12th century Arabic logic diagrams: practice and theory

Wilfrid Hodges

Our starting-point is an attempt in the early twelfth century, by Abu al-Bakarat al-Baghdadi, to rebuild logic on the basis of a system of line diagrams. To see what he was trying to do, we have to reconstruct it with modern knowledge. At present it seems (1) that he was working with a linear form of Gergonne diagrams rather than Euler or Venn diagrams, and (2) that he was developing an idea of Ibn Sina for replacing proof-theoretic entailment by model-theoretic entailment. Calculations show that the procedures he was trying to introduce were feasible in principle but out of reach in practice, not least given the cost of paper.