Abstract
\nWhy is medieval logic not mathematized? This is a longstanding problem in the historiography of medieval logic. I suggest flipping that question on its head: rather than asking why medieval logic \;was not mathematized\, it is more felicitous to asks how developments in logic shaped contemporaneous and subsequent developments in the philosophy and practice of mathematics.
\n
The case in point is precise and consequential. I argue that the algebraic treatment and philosophical problematisation of complex numbers\, emerging in 16th-century mathematics\, has its conceptual and historical roots in a decisive shift in 14th-century modal semantics. This shift transformed the absolutely impossible into something imaginable and understandable\, and the
imaginable into something mathematically operable.
In ancient and medieval logic and mathematics\, necessarily empty terms &mdash\; i.e.\, those terms signifying something intrinsically contradictory and therefore absolutely impossible &mdash\; and the square roots of negative numbers occupied the same conceptual space: both were dismissed as inconceivable\, as violations of the boundaries of rational thought itself. The parallel is not \;incidental. It reflects a shared metaphysical commitment to the limits of the thinkable.
\nWhat breaks this impasse is a profound semantic reorientation. In late-14th-century modal logic\, most notably in the work of Marsilius of Inghen and his followers\, absolute impossibilities are drawn into the logical domain: while not real\, there are conceivable\; they remain nonexistent but \;are manipulable.
\nThe reception of this new semantics of imaginable impossibilities across the 15th and 16th centuries was widespread and influential This paper traces a direct line of conceptual continuity &mdash\;through views\, texts\, and theories &mdash\; from Marsilius of Inghen to Girolamo Cardano\, arguing that new approach to imaginable impossibilities launched by late-medieval logicians is precisely what \;made the mathematical imagination of complex numbers possible.
ORGANIZER;CN=Jan Heylen;CN=Sylvia Wenmackers;CN=Shahab Khademi;CN=Nena Bobovnik: METHOD:PUBLISH END:VEVENT BEGIN:VEVENT DTSTAMP:20260417T023351Z DTSTART;TZID=Europe/Brussels:20260519T170000 DTEND;TZID=Europe/Brussels:20260519T183000 SUMMARY:How many points are in a line segment? From Grosseteste to numerosities UID:20260423T174917Z-iCalPlugin-Grails@philevents-web-f5d4878dd-x5n6c TZID:Europe/Brussels LOCATION:Kardinaal Mercierplein 2\, Leuven\, Belgium\, 3000 DESCRIPTION:In his commentary on Aristotle&rsquo\;s Physics\, Robert Grosseteste (ca. 1175-1253)\, Oxford theologian and Chancellor of the University\, wrote: "Moreover\, [God] created everything by number\, weight\, and measure\, and He is the first and most accurate Measurer. By infinite numbers which are finite to Him\, he measured the lines which He created. By some infinite number which is fixed and finite to Him\, He measured and numbered the one-cubit line\; and by an infinite number twice that size\, He measured the two-cubit line\; and by an infinite number half that size\, He measured the half-cubit line." In Grosseteste's account the numerosity of the points in a finite line segment covaries with the length of the line segment. This position gave rise to an interesting number of debates in the XIIIth century especially as a consequence of a challenge raised by the Oxford theologian Richard Fishacre (1205-1248) who set up a one to one correspondence between the points in line segments of different lengths. I will reconstruct some aspects of this medieval debate\, connect it to later intuitions (Bolzano and Cantor)\, and then discuss recent results from the theory of numerosities to the effect that the counting of points in a line segment preserving the part-whole principle is compatible with Lebesgue measure. I conclude that Grosseteste's intuitions can find a suitable mathematical implementation.
ORGANIZER;CN=Jan Heylen: METHOD:PUBLISH END:VEVENT BEGIN:VEVENT DTSTAMP:20260417T023351Z DTSTART;TZID=Europe/Brussels:20260519T170000 DTEND;TZID=Europe/Brussels:20260519T183000 SUMMARY:How many points are in a line segment? From Grosseteste to numerosities UID:20260423T174918Z-iCalPlugin-Grails@philevents-web-f5d4878dd-x5n6c TZID:Europe/Brussels LOCATION:Kardinaal Mercierplein 2\, Leuven\, Belgium\, 3000 DESCRIPTION:Abstract\nIn his commentary on Aristotle&rsquo\;s Physics\, Robert Grosseteste (ca. 1175-1253)\, Oxford theologian and Chancellor of the University\, wrote: "Moreover\, [God] created everything by number\, weight\, and measure\, and He is the first and most accurate Measurer. By infinite numbers which are finite to Him\, he measured the lines which He created. By some infinite number which is fixed and finite to Him\, He measured and numbered the one-cubit line\; and by an infinite number twice that size\, He measured the two-cubit line\; and by an infinite number half that size\, He measured the half-cubit line." In Grosseteste's account the numerosity of the points in a finite line segment covaries with the length of the line segment. This position gave rise to an interesting number of debates in the XIIIth century especially as a consequence of a challenge raised by the Oxford theologian Richard Fishacre (1205-1248) who set up a one to one correspondence between the points in line segments of different lengths. I will reconstruct some aspects of this medieval debate\, connect it to later intuitions (Bolzano and Cantor)\, and then discuss recent results from the theory of numerosities to the effect that the counting of points in a line segment preserving the part-whole principle is compatible with Lebesgue measure. I conclude that Grosseteste's intuitions can find a suitable mathematical implementation.
