{"id":547,"date":"2023-05-07T15:20:13","date_gmt":"2023-05-07T15:20:13","guid":{"rendered":"https:\/\/rtwarthur.ca\/?page_id=547"},"modified":"2026-09-18T14:47:17","modified_gmt":"2026-09-18T18:47:17","slug":"the-infinite","status":"publish","type":"page","link":"https:\/\/rtwarthur.ca\/?page_id=547","title":{"rendered":"the infinite"},"content":{"rendered":"[et_pb_section fb_built=&#8221;1&#8243; _builder_version=&#8221;4.21.0&#8243; _module_preset=&#8221;default&#8221; background_color=&#8221;gcid-f5584efe-a07f-4926-882d-1e539cbe465b&#8221; global_colors_info=&#8221;{%22gcid-f5584efe-a07f-4926-882d-1e539cbe465b%22:%91%22background_color%22%93}&#8221;][et_pb_row _builder_version=&#8221;4.21.0&#8243; _module_preset=&#8221;default&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_column type=&#8221;4_4&#8243; _builder_version=&#8221;4.21.0&#8243; _module_preset=&#8221;default&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_text _builder_version=&#8221;4.21.0&#8243; _module_preset=&#8221;default&#8221; global_colors_info=&#8221;{}&#8221;]<h1 style=\"text-align: center;\">the infinite<\/h1>[\/et_pb_text][\/et_pb_column][\/et_pb_row][et_pb_row _builder_version=&#8221;4.21.0&#8243; _module_preset=&#8221;default&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_column type=&#8221;4_4&#8243; _builder_version=&#8221;4.21.0&#8243; _module_preset=&#8221;default&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_text _builder_version=&#8221;4.21.0&#8243; _module_preset=&#8221;default&#8221; global_colors_info=&#8221;{}&#8221;]<p><\/p>\n<p class=\"wp-block-paragraph\"><\/p>\n<p class=\"wp-block-paragraph\">\u201cMonads, Situation and Infinite Explanation,\u201d with Filippo Costantini, <strong><em>British Journal for the History of Philosophy<\/em><\/strong>, April, 2025: [<strong>Monads situation and infinite explanation.pdf<\/strong>] \u2014also at <a href=\"https:\/\/doi.org\/10.1080\/09608788.2025.2478974\">https:\/\/doi.org\/10.1080\/09608788.2025.2478974<\/a>.<\/p>\n<p>\u201cMonads and Points, Contiguity and Transcreation: on the Development of Leibniz\u2019s Metaphysics of the Continuum,\u201d <em><strong>Archiv f\u00fcr Geschichte der Philosophie<\/strong><\/em>, August 2025, [<a href=\"https:\/\/macdrive.mcmaster.ca\/d\/e5049a06fdfe4585bfc4\/files\/?p=\/Monads%20and%20Points.pdf\">Monads and Points.pdf<\/a>]<\/p>\n<p>\u201cOn the Unviability of Interpreting Leibniz\u2019s Infinitesimals through Nonstandard Analysis\u201d, with David Rabouin, <em><strong>Historia Mathematica<\/strong>,<\/em> March 2024, vol. 66, 26-42; [<a href=\"https:\/\/macdrive.mcmaster.ca\/d\/e5049a06fdfe4585bfc4\/files\/?p=\/Unviability.pdf\"><strong>Unviability.pdf<\/strong><\/a>]<\/p>\n<p>\u201cLeibniz and the Three Degrees of Infinity\u201d, pp. 25\u201346, in <strong><em>Leibniz Review<\/em><\/strong>, 32, 2022; with a reply from Ohad Nachtomy [<a href=\"https:\/\/macdrive.mcmaster.ca\/d\/e5049a06fdfe4585bfc4\/files\/?p=\/Three.Degrees.LR.2022.pdf\"><strong>Three.Degrees.LR.2022.pdf<\/strong><\/a>].<\/p>\n<p>A Question of Fundamental Methodology: Reply to Mikhail Katz\u201d, co-authored with Tom Archibald, Giovanni Ferraro, Jeremy Gray, Douglas Jesseph, Jesper L\u00fctzen, Marco Panza, David Rabouin, and Gert Schubring, pp. 360\u2013363 in <em><strong>The Mathematical Intelligencer,<\/strong><\/em> 44, 4, Winter 2022. [<a href=\"https:\/\/macdrive.mcmaster.ca\/d\/e5049a06fdfe4585bfc4\/files\/?p=\/A%20Question%20of%20Fundamental%20Methodology.pdf\"><strong>A Question of Fundamental Methodology.pdf<\/strong><\/a>]<\/p>\n<p>\u201cLeibniz\u2019s syncategorematic infinitesimals II: their existence, their use and their role in the justification of Differential Calculus\u201d (co-authored with David Rabouin), <strong><em>Archive for History of Exact Sciences<\/em><\/strong>, 2020, 74, 5, 401 \u2013 443; DOI: 10.1007\/s00407-020-00249-w.