Facilitators: Dr Lopamudra Choudhury, Professor Mihir Chakraborty and Reetu Bhattacharya
Course Summary
This course has two main components.
Open universe (from venn-i to venn-io): The diagrammatic system called Venn-i has been developed as an extension of Shin’s Venn-II system by incorporating constant symbols. In particular, this system contains symbols representing the absence (taking a cue from the notion of abhāva‘ existing in ancient Indian knowledge system) of individuals as well as the presence of individuals. Absence brings along with it certain interesting properties. We introduce the notion of an open universe and develop a natural extension of Venn-i to interpret the system using an open universe. The underlying logic and features of open universe will be discussed in the session.
Absence and square of opposition: We will introduce two traditions of diagrammatic studies, one, the Euler–Venn–Peirce diagram and the other, following tradition of Aristotle, the square of oppositions. We put together both the traditions to study representations of singular propositions (through a diagram system, Venn-i, involving constants), their negations and the inter relationship between the two. Along with classical negation we have incorporated negation of another kind viz. absence. We have also considered the changes that take place in the square of opposition in the context of open universe.
Prerequisite Knowledge
Knowledge of the historical development of diagrammatic logics from Euler through to Shin and the preliminaries of spider diagrams. This material will be covered during the sessions on diagrammatic logics. Also knowledge of the square of oppositions would be helpful.
Outcomes
Attendees will gain knowledge of the different choices that can be made when including constants in diagrammatic logics and how to interpret such logics using an open universe. The relation of opposition among propositions has interested logicians for ages. This study will show pictorial relation between singular and general propositions.
Course Materials
Slides are available for download below.