\n ORGANIZER;CN=Jan Heylen;CN=Sylvia Wenmackers;CN=Shahab Khademi;CN=Nena Bobovnik: METHOD:PUBLISH END:VEVENT BEGIN:VEVENT DTSTAMP:20260417T023351Z DTSTART;TZID=America/New_York:20260528T160000 DTEND;TZID=America/New_York:20260531T170000 SUMMARY:Aquinas on Act and Potency UID:20260423T174919Z-iCalPlugin-Grails@philevents-web-f5d4878dd-x5n6c TZID:America/New_York LOCATION:487 Michigan Ave NE\, Brookland\, United States\, 20017 DESCRIPTION:Now celebrating its 15th anniversary\, the Aquinas Philosophy Workshop brings together renowned scholars from universities worldwide for lectures and discussions. Join us in Washington\, D.C. this May to explore Aquinas in the company of leading scholars and students! The theme for this year&rsquo\;s conference is &ldquo\;Aquinas on Act and Potency.&rdquo\; It is an exciting opportunity to do a deep dive into this important doctrine and its implications for a variety of different disciplines\, from metaphysics to politics. \; \;
\nFeatured Speakers:
\nProf. Gregory Doolan (The Catholic University of America)\, Prof. Matthew Minerd (Byzantine Catholic Seminary of Saints Cyril and Methodius)\, Prof. Jeffrey Brower (Purdue University)\, Prof. Jennifer Frey (University of Tulsa)\, Prof. Catherine Peters (Loyola Marymount University)\, Fr. Ambrose Little\, O.P. (Dominican House of Studies)
ORGANIZER: METHOD:PUBLISH END:VEVENT BEGIN:VEVENT DTSTAMP:20260417T023351Z DTSTART;TZID=America/New_York:20260531T090000 DTEND;TZID=America/New_York:20260611T170000 SUMMARY:Call for Applicants: Medieval Philosophy Fellowship - Center for Canon Expansion and Change UID:20260423T174920Z-iCalPlugin-Grails@philevents-web-f5d4878dd-x5n6c TZID:America/New_York LOCATION:Minneapolis\, United States DESCRIPTION:Call for Applicants: Medieval Philosophy Fellowship (3 positions open)
\nThe Center for Canon Expansion and Change (CCEC) at the University of Minnesota Twin Cities invites applications for the Fellowship in Medieval Philosophy. This program is an exciting opportunity to contribute to a groundbreaking initiative aimed at diversifying and expanding the philosophical canon. Over the next several years\, the CCEC will expand its curriculum beyond the early modern period to include the ancient\, medieval\, and early analytic periods. In 2026\, the focus will be on medieval Philosophy!
\nProgram Overview
\nCCEC&rsquo\;s Fellowship seeks to employ scholars who are passionate about philosophy and committed to creating teaching modules that reflect the richness and diversity of the medieval philosophical tradition. This initiative builds upon the Center&rsquo\;s success in reimagining the teaching of early modern philosophy to include voices historically marginalized in the discipline and falls on the heels of the 2025 ancient fellowship program. The program aims to develop teaching resources that promote inclusive pedagogy and inspire students to see themselves as philosophers.
\nEligibility
\nApplicants must be career scholars in philosophy. Preference will be given to early career medieval scholars\, and open to recent PhD graduates\, adjuncts\, assistant/associate professor\, and/or contingent faculty. \;
\nStrong expertise in Medieval Philosophy is required.
\nA demonstrated commitment to inclusive pedagogy and/or interest in expanding the philosophical canon is required.
\nResponsibilities
\nCollaborate with the CCEC team to develop comprehensive 6 to 9 teaching modules on medieval philosophy.
\nCreate resources for classroom use\, including syllabi\, lectures\, and assignments that highlight underrepresented figures and perspectives.
\nParticipate in the CCEC Summer Program at the University of Minnesota Twin Cities (May 31- June 6\, 2026)
\nTake part in a post-summer program retreat (~3 days\, June 9-11\, 2026) to begin developing the plan for a medieval version of the CCEC Summer Program.
\nAs part of the compensation\, commit to be available to participate in CCEC 2027 (May 30 - June 5).
\nCompensation
Selected scholars will receive a competitive stipend of $2500-3000 for their contributions to the program.
Key Dates
\nApplication Deadline: April 5\, 2026 (extended)
\nNotification of Decision: April 15\, 2026
\nProgram Start Date: May 31\, \; 2026
\nApplication Requirements
\nA current CV.
\nA cover letter detailing your research in medieval philosophy and commitment to inclusive pedagogy.
