From Aristotle’s Square of Opposition to the “Tri-unity’s Concordance”: Cusanus’ Non-classical Reasoning

  • Antonino DragoEmail author
Part of the Studies in Universal Logic book series (SUL)


It is well-known that Cusanus (1401–1464) introduced the surprising notion of the coincidence of opposites, which in fact shrinks Aristotle’s square of opposition into a segment. Almost a century ago Cassirer suggested that Cusanus had looked for a new kind of logic. Indeed, an accurate inspection of Cusanus’ texts shows that in order to discover new names of God by means of coincidences of opposites, Cusanus invented several names belonging to different kinds of non-classical logic—i.e. positive, paraconsistent, modal and intuitionist—, which were formalised in the last century. When, in his more important book, he invented an intuitionist name he implicitly reasoned about it according to the intuitionist square of opposition so precisely that he was able to organize his theories in a new way; it was based not on axioms- principles, but on the search for a new method for solving a general problem. Moreover, he wanted to refer his reasoning not to the square of opposition but to a new logical scheme, a “tri-unity of concordance”, for which he suggested an original definition. Here this tri-unity is represented by means of a geometrical figure.


Cusanus Square of opposition Non-classical logics 

Mathematical Subject Classification

Primary 03A05 Secondary 03B53 03B22 03B45 03B20 



I am grateful to Prof. David Braithwaite for having revised my poor English and to an anonymous referee for an important suggestion.


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© Springer International Publishing Switzerland 2017

Authors and Affiliations

  1. 1.University of PisaPisaItaly

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