Around and Beyond the Square of Opposition

Part of the series Studies in Universal Logic pp 93-110

John Buridan’s Theory of Consequence and His Octagons of Opposition

  • Stephen ReadAffiliated withDepartment of Philosophy, University of St Andrews Email author 

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One of the manuscripts of Buridan’s Summulae contains three figures, each in the form of an octagon. At each node of each octagon there are nine propositions. Buridan uses the figures to illustrate his doctrine of the syllogism, revising Aristotle’s theory of the modal syllogism and adding theories of syllogisms with propositions containing oblique terms (such as ‘man’s donkey’) and with propositions of “non-normal construction” (where the predicate precedes the copula). O-propositions of non-normal construction (i.e., ‘Some S (some) P is not’) allow Buridan to extend and systematize the theory of the assertoric (i.e., non-modal) syllogism. Buridan points to a revealing analogy between the three octagons. To understand their importance we need to rehearse the medieval theories of signification, supposition, truth and consequence.


Octagons of opposition Assertoric syllogism Modal syllogism Oblique syllogism Signification Buridan

Mathematics Subject Classification

01A35 03-03 03A05