proper time and the so-called “clock hypothesis” raised by Harvey Brown's discussion of them in his recent book, Physical Relativity. I attempt to clarify the connection between time and inertia, as well as the deficiencies in Newton's “derivation” of Corollary 5, by giving a group theoretic treatment original with J.-P. Provost. This shows how both the Galilei and Lorentz transformations may be derived from the relativity (...) principle on the basis of certain elementary assumptions regarding time. I then reflect on the implications of this derivation for understanding proper time and the clock hypothesis. (shrink)

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)

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)

Before establishing his mature interpretation of infinitesimals as fictions, Gottfried Leibniz had advocated their existence as actually existing entities in the continuum. In this paper I trace the development of these early attempts, distinguishing three distinct phases in his interpretation of infinitesimals prior to his adopting a fictionalist interpretation: (i) (1669) the continuum consists of assignable points separated by unassignable gaps; (ii) (1670-71) the continuum is composed of an infinity of indivisible points, or parts smaller than any assignable, with no (...) gaps between them; (iii) (1672- 75) a continuous line is composed not of points but of infinitely many infinitesimal lines, each of which is divisible and proportional to a generating motion at an instant (conatus). In 1676, finally, Leibniz ceased to regard infinitesimals as actual, opting instead for an interpretation of them as fictitious entities which may be used as compendia loquendi to abbreviate mathematical reasonings. (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)

Revenge is universal in human cultures, and is essentially personal and retributive. Its moral status is contested, as is its rationality. Revenge is traditionally associated with pleasure, but this association is not accounted for in contemporary philosophical treatments of revenge. Here I supply a theory of normal narcissistic functioning that can explain this association. Normal narcissism is an adaptive form of inter-psychic processing which has to do with the regulation of a coherent set of meta-representations of the agent. It can (...) be given a general account by integrating views drawn from clinical traditions, empirical psychology, and contemporary cognitive neuroscience. I explore the neural correlates of normal narcissism, its characteristic accompanying emotions and pleasures/displeasures, and its fundamental dynamics. It is proposed that this allostatic regulatory system plays a prominent role in retributive behavior, including revenge. Revenge is understood as a form of narcissistic repair, and a variety of puzzles concerning revenge are solved from this point of view. (shrink)

The Defining Issues Test 2 (DIT-2) and Engineering Ethical Reasoning Instrument (EERI) are designed to measure ethical reasoning of general (DIT-2) and engineering-student (EERI) populations. These tools—and the DIT-2 especially—have gained wide usage for assessing the ethical reasoning of undergraduate students. This paper reports on a research study in which the ethical reasoning of first-year undergraduate engineering students at multiple universities was assessed with both of these tools. In addition to these two instruments, students were also asked to create personal (...) concept maps of the phrase “ethical decision-making.” It was hypothesized that students whose instrument scores reflected more postconventional levels of moral development and more sophisticated ethical reasoning skills would likewise have richer, more detailed concept maps of ethical decision-making, reflecting their deeper levels of understanding of this topic and the complex of related concepts. In fact, there was no significant correlation between the instrument scores and concept map scoring, suggesting that the way first-year students _conceptualize_ ethical decision making does not predict the way they behave when _performing_ scenario-based ethical reasoning (perhaps more situated). This disparity indicates a need to more precisely quantify engineering ethical reasoning and decision making, if we wish to inform assessment outcomes using the results of such quantitative analyses. (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.

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.

G. E. Moore attended Russell’s lectures on Leibniz in 1899 and kept detailed notes which have been preserved among his papers. The present article prints his notes in their entirety with annotations.