Beyond syllogisms: Carroll's (marked) quadriliteral diagram

Abstract

The logician Lewis Carroll (1832-1898) invented a diagrammatic scheme for syllogisms and described how it could be used for logic problems involving more than 3 terms. Curiously, he never provided in print any diagrammatic solution for such a complex problem. The aim of this paper is to make sense of a manuscript where Carroll attempts to solve a sorite using his quadriliteral diagram. In this problem, three propositions are offered as premises. The purpose is to look for what information can be gathered as to the relation between two given terms involved in the argument. This case study provides some insights about the use of diagrams to solve elimination problems that were highly considered by early symbolist logicians.