Over the past four decades - and most especially in recent years as issues of identity continue to play out across the public stage - identity theory has developed into one of the most fascinating and active research programs within the spheres of sociological social psychology. Having emerged out of a landmark 2014 national conference that sought to integrate various research programs and to honor the groundbreaking work of Dr. Peter J. Burke, New Directions in Identity Theory and Research brings (...) together the pioneers, scholars, and researchers of identity theory as they present the important theoretical, methodological, and substantive work in identity theory today.Edited by Dr. Jan E. Stets and Dr. Richard T. Serpe, this volume asserts that researchers and scholars can no longer rely on using samples, measures, concepts, and mechanisms that limit the overall advancement of identity theory and research. Instead, as Stets and Serpe contend in their introductory chapter. (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)

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 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 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)

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)

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 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)

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.

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.

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)

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)

Much of what we understand about heterochromatin formation in mammals has been extrapolated from forward genetic screens for modifiers of position‐effect variegation (PEV) in the fruit fly Drosophila melanogaster. The recent identification of the HUSH (Human Silencing Hub) complex suggests that more recent evolutionary developments contribute to the mechanisms underlying PEV in human cells. Although HUSH‐mediated repression also involves heterochromatin spreading through the reading and writing of the repressive H3K9me3 histone modification, clear orthologues of HUSH subunits are not found in (...) Drosophila but are conserved in vertebrates. Here we compare the insights into the mechanisms of PEV derived from genetic screens in the fly, the mouse and in human cells, review what is currently known about the HUSH complex and discuss the implications of HUSH‐mediated silencing for viral latency. Future studies will provide mechanistic insight into HUSH complex function and reveal the relationship between HUSH and other epigenetic silencing complexes. (shrink)

Following the lead of Hans Reichenbach in the early twentieth century, many authors have attributed a causal theory of time to Leibniz. My exposition of Leibniz’s theory of time in a paper of 1985 has been interpreted as a version of such a causal theory, even though I was critical of the idea that Leibniz would have tried to reduce relations among monadic states to causal relations holding only among phenomena. Since that time previously unpublished texts by Leibniz have become (...) available in which he himself explains temporal precedence in terms of causal precedence, and these texts have been given careful scrutiny by other scholars, such as Jan Cover, Stefano Di Bella and Michael Futch. In this paper I respond to their analyses, and try to make precise the way in which Leibniz’s views on time and on causality fit together in his metaphysics. (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.

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)

Descartes' allusions, in the Meditations and the Principles, to the individual moments of duration, has for some years stirred controversy over whether this commits him to a kind of time atomism. The origins of Descartes' way of treating moments as least intervals of duration can be traced back to his early collaboration with Isaac Beeckman. Where Beeckman (in 1618) conceived of moments as (mathematically divisible) physical indivisibles, corresponding to the durations of uniform motions between successive impacts on a body by (...) microscopic particles, Descartes was able to give a mathematical treatment of the problem of fall in which moments were rendered mathematical minima of motion that were necessarily devoid of extension. This achievement, coupled with his innovation of conceiving force as instantaneous tendency to motion, subsequently led him to disdain Beeckman's discretist physics with its extended indivisible moments. Nevertheless, he was not able to eradicate a fundamental tension in his philosophy between force as a quantity of motion, and force as an instantaneous tendency to motion. For by his principles, action, motion, quantity of motion, and indeed existence, all require some minimal interval of duration. This explains his need to refer to moments as least conceivable parts of duration, and this is what has given rise to the impression that he supposed duration to be composed of such parts, contrary to his commitment to continuous creation. (shrink)

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.

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 these remarks on Ohad Nachtomy’s account of Leibniz’s philosophy of the infinite in his recent book, Living Mirrors, I focus on his suggestion that living creatures be interpreted as exemplifying the second of the three degrees of infinity that Leibniz articulates in 1676, as things which are infinite in their own kind. For the infinity characterizing created substances cannot be the highest degree, which is reserved by Leibniz for the divine substance, while Nachtomy sees the lowest degree as applicable (...) only to “entia rationis such as numbers and relations”. Against this, I argue that the lowest or syncategorematic infinite applies to any multiplicity or magnitude that is greater than any assignable, so that something further can always be added; whereas the second degree applies to the divine attributes or perfections, which are maximal in that nothing further of that kind can be added. (shrink)

