# “A Venn Diagrammatical Analysis of Set Membership and Identity” by Robert Boyles (22 Nov)

In elementary logic, Venn diagrams are used to represent categorical statements and analyze and evaluate categorical syllogisms. Thus, the four traditional categorical statements, viz., A, E, I, and O, have their respective Venn diagrams. Also, the validity of syllogisms is easily determined by using Venn diagrams. Though the Venn diagram is a powerful analytical tool, it still has limitations. For one, it fails to represent singular statements of the form, “a is F;” in another, it fails to represent identity statements of the form, “a is b.” Since this is so, it follows that it also fails to give an account of the validity of some obviously valid inferences that contains these types of statements as constituents (e.g., All men are mortal. Socrates is a man. So, Socrates is mortal). In this paper, we offer a way of supplementing the rules of the Venn diagram so that it could surpass these limitations. To go about this, we take the standard principles of Venn diagrams at face value. Next, we add some formation rules that would account for membership and identity. Note that these rules are consistent with the rules of first-order logic and set theory. Finally, we shall demonstrate how this reformulated Venn diagram technique is supposed to work.

Philosophy Seminar Series.
Date: Thursday, 22 Nov 2012
Time: 2pm – 4pm
Venue: Philosophy Resource Room (AS3 #05-23)
Speaker: Sidney Diamante, Lecturer in Philosophy, De La Salle University, Manila, Philippines
Moderator: Dr. Neil Sinhababu