Article ID: CBB011647892

Boolean Considerations on John Buridan's Octagons of Opposition (2019)


This paper studies John Buridan's octagons of opposition for the de re modal propositions and the propositions of unusual construction. Both Buridan himself and the secondary literature have emphasized the strong similarities between these two octagons (as well as a third one, for propositions with oblique terms). In this paper, I argue that the interconnection between both octagons is more subtle than has previously been thought: if we move beyond the Aristotelian relations, and also take Boolean considerations into account, then the strong analogy between Buridan's octagons starts to break down. These differences in Boolean structure can already be discerned within the octagons themselves; on a more abstract level, they lead to these two octagons having different degrees of Boolean complexity (i.e. Boolean closures of different sizes). These results are obtained by means of bitstring analysis, which is one of the key tools from contemporary logical geometry. Finally, I argue that this historical investigation is directly relevant for the theoretical framework of logical geometry, and discuss how it helps us to address certain open questions in this framework.

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Authors & Contributors
Mazet, Edmond
Stevens, Wesley M.
Folkerts, Menso
Rommevaux, Sabine
Hiscock, Nigel
Sylla, Edith Dudley
Iranian Studies
Revue d'Histoire des Mathématiques
Revue d'Histoire des Sciences
Early Science and Medicine: A Journal for the Study of Science, Technology and Medicine in the Pre-modern Period
Archive for History of Exact Sciences
Suhayl: Journal for the History of the Exact and Natural Sciences in Islamic Civilisation
Ashgate, Variorum
Verlag der Bayerischen Akademie der Wissenschaften
Duke University
Arab/Islamic world, civilization and culture
Philosophy of mathematics
Latin language
Oresme, Nicole
Buridan, Jean
Regiomontanus (Jahannes Mueller)
Bradwardine, Thomas
Time Periods
14th century
16th century
Early modern
Persia (Iran)

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