Dark Age (But Not Obscure) Logic A Brief Excursion

The 20th century has witnessed a vertiginous development of logic: a discipline that traditionally belonged to the domain of philosophy, but whose recent development is due to the use of mathematics as its meta-language. Considered as one of the greatest of Greek gifts to humanity, logic is now essential as the foundational model for Computer Science. Some scholars assimilate Mathematics and Logic, some think of Logic as part of Mathematics, others include it in Philosophy, and so on. When we were planning this special volume of the Bolet́ın de la Asociación Matemática Venezolana, an article on Mediaeval Logic seemed to be appropriate. This paper is an outline of that field. We follow tradition in starting this history with Aristotle, although pre-Aristotelian logic is of considerable interest, if somewhat controversial. Following Aristotle, we take a brief excursion through Roman and Early Mediaeval logic. We stop in the 13th century AD because of the influence of the work of this period on the 20th century. The natural continuation of Mediaeval Logic occurred in the 1960’s when logicians started to base new developments on translated Mediaeval texts. Two further articles dedicated to History of logic will be needed to trace these developments. This paper, then, is an outline of Mediaeval Logic, its origins and its future.