The aim of this paper is to explain the significance of Alfred A. Robb’s philosophy of time stemming from his interpretation of relativity theory; and at the same time, to investigate the reasons for the failure of his philosophical contemporaries to appreciate its significance, with special attention to its reception on Russell’s part. The study of Russell’s reaction to Robb exposes shortcomings in Russell’s own philosophy of time, which has been extremely influential through the years. It also highlights the philosophical (...) differences between Minkowski and Robb, the shared idealistic premises of Russell and McTaggart, and the confluences between the views of Russell, Eddington and McTaggart. The paper closes with an account of how Robb’s interpretation has been vindicated by its adoption in modern physics. (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 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)

Leibniz never tired of stressing the fundamental importance of the concept of continuity for philosophy, nor was he shy of attributing major importance to his own struggle through “the labyrinth of the continuum” for the subsequent development of his whole system of thought. Unfortunately, however, his own thought on the subject is something of a labyrinth itself, and from a modern point of view many of his pronouncements are apt to seem blatantly contradictory.Certain quotations seem to commit him unambiguously to (...) atomism. Thus to de Voider he writes: “Matter is not continuous, but discrete…. The same holds for changes, which are not truly continuous.” (To de Voider, 11th October 1705: G.II.279).2. (shrink)

This essay is an appreciation of Massimo Mugnai’s many contributions to Leibniz scholarship, as well as to the history of logic and history of philosophy more generally.

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.

This is a reply to Samuel Levey's fine review of my Monads, Composition and Force (Oxford UP, 2018) in the same issue of the Leibniz Review. In it I take up various difficulties raised by Levey that may be thought to collapse Leibniz's position into idealism after all, and attempt to provide convincing responses to them.

At the turn of the century Bertrand Russell advocated an absolutist theory of space and time, and scornfully rejected Leibniz’s relational theory in his Critical Exposition of the Philosophy of Leibniz. But by the time of the second edition, he had proposed highly influential relational theories of space and time that had much in common with Leibniz’s own views. Ironically, he never acknowledges this. In trying to get to the bottom of this enigma, I looked further at contemporary texts by (...) Russell, and also those he might have relied on, especially that of Robert Latta. I found that, like Latta’s, Russell’s interpretation of Leibniz was heavily conditioned by his immersion in neo-Hegelian and neo-Kantian philosophy prior to 1898, and that the doctrine of internal relations he attributes to Leibniz was more nearly the view of Lotze. (shrink)

In this paper I attempt to throw new light on Leibniz's apparently conflicting remarks concerning the continuity of matter. He says that matter is "discrete" yet "actually divided to infinity" and (thus dense), and moreover that it fills (continuous) space. I defend Leibniz from the charge of inconsistency by examining the historical development of his views on continuity in their physical and mathematical context, and also by pointing up the striking similarities of his construal of continuity to the approach taken (...) by 20th century Combinatorial Topology. (shrink)

William Hunter's anatomical inquiry employed all of his senses, but how did his personal experiences with the cadaver become generalized scientific knowledge teachable to students and understandable by fellow practitioners? Moving beyond a historiographical focus on Hunter's images and extending Lorraine Daston's (2008) concept of an ‘ontology of scientific observation’ to include non-visual senses, I argue that Hunter's work aimed to create a stabilized object of the cadaver that he and his students could perceive in common. Crucial to this stabilization (...) was the sense of touch and its interaction with other senses, creating intersensory knowledge of the cadaver. Through a close reading of his neglected posthumous publication An Anatomical Description of the Human Gravid Uterus (1794), I demonstrate that Hunter wrote extensively about touch and other sensory experiences, using comparative metaphors and other linguistic strategies to engender clear ideas of the cadaver in the mind of the reader. That these ideas could be consistent between practitioners was guaranteed by God, but required practitioners to appropriately reflect on their sensory experiences with cadavers. Hunter's experimental practice encompassed both simple and complex methods, all aimed at increasing the range of sensorial experiences he had with the gravid uterus. His preservations of these experiences in text, image and preparation could then be used to support further anatomical investigations. (shrink)

Richard Arthur’s _Natural Deduction_ provides a wide-ranging introduction to logic. 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.