[<a href=\"https:\/\/macdrive.mcmaster.ca\/d\/e5049a06fdfe4585bfc4\/files\/?p=\/Rabouin-Arthur-infinitesimals.pdf\"><strong>Rabouin-Arthur-infinitesimals.pdf<\/strong><\/a>]<\/p>\n<p>\u201cLeibniz in Cantor\u2019s Paradise: A Dialogue on the Actual Infinite\u201d, ch. 3, pp. 71-109 in <em><strong>Leibniz and the Structure of Sciences<\/strong><\/em>: Modern Perspectives on the History of Logic, Mathematics, Epistemology, ed. Vincenzo De Risi, Cham, Switzerland: Springer, 2019. [<a href=\"https:\/\/macdrive.mcmaster.ca\/d\/e5049a06fdfe4585bfc4\/files\/?p=\/Leibniz%20in%20Cantor%27s%20Paradise.pdf\"><strong>Leibniz in Cantor&#8217;s Paradise.pdf<\/strong><\/a>]<\/p>\n<p>\u201cLeibniz\u2019s Syncategorematic Actual Infinite\u201d, pp. 155-179 in <strong><em>I<\/em><em>nfinity in Early Modern Philosophy<\/em><\/strong>, eds. Ohad Nachtomy and Reed Winegar, Springer Verlag, 2018. [<a href=\"https:\/\/macdrive.mcmaster.ca\/d\/e5049a06fdfe4585bfc4\/files\/?p=\/L%27s.Sync.Actu.Inf.pdf\"><strong>L&#8217;s.Sync.Actu.Inf.pd<\/strong>f<\/a>].<\/p>\n<p>\u201cThe Labyrinth of the Continuum\u201d, in Maria Rosa Antognazza (ed.),\u00a0<em><strong>Oxford Handbook of Leibniz<\/strong><\/em>; published online at (www.oxfordhandbooks.com), Oxford: Oxford University Press, December 2013. [<a href=\"https:\/\/macdrive.mcmaster.ca\/d\/e5049a06fdfe4585bfc4\/files\/?p=\/The_Labyrinth_of_the_Continuum.pdf\"><strong>The_Labyrinth_of_the_Continuum.pdf<\/strong><\/a>]<\/p>\n<p>\u201cLeibniz&#8217;s Syncategorematic Infinitesimals, Smooth Infinitesimal Analysis, and Second Order Differentials\u201d,\u00a0<em><strong>Archive for History of Exact Sciences<\/strong><\/em>, April 2013. <a href=\"https:\/\/macdrive.mcmaster.ca\/d\/e5049a06fdfe4585bfc4\/files\/?p=\/LSI.pdf\">[<\/a><strong><a href=\"https:\/\/macdrive.mcmaster.ca\/d\/e5049a06fdfe4585bfc4\/files\/?p=\/LSI.pdf\">LSI.pdf<\/a>]<\/strong><\/p>\n<p>&#8220;Leibniz&#8217;s Actual Infinite in Relation to his Analysis of Matter\u201d, 137-156 (chapter 7) in <em><strong>G. W.\u00a0Leibniz on the interrelations between mathematics and philosophy<\/strong><\/em>, (Springer: Archimedes Series), ed. Norma Goethe, Philip Beeley and David Rabouin, 2012. [<a href=\"https:\/\/macdrive.mcmaster.ca\/d\/e5049a06fdfe4585bfc4\/files\/?p=\/Lairam.pdf\"><strong>Lairam.pdf<\/strong><\/a>]<strong><\/strong><\/p>\n<p>\u201cPresupposition, Aggregation, and Leibniz\u2019s Argument for a Plurality of Substances\u201d, <em><strong>Leibniz Review<\/strong><\/em>, 21, 91-116, 2011. [<a href=\"https:\/\/macdrive.mcmaster.ca\/d\/e5049a06fdfe4585bfc4\/files\/?p=\/PresuppAggLAPS.pdf\"><strong>PresuppAggLAPS.pdf<\/strong><\/a>]<\/p>\n<p>\u201cActual Infinitesimals in Leibniz\u2019s Early Thought\u201d, in\u00a0<em><strong>The Philosophy of the Young Leibniz<\/strong><\/em>, Studia Leibnitiana Sonderhefte 35, ed. Mark Kulstad, Mogens Laerke and David Snyder, 2009, pp. 11-28. [<a href=\"https:\/\/macdrive.mcmaster.ca\/d\/e5049a06fdfe4585bfc4\/files\/?p=\/Actual_Infinitesimals.pdf\"><strong>Actual_Infinitesimals.pdf<\/strong><\/a>]<\/p>\n<p>\u201cLeery Bedfellows: Newton and Leibniz on the Status of Infinitesimals,\u201d pp. 7-30 in\u00a0<em>Infinitesimal Differences: Controversies between Leibniz and his Contemporaries<\/em>, ed. Ursula Goldenbaum and Douglas Jesseph, Berlin and New York: De Gruyter, 2008. [<a href=\"https:\/\/macdrive.mcmaster.ca\/d\/e5049a06fdfe4585bfc4\/files\/?p=\/Leery.Bedfellows2008.pdf\"><strong>Leery.Bedfellows2008.pdf<\/strong><\/a><a href=\"http:\/\/www.humanities.mcmaster.ca\/~rarthur\/papers\/Leery.