Aaron Schuyler: The Missing Link Between Euler and Venn Diagrams?

Abstract

The elementary idea of intersecting circles to express combinations of concepts was already present in Ramón Llull and Leibniz, while Venn is credited with the breakthrough that only with the intersection of two circles can we express all the required classes that arise by combining S and P in Boolean algebra. However, Aaron Schuyler published his popular manual Principles of Logic for High Schools and Colleges in 1869, ten years before Venn’s work. Reading Venn’s Symbolic Logic, we notice some similarities to this textbook, probably justified in the spirit of the age, as Venn never cited Schuyler. This American author made the same mistake as Venn in stating that the representation of the universal negative (E) was the only unambiguous diagram and shows how to represent the classes SP, S¬P, P¬S and ¬SP within the regions of the intersection of two circles. He also drew an original and novel diagram by eliminating the region between S and P from the Euler diagram that represents the universal negative proposition. Furthermore, their diagrams can be of great help in understanding the differences between Venn and Hamilton’s proposals on the fundamental structure of propositions. Finally, Schuyler was one of the few 19th century authors who took the step of expressing propositions with a negative subject, something that did not make sense for Aristotelian logic, but it did for symbolic logic. For all these reasons, we consider Aaron Schuyler to be a good candidate for the missing link between Euler and Venn diagrams.