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:20260511T055018Z DTSTART;TZID=Europe/Brussels:20260519T144500 DTEND;TZID=Europe/Brussels:20260519T154500 SUMMARY:Bolzano\, continuum\, and the Part-Whole Principle UID:20260520T151834Z-iCalPlugin-Grails@philevents-web-6b96c54f56-bljdq TZID:Europe/Brussels LOCATION:Kardinaal Mercierplein 2\, Leuven\, Belgium\, 3000 DESCRIPTION:Abstract \;
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Bolzano's concept of the continuum\, proposed in his last work Paradoxes of the Infinite\, has long been considered erroneous or even inconsistent. In this talk\, I will argue that Bolzano&rsquo\;s framework provides a plausible theory with a clear analogy in contemporary mathematics. He defines two quantities associated with continuous extension: magnitude and multitude. Magnitude corresponds to the Lebesgue measure. As for multitudes\, Bolzano insisted on the Part-Whole Principle\, in contrast to Cantor's notion of cardinality. Nevertheless\, multitudes can also be consistently interpreted within the framework of Numerosity theory. The relationship between Bolzano's magnitude and multitude corresponds to the relationship between the Lebesgue measure and numerosity.
\n\n ORGANIZER;CN=Jan Heylen;CN=Sylvia Wenmackers;CN=Shahab Khademi;CN=Nena Bobovnik: METHOD:PUBLISH END:VEVENT BEGIN:VEVENT DTSTAMP:20260511T055018Z DTSTART;TZID=Europe/Brussels:20260519T170000 DTEND;TZID=Europe/Brussels:20260519T183000 SUMMARY:How many points are in a line segment? From Grosseteste to numerosities UID:20260520T151835Z-iCalPlugin-Grails@philevents-web-6b96c54f56-bljdq 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:20260511T055018Z DTSTART;TZID=Europe/Brussels:20260519T170000 DTEND;TZID=Europe/Brussels:20260519T183000 SUMMARY:How many points are in a line segment? From Grosseteste to numerosities UID:20260520T151836Z-iCalPlugin-Grails@philevents-web-6b96c54f56-bljdq 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:20260511T055018Z DTSTART;TZID=Europe/Brussels:20260528T120000 DTEND;TZID=Europe/Brussels:20260530T170000 SUMMARY:Leuven Kant Conference UID:20260520T151837Z-iCalPlugin-Grails@philevents-web-6b96c54f56-bljdq TZID:Europe/Brussels LOCATION:Andreas Vesaliusstraat 2\, Leuven\, Belgium DESCRIPTION:Program (please see the website for more details):
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\nMay 28
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\nAman Sakhardande (University of Toronto) &ndash\; Is Time an A Priori Representation? Kant contra Locke
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\nDavid Sommer (University College London) &ndash\; Forma dat esse rei: Lambert and the Origin of Kant&rsquo\;s Transcendental Hylomorfism
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\nYinfei Xu (University of Bonn / Renmin University of China) &ndash\; The Dual Meaning of Kant&rsquo\;s Concept of Freedom and its Origin: Taking the Dialogue in the New Elucidation as a Point of Entry
\n\nJoel Thiago Klein (Goethe-University Frankfurt / Federal University of Paraná\;) &ndash\; Pratical Reason in Practice: The Case of Revolution and the Issue of Conflicting Moral Duties in Kant's Practical Philosophy
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\nKeynote: Antoine Grandjean (Université\; de Lille) &ndash\; A German Philosopher: A Contextual Reading of the Kant-Constant Controversy
Respondent: Martina Favaretto (University of Groningen)
\n \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \;
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\nMay 29
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\nMarí\;a Guadalupe Martinez Fischer (Paranamerican University) &ndash\; The Idea of the &ldquo\;State of Nature&rdquo\; in the Critique of Pure Reason
\n\nShahab Vesali (KU Leuven) &ndash\; The Dual Sense of Self-Consciousness in Kant &rsquo\;s Critique of Pure Reason
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\nCaleb Reidy (University of Pittsburgh) &ndash\; Objective Validity as Truth-Entailing in Kant
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\nBennet Salzmann (University of Heidelberg) &ndash\; Kant&rsquo\;s Stoic Concept of Moral Progress
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\nCarolina Paulsen (Federal University of Pelotas / University of Hamburg) &ndash\; From Egoism to Cosmopolitanism: Kant&rsquo\;s Vision of Human Nature and the Path to Perpetual Peace
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\nKeynote: Melissa Merritt (University of New South Wales) &ndash\; Kant and Stoic Cosmopolitanism
Respondent: Marijana Vujosevic (Leiden University)
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\n\nMay 30
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\nYuyue Zhang (Tsinghua University) &ndash\; Pure Music and the Unity of Kant&rsquo\;s Aesthetic System
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\nKavin Chada (Indiana University) &ndash\; A Third Kind of Causality in Kant&rsquo\;s Third Critique?
