Amirouche Moktefi

A History of Logic Diagrams

Diagrams, however we may define them, are one of the most widely used tools by humans — from ordinary life communication to brainstorming for complicated problems or outlining the overall structure of talks, papers, etc. Some philosophers and psychologists extend the territory of diagrams by embracing mental images under the same category. Diagrams, external or internal, cover such a vast area of human activities that different disciplines, not surprisingly, have approached the topic from different angles.

Visual reasoning with diagrams

Preface.- 1. What is a logical diagram? (Catherine Legg).- 2. The geometry of diagrams and the logic of syllogisms (Richard Bosley).- 3. A diagrammatic calculus of syllogisms (Ruggero Pagnan).- 4. Beyond syllogisms: Carrolls (marked) quadriliteral diagram (Amirouche Moktefi).- 5. A diagrammatic bridge between classical and fuzzy logics (Ferdinando Cavaliere).- 6. Diagrammatic reasoning with Classes and relationships (Jorgen Fischer Nilsson).- 7. On the completeness of spider diagrams augmented with constants (Gem Stapleton, John Howse, Simon Thompson, John Taylor and Peter Chapman).- 8. A practice-based approach to diagrams (Valeria Giardino).- 9. Figures, formulae, and functors (Zach Weber).- 10. Diagrams and concepts of graph theory (Mitsuko Mizuno).

Lewis Carroll's Logic

This chapter discusses the concept of Lewis Carrolls logic. Lewis Carroll is one of those writers on logic obscured by contradictory influences, balanced between the old logic and the new trends. He is a mathematical teacher, the author of childrens tales, and photographer. He is also a very prolific letter-writer and puzzle-maker, and regularly wrote pamphlets and letters to periodicals on matters as various as vaccination, teaching sciences at the university, child actors, and vivisection. Like the majority of his contemporary British colleagues, Carrolls work quickly became out-dated. His only logical contributions, which one still meet(s) with in modern textbooks, are his logic diagrams and Mind problems. Carrolls logical work shows also that he is acquainted with the logical players of his time. Reading Lewis Carroll reveals conflicting influences from both traditional and modern logicians. It also shows some interesting inventions, which deserve more attention from logicians and historians of logic.

Beyond Syllogisms: Carroll’s (Marked) Quadriliteral Diagram

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.