BEGIN:VCALENDAR PRODID:-//Grails iCalendar plugin//NONSGML Grails iCalendar plugin//EN VERSION:2.0 CALSCALE:GREGORIAN METHOD:PUBLISH BEGIN:VEVENT DTSTAMP:20260415T165311Z DTSTART;TZID=Europe/Brussels:20260519T133000 DTEND;TZID=Europe/Brussels:20260519T143000 SUMMARY:From the Mathematization of Logic to the "Logicalization" of Mathematics? Imagination and Impossibility Between Late-Medieval Semantics and the Rise Complex Mathematics UID:20260417T131642Z-iCalPlugin-Grails@philevents-web-f5d4878dd-x5n6c TZID:Europe/Brussels LOCATION:Kardinaal Mercierplein 2\, Leuven\, Belgium\, 3000 DESCRIPTION:

Abstract

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Why 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.

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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.

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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.

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What 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.

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The 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 END:VCALENDAR