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\nMartin Obreque (Diego Portales University / Complutense University of Madrid) &ndash\; &ldquo\;Freiheit ist das ursprü\;ngliche Leben&rdquo\;: The Concept of Life in Kant&rsquo\;s Critical Philosophy
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\nCarlina Schreiber (University of Cologne) &ndash\; Kant on &ldquo\;Inner Morality&rdquo\; and Political Obligation
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\nMichael Kryluk (University of Friburg) &ndash\; Kant and Democracy: Republicanism vs Despotism\, Representation vs Populism
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\nKeynote: Konstantin Pollok (Johannes-Gutenberg University Mainz) &ndash\; Kant&rsquo\;s Road to Perpetual Peace: On the Concluding Remark of the Doctrine of Right
\n\nRespondent: Egyle Hannah do Nascimiento Lopes (Federal University of Paraná\; / University of Vechta)
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\nOrganizers: Karin de Boer (KU Leuven)\, David Del Bianco (KU Leuven)\, Shahab Vesali (KU Leuven)\, Henny Blomme (Université\; libre de Bruxelles)
ORGANIZER;CN=Karin de Boer;CN=Luis Fellipe Garcia;CN=Shahab Vesali;CN=Henny Blomme: METHOD:PUBLISH END:VEVENT BEGIN:VEVENT DTSTAMP:20260511T055018Z DTSTART;TZID=Europe/Brussels:20260924T100000 DTEND;TZID=Europe/Brussels:20260926T170000 SUMMARY:EACME 2026 UID:20260520T151838Z-iCalPlugin-Grails@philevents-web-6b96c54f56-bljdq TZID:Europe/Brussels LOCATION:Janseniusstraat 1\, Leuven\, Belgium\, 3000 DESCRIPTION:EACME Annual Conference 2026
\nSeptember 24th&ndash\;26th\, 2026\, Leuven\, Belgium
\nCelebrating European Bioethics
\n40th Anniversary European Association of Centres for Medical Ethics and \;Centre for Biomedical Ethics and Law\, KU Leuven
\nRegistrations are open for EACME2026
\nIn 2026\, we celebrate a remarkable milestone: the 40th anniversary of both the European Association of Centres for Medical Ethics and the Centre for Biomedical Ethics and Law\, KU Leuven. Join us to be part of this historic moment.
\nFor four decades\, both organizations have been at the forefront of tackling complex ethical challenges in medicine and healthcare\, in research and education\, bringing together young and established scholars in a collaborative dialogue.
\nThe anniversary conference will reflect on this journey while looking forward to new developments in the field.
\nThe historic town center of Leuven\, home of the oldest university in the Low Countries\, offers an ideal setting for both academic exchange and social activities.
\n\nCall for Abstracts
\nAttendees will have the opportunity to engage in discussions on a wide range of topics. We are particularly committed to a radically inclusive approach with regard to the topics eligible for the parallel sessions. Participants are invited to submit abstracts on all topics related to the field of medical ethics and bioethics in the broad sense. We hope this thematic inclusiveness will encourage young researchers to bring their creativity and diverse perspectives to the conversation. Please submit your abstract via https://eacme2026.org
\nAbstract submission deadline is 1st of March 2026.
\n\nMore Information
\nCentre for Biomedical Ethics and Law
\nDepartment of Public Health and Primary Care &ndash\; Faculty of Medicine &ndash\; KU Leuven
\nKapucijnenvoer 7
\n3000 Leuven &ndash\; BELGIUM
\nEmail: eacme2026@kuleuven.be Website: https://eacme2026.org
ORGANIZER: METHOD:PUBLISH END:VEVENT END:VCALENDAR