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><\/a>]<\/p>\n<p><em>Also available are these preprints:<\/em><\/p>\n<p class=\"wp-block-paragraph\">\u201cLeibniz\u2019s Archimedean infinitesimals,\u201d\u00a0<em>Proceedings of the Canadian Society for History and Phil. of Mathematics<\/em>, 21, 1-10, 2008. [<a href=\"http:\/\/rtwarthur.com\/papers\/lai2.pdf\">preprint<\/a>]<\/p>\n<p>\u201cLeibniz and Cantor on the Actual Infinite,\u201d pp. 41-46 in\u00a0<strong><em>Nihil sine ratione<\/em>\u00a0<\/strong>, Vol. 1, ed. Hans Poser, Berlin: Gottfried-Willhelm-Leibniz-Gesellschaft, 2001. [<a href=\"http:\/\/rtwarthur.com\/papers\/leibcant.pdf\">preprint<\/a>]<\/p>\n<p>&#8220;The remarkable fecundity of Leibniz&#8217;s work on infinite series&#8221;: a review article on 2 Akademie volumes of Leibniz&#8217;s writings, VII, 3: 1672-76: Differenzen, Folen Reihen, and III, 5: Mathematischer, naturwissenschaftlicher und technischer Briefwechsel, 2012. [<a href=\"http:\/\/www.humanities.mcmaster.ca\/~rarthur\/papers\/Fecundity.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">preprint<\/a>] \u00a0<\/p>\n<p><!-- \/wp:post-content --> <!-- wp:paragraph --><\/p>\n<p>September 13, 2026<\/p>\n<p><!-- \/wp:paragraph --><\/p>\n<p><!-- \/wp:paragraph --><\/p>[\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]","protected":false},"excerpt":{"rendered":"<p>the infinite \u201cMonads, Situation and Infinite Explanation,\u201d with Filippo Costantini, British Journal for the History of Philosophy, April, 2025: [Monads situation and infinite explanation.pdf] \u2014also at https:\/\/doi.org\/10.1080\/09608788.2025.2478974. \u201cMonads and Points, Contiguity and Transcreation: on the Development of Leibniz\u2019s Metaphysics of the Continuum,\u201d Archiv f\u00fcr Geschichte der Philosophie, August 2025, [Monads and Points.pdf] \u201cOn the Unviability [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"nf_dc_page":"","_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","footnotes":""},"class_list":["post-547","page","type-page","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.7 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>the infinite - Richard T. 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Arthur","og_description":"the infinite \u201cMonads, Situation and Infinite Explanation,\u201d with Filippo Costantini, British Journal for the History of Philosophy, April, 2025: [Monads situation and infinite explanation.pdf] \u2014also at https:\/\/doi.org\/10.1080\/09608788.2025.2478974. \u201cMonads and Points, Contiguity and Transcreation: on the Development of Leibniz\u2019s Metaphysics of the Continuum,\u201d Archiv f\u00fcr Geschichte der Philosophie, August 2025, [Monads and Points.pdf] \u201cOn the Unviability [&hellip;]","og_url":"https:\/\/rtwarthur.ca\/?page_id=547","og_site_name":"Richard T. W. Arthur","article_modified_time":"2026-09-18T18:47:17+00:00","twitter_card":"summary_large_image","schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/rtwarthur.ca\/?page_id=547","url":"https:\/\/rtwarthur.ca\/?page_id=547","name":"the infinite - Richard T. W. 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