\nA writing sample or portfolio demonstrating expertise in the field.
\nContact information for two references.
\nHow to Apply
\nApplications must be submitted online
\nApplication deadline: April 5\, 2026.
\nAbout Center for Canon Expansion and Change
Founded in 2021\, the Center for Canon Expansion and Change is dedicated to transforming the face of philosophy through justice-driven approaches to teaching and curriculum design. The Center has already engaged hundreds of educators and thousands of students worldwide in reimagining the discipline. The CCEC is housed in the Department of Philosophy at the University of Minnesota Twin Cities and is supported by the Institute for Advanced Study at the University of Minnesota with a grant from the Mellon Foundation. www.minnesotaccec.com
Join us in shaping a more inclusive future for philosophy!
\nAbstracts of 250-300 words (for papers or complete sessions) can be submitted between November 1 and December 31\, 2025 through an online submission portal. For more information\, see the call for papers on the website of the SMRP: \;https://smrpblog.wordpress.com/conferences/. \;
ORGANIZER;CN="Can Laurens Löwe";CN=Susan Brower-Toland: METHOD:PUBLISH END:VEVENT BEGIN:VEVENT DTSTAMP:20260417T023351Z DTSTART;TZID=Europe/Lisbon:20260615T090000 DTEND;TZID=Europe/Lisbon:20260619T170000 SUMMARY:Petrus Hispanus' Tractatus: Logic and Philosophy from the Middle Ages to Modernity UID:20260423T174923Z-iCalPlugin-Grails@philevents-web-f5d4878dd-x5n6c TZID:Europe/Lisbon LOCATION:Via Panorâmica s/n\, Porto\, Portugal\, 4150-564 DESCRIPTION:Call for participation
\n3rd Porto Medieval and Early Modern Philosophy Summer School Porto\, 15 to 19 June 2026 Petrus Hispanus' Tractatus: Logic and Philosophy from the Middle Ages to Modernity
\nGeneral information: \;https://ifilosofia.up.pt/activities/3rd-porto-mempss \; \;
\nInvited speakers
\n&mdash\; Ana-Marí\;a Mora Má\;rquez (Lunds Universitet)
\n&mdash\; Aurora Panzica (Universitä\;t Basel)
\n&mdash\; Julie Brumberg-Chaumont (PSL/CNRS\, Paris)
\n&mdash\; Mikko Yrjö\;nsuuri (University of Jyvä\;skylä\;) \;
\nThe summer school aims to survey the current state of the art and to promote further research on the \;Tractatus \;and its reception. We welcome contributions on Petrus Hispanus&rsquo\; \;Tractatus \;(Summulae logicales) and its tradition\, covering a broad range of topics\, including (but not limited to) those listed here: \;https://ifilosofia.up.pt/activities/3rd-porto-mempss \;
\nParticipation and call
\nParticipation is reserved for PhD students\, advanced master's students\, junior researchers who intend to pursue a PhD\, and young scholars.
\nWe invite submissions of proposals for 30-minute presentations followed by a 15-minute discussion. Along with the title\, the abstract (up to 600 words)\, references and 5 keywords\, the proposal should include a short biographical note.
\nPlease\, send your proposal by March 30\, 2026\, to this address: \;gfm_summerschool@letras.up.pt \; The decision of acceptance will be released to the applicants by April 15\, 2026.
\nThe school will accept 10 to 15 participants. No fees apply to the selected participants. Catering and all school materials will be provided by the organisation.
\nParticipants from outside Porto can apply for a travel and accommodation grant (up to 500 euros).
\nOrganisation
\nGabinete de Filosofia Medieval / Medieval and Early Modern Philosophy thematic line of the Institute of Philosophy of the University of Porto. \;
ORGANIZER;CN="José Meirinhos";CN=Vera Rodrigues: METHOD:PUBLISH END:VEVENT BEGIN:VEVENT DTSTAMP:20260417T023351Z DTSTART;TZID=Europe/Amsterdam:20260623T090000 DTEND;TZID=Europe/Amsterdam:20260625T170000 SUMMARY:XXV European Symposium on Medieval Logic and Semantics UID:20260423T174924Z-iCalPlugin-Grails@philevents-web-f5d4878dd-x5n6c TZID:Europe/Amsterdam LOCATION:Vennenpad\, 5\, Nunspeet\, Netherlands DESCRIPTION:We are very pleased to announce that the XXV European Symposium on Medieval Logic and
Semantics will be hosted by Radboud University (Netherlands) on June 23-25\, 2026.
The topic\, chosen at the last ESMLS in Parma\, is Logic and the Sciences. We invite potential
speakers to send us proposals for talks of 30 minutes (plus 15 for discussion) on the interplay
between logic (broadly construed) and the sciences (including the natural and mathematical
sciences and the sciences of language and theology) during the Long Middle Ages (200&ndash\;1700).
We welcome submissions relating to any branch of the Western philosophical tradition (Latin\,
Arabic\, Greek\, etc.).