The Philosophy of Logical Notations and Diagrams

The phrase “philosophy of notation” was coined in 1885 by C. S. Peirce in “On the Algebra of Logic: A Contribution to the Philosophy of Notations” to mean the illustration of principles which underlie all logical notation, both algebraic and graphical. In recent years there has been a renewed interest in the philosophical analysis of formal languages from areas as different as the history of logic, the philosophy of mathematical practice, and cognitive science. In parallel developments that began in the 1990s, research on logical diagrams has shown that these notations are not mere heuristic tools but real logical languages that can be fruitfully formalised, analysed, categorised and compared. Whether this study arises from mathematical, logical or linguistic perspectives, it must share the assumption that, in general, logical languages that can be shown to be expressively equivalent may differ in various ways. However, the precise, philosophicalmeaning of “notational difference” has never been subject to analytical scrutiny. This special issue of Logique et Analyse follows on from new research presented at the second International Workshop on the Philosophy of Notation (May 2019) and is dedicated to historical, philosophical and formal/analytical research on logical notations, including diagrammatic forms of logical representation. Topics may include the history of logical notations; the virtues and the limits of different logical language and notational systems; the design and the role of notations in logic; the circulation of notations in and outside logic; diagrammatic reasoning and visual thinking in logic; parameters of notational variety, and the comparison of notationally distinct but expressively equivalent systems.