research interests

seventeenth century philosophyMy main area of research over the past 30 years or so has been seventeenth century philosophy, particularly that of Gottfried Leibniz. I give a fresh overview of his thought intended for all interested readers in my Leibniz, (Polity Press, 2014). 


The focus of my research on Leibniz has been on what he took to be a central philosophical problem, that of the composition of the continuum, one of the two labyrinths in which he claimed the human mind becomes enmeshed (the other being that of free will and determinism). The outcome of my earliest studies on this was a volume of translations of manuscripts Leibniz had written (mostly in Latin) in his formative years, Leibniz: The Labyrinth of the Continuum (Yale University Press, 2001). For many years I had a manuscript in the works (Ariadnean Threads), but this became unwieldy, and fissured into several other tomes. The first was Monads, Composition and Force: Ariadnean Threads through Leibniz's Labyrinth, (Oxford University Press 2018), in which I trace the various strands of thought going into the formation of Leibniz's theory of substance as a solution to the labyrinth of the continuum. I situate Leibniz's thought in the context of his early immersion in chymical atomism and the Scholastic tradition of the Plurality of Forms, and his equally profound commitment to mechanism, and show how his dynamics emerges as a solution to the problem of the composition of motion. Highlights include new readings of Leibniz's conception of organic body and its relation to teleology, of the status of corporeal substance and passive force, of the hypothesis of substantial bonds, and of the compatibility of the continuous existence of substance with the discreteness of monadic states.   

I have just completed a companion volume, Leibniz on time, space and relativity, in which I treat Leibniz’s theories of time, space, and motion in a historically accurate way, and also with an eye to their implications for modern science. Further offshoots of this project are two collaborative ventures: 1) Leibniz on the Foundations of the Differential Calculus, with David Rabouin (Université Paris Diderot), which features an introduction giving new perspectives on Leibniz’s subtle views, together with a substantial selection of relevant texts in English, almost all translated for the first time; and 2) Leibniz on the Metaphysics of the Infinite, with Osvaldo Ottaviani, a selection of previously untranslated (almost all previously unknown) writings on that topic, with transcriptions by Osvaldo, accepted for publication with Oxford University Press in consort with the British Journal for the History of Philosophy. 

Before I set about the latter two in earnest (although most of the translations are done) I am completing another translation volume, Leibniz's Publications on Natural Philosophy, which has also been accepted for publication by Oxford University Press, with translations by myself, Jeff McDonough, Sam Levey, Lea Schroeder, Tzuchien Tho, and Richard Francks. A complete draft is almost finished.

Another co-authored volume in progress, this time with my McMaster colleague Nick Griffin, is a book length study, Russell on Leibniz. We are writing two chapters each; mine are “The Hegelian Roots of Russell's Critique of Leibniz”, “Russell’s Rejection of the Relational Theory: Leibniz, Lotze, and Internal Relations” (both written). The two of us, along with Jolen Galaugher, also edited a transcription of Russell's notes on Leibniz from 1898, as well as his marginalia on his copies of the Gerhardt Leibniz, both contained in the Russell Archives in the library at McMaster University, together with G. E. Moore’s notes on Russell’s lectures, a discarded preface, and the preface to the French edition; this has appeared as one complete issue of the journal Russell (Summer 2017; edited, and contributed to, by Ken Blackwell), thus gathering in one place all the materials that went into the making of Russell’s justly celebrated A Critical Exposition of the Philosophy of Leibniz —a work which not only transformed scholarship on Leibniz, but also had significant impact on the development of Russell’s own thought, as we have tried to demonstrate. 

Another research area I have been investigating is the lively atomist tradition of the early seventeenth century and its connection with biology, theology, and the chymical tradition, particularly in the work of Daniel Sennert, and before him, Julius Caesar Scaliger. Here my contacts with Japanese scholars, particularly Hiro Hirai and Kuni Sakamoto, have been invaluable. Our joint workshop in Toyama, Japan, in early 2016 showcased our research  on Sennert, Scaliger and Leibniz respectively, which has thrown light on the importance of these late scholastic thinkers, and not just as precedents to Leibniz. 

