Ciola Lab

Radboud University Nijmegen

Oost-Nederland (NL2) · Netherlands

ERC-funded
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ERC Starting Grant · 2022

The Impossible and the Imaginable: Late-Medieval Semantics of Impossibility and the Roots of Complex Mathematics

A popular view in the history of philosophy and science holds that we only conceive what is in some sense possible and cannot truly understand anything intrinsically contradictory. The Chimera is the paradigmatic example of such an inconceivable absolute impossibility in medieval logic. "Chimera" is a necessarily empty term lacking signification and reference. Analogously premodern mathematics dismisses the square root of a negative number as the impossible result of an impossible operation, i.e. something as nonsensical as the Chimera. Yet by the 16th century complex numbers–i.e. those numbers having an imaginary part i = the numerical value of [root–1]–start being used and problematised.…

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