history of the exact sciences

“Leibniz’s Principle of Equivalence and the Origins of his Dynamics”, Vorträge des XI. Internationalen Leibniz-Kongresses, 2023, ed. Wenchao Li, Charlotte Wahl, Sven Erdner, Bianca Carina Schwarze and Yue Dan, Band 1, 27-38. [offprint]

“A Question of Fundamental Methodology: Reply to Mikhail Katz”, co-authored with Tom Archibald, Giovanni Ferraro, Jeremy Gray, Douglas Jesseph, Jesper Lützen, Marco Panza, David Rabouin, and Gert Schubring, pp. 360–363 in The Mathematical Intelligencer, 44, 4, Winter 2022.

“On the Significance of A. A. Robb’s Philosophy of Time, Especially in Relation to Russell’s”, pp. 251–273 in British Journal for the History of Philosophy, 31, 2, a special issue of BJHP guest-edited by Emily Thomas, (online April 2022).

“Leibniz as a Precursor to Chaitin’s Algorithmic Information Theory”, chapter 9 (153-176) in Information and the History of Philosophy, ed. Chris Meyns, London: Routledge, 2021. [offprint]

“Leibniz’s syncategorematic infinitesimals II: their existence, their use and their role in the justification of Differential Calculus” (co-authored with David Rabouin), Archive for History of Exact Sciences, 2020, 1-43. [offprint]

“Mario Bunge on causality: some key insights and their Leibnizian precedents”, chapter 11 (pp. 185-204) in Mario Bunge: A Centenary Festschrift, ed. Michael R. Matthews, Springer Verlag, 2019. [offprint]

“Leibniz in Cantor’s Paradise: A Dialogue on the Actual Infinite”, ch. 3, pp. 71-109 in Leibniz and the Structure of Sciences: Modern Perspectives on the History of Logic, Mathematics, Epistemology, ed. Vincenzo De Risi, Cham, Switzerland: Springer, 2019. [offprint]

“Leibniz and Quantum Theory”, a presentation for Leibniz and the Sciences, a workshop at the Max Planck Institute for Mathematics in the Sciences, Leipzig, 15th November, 2016 [pdf of slides]. 

“Newton and Leibniz on the relativity of motion”, for the Oxford Handbook of Newton, ed. Chris Smeenk and Eric Schliesser, 2015 (www.oxfordhandbooks.com), [preprint]. 

“On the mathematization of free fall: Galileo, Descartes and a history of misconstrual”,81-111 in The Language of Nature, volume 20 of Minnesota Studies in Philosophy of Science, ed. Geoffrey Gorham, Benjamin Hill, Edward Slowik and C. Kenneth Waters, 2016 [preprint]

“Leibniz’s Actual Infinite in Relation to his Analysis of Matter”, forthcoming in Leibniz on the interrelations between mathematics and philosophy, (Springer: Archimedes Series), ed. Norma Goethe, Philip Beeley and David Rabouin, 2015. [preprint] [offprint]

“Leibniz’s Syncategorematic Infinitesimals, Smooth Infinitesimal Analysis, and Second Order Differentials”, Archive for History of Exact Sciences, 67: 553–593, April 2013 [offprint].

“The Labyrinth of the Continuum”, in Maria Rosa Antognazza (ed.), Oxford Handbook of Leibniz; published online at (www.oxfordhandbooks.com), Oxford: Oxford University Press, December 2013.  [preprint]

“Time Atomism and Ash’arite Origins for Cartesian Occasionalism, Revisited” forthcoming in Asia, Europe and the Emergence of Modern Science: Knowledge Crossing Boundaries, ed. Arun Bala, Palgrave McMillan, 2012. [preprint]

“Leery Bedfellows: Newton and Leibniz on the Status of Infinitesimals,” pp. 7-30 in Infinitesimal Differences: Controversies between Leibniz and his Contemporaries, ed. Ursula Goldenbaum and Douglas Jesseph, Berlin and New York: De Gruyter, 2008.  [preprint]

“Leibniz’s Archimedean Infinitesimals,” Proceedings of the Canadian Society for History and Phil. of Mathematics, 21, 1-10, 2008—a preliminary version of the paper below to be published by the Royal Academy.  [preprint]

“‘x + dx = x’: Leibniz’s Archimedean infinitesimals”, supposed to appear as a chapter in Structure and Identity, ed. Karin Verelst, Royal Academy, Brussels (unpublished; written 2007)  [preprint]

“The transcendentality of π (pi) and Leibniz’s philosophy of mathematics”, Proceedings of the Canadian Society for History and Philosophy of Mathematics, 12, 13-19, 1999. Here I show that in an unpublished paper of 1676 (A VI iii N69) Leibniz conjectured that π (pi) cannot be expressed even as the irrational root “of an equation of any degree”, thus anticipating Legendre’s famous conjecture of the transcendentality of π by some 118 years.  [preprint]

“The remarkable fecundity of Leibniz’s work on infinite series”: a review article on 2 Akademie volumes of Leibniz’s writings, VII, 3: 1672-76: Differenzen, Folen Reihen, and III, 5: Mathematischer, naturwissenschaftlicher und technischer Briefwechsel . [preprint] Oct 12, 2020 at 8:30 PM © Richard Arthur 2012