Article ID: CBB011647892

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

unapi

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
Celeyrette, Jean
De Risi, Vincenzo
Welsh, Whitney Elizabeth
Vitrac, Bernard
Tura, Adolfo
Concepts
Mathematics
Geometry
Arab/Islamic world, civilization and culture
Translations
Philosophy of mathematics
Cross-cultural interaction; cultural influence
Time Periods
Medieval
Ancient
Early modern
14th century
Modern
10th century
Places
Mediterranean region
Europe
Persia (Iran)
Italy
Greece
France
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