The Proto-exposition of Aristotelian Categorical Logic

  • Manuel CorreiaEmail author
Part of the Studies in Universal Logic book series (SUL)


The aim of this paper is to state that the oldest Western treatises on categorical logic, the one attributed to Apuleius of Madaurus (I–II AD) and the other written by Boethius (VI AD), follow a common plan rather than a common written source. I call this common plan the proto-exposition of categorical logic as much as it can be reconstructed in its formality. Its limits exceed those of Aristotle’s written works on logic, and both Apuleius and Boethius suggest that Aristotle’s first disciples, Theophrastus and Eudemus, play an important role in its arrangement. After remarking its main characteristics, I describe its limits, by including indefinite terms in syllogistic premises, in connection with three general rules or Axioms making decidable every categorical syllogism. Accordingly, I analyze some study cases in order to distinguish strict conclusions from non-strict ones, which represents a new discernment on existential-import discussion. Then, I remark the importance of the concept of quantitative symmetry by showing how the three general rules can assess the validity of classical hypothetical syllogistic. Thus, the paper presents an extension of Aristotelian logic by taking its proto-exposition as starting point.


Aristotelian logic Ancient commentators Syllogistic Existential import Indefinite terms 

Mathematical Subject Classification

Primary 03-02 Secondary 03B5 



This article was made possible thanks to Fondecyt N°1141135. I am grateful to Prof. Dr. Jean-Yves Beziau for his invitation to the 4th World Congress on the Square of Opposition, May 5-9, 2014, Vatican City, where a first version of this paper was given. I am also thankful to the editor and the referees for their useful comments.


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© Springer International Publishing Switzerland 2017

Authors and Affiliations

  1. 1.Facultad de FilosofíaPontificia Universidad Católica de Chile, Campus San JoaquínMaculChile

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