I have done substantial work on Descartes, beginning with my 1988 publication, “Continuous Creation, Continuous TIme: A Refutation of the Alleged Discontinuity of Cartesian Time,” continuing with studies of Beeckman's inflence on his thought (on which I spoke recently at the Sorbonne), and also with my entries on “Atoms” and “Time” in the Cambridge Descartes Lexicon, ed. Lawrence Nolan. I have also treated the mathematical philosophy of Newton in several publications across my career.


philosophy of physics: My latest book, The Reality of Time Flowcame out with Springer in May, 2019. It consists in a defence of the reality of local becoming in modern physics. In successive chapters I explain 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, I contend that the passage of time, understood as a becoming of events out of those in their local past at varying rates, is not only compatible with the theories of modern physics, but implicit in them.

Other work: In 2015 I published a paper on virtual processes, showing the close relationship between them and the phenomenon of quantum tunnelling; I argue that neither can be interpreted in terms of particle transmission, since (among other objections) that would involve processes with imaginary mass travelling backwards in time. I have also published a paper on "Proper Time and the Clock Hypothesis", arguing that this is not a separate hypothesis that needs positing independently, but implicit in the formulations of both special and general relativity; and 2 papers on time in special relativity. A longstanding interest of mine is the close relationship between time and inertia, on which I have written two papers , "Time, Inertia and the Relativity Principle" (archived paper) in Minnesota, and "Time and Inertia" in Montreal.  The Time and Universe (tau) Cluster, a collaborative venture with other physicists and philosophers in Canada and around the world, seems now to be defunct, having failed to secure the funding applied for from SSHRC, despite initial promise of success. This kind of interdisciplinary endeavour seemingly cannot get funded in Canada, for all the bombast about “outreach”, “partnerships" and “interdisciplinary studies".

history and philosophy of time: Descartes has a profound debt to Isaac Beeckman in his natural philosophy, issuing in both some of his most seminal advancements, but also in some of the tensions in his philosophy, as I have argued in various papers. These studies, together with related studies on Descartes, Galileo, Gassendi, and various less celebrated thinkers like Arriaga, Le Tenneur, and Fabry, form part of a project treating the interconnection of views on time, force and activity in seventeenth century natural philosophy, under the title Matters of Moment: studies on the birth of modern science. My paper "On the mathematization of free fall" comes out of this research. 

philosophy of the infinite: Fourth, arising out of my work on Leibniz, I have been defending an account of the actual infinite that is a rival to the Cantorian account, but which eschews infinite sets. On this topic I wrote a dialogue between Leibniz and Cantor in 2000, which has finally been published (2020). I have also published five related papers: one on the development of Leibniz's early thinking on infinitesimals; a second comparing Newton and Leibniz on infinitesimals; a third in which I compare Leibniz's syncategorematic interpretation of infinitesimals with that of Smooth Infinitesimal Analysis; a fourth in which (inter alia) I offer a largely sympathetic critique of Deleuze's interpretation of Leibniz's calculus with regard to the rise of structuralism; and a fifth on Leibniz’s syncategorematic actual infnite.

epistemology of science: Fifth, I am part of a cluster of scholars interested in thought experiments. I published an article on Galileo's thought experiment on falling bodies and Jim Brown's Platonist interpretation of it, incorporating a weird dream, a partial defence of Feyerabend's views, and my interest in Diderot's materialist philosophy. More recently I published a paper (first read at a workshop in Halifax) on one of the world's oldest TEs, Aristotle's Wheel, perhaps originating with Archytas of Tarentum; and then an entry in the The Routledge Companion to Thought Experiments, (ed. James Robert Brown, Yiftach Fehige, and Michael T. Stuart), "Thought Experiments in Newton and Leibniz”. Other endeavours in epistemology: in Pisa in September 2010 I co-hosted a workshop (with Niccolò Guicciardini) on the (contested) expanding role of applied mathematics from the Renaissance to the Enlightenment; and in 2012, I attended an international workshop on the Language of Nature at the Rotman Institute at Western (London, Ontario), and my "On the Mathematization of Free Fall Galileo, Descartes, and a History of Misconstrual” was published in the resulting volume in 2016.

© Richard TW Arthur 2016