Peirce’s Philosophy of Notation

Organizers: Francesco Bellucci (University of Bologna), Frederik Stjernfelt (Aalborg University Copenhagen), and Ahti-Veikko Pietarinen (Hong Kong Baptist University)

Francesco Bellucci is Associate Professor of Philosophy and Theory of Language at the University of Bologna. He is the author of Peirce’s Speculative Grammar (Routledge 2017), Signs and Demonstrations from Aristotle to Radulphus Brito (with C. Marmo, Brill 2023) and the editor of Charles S. Peirce. Selected Writings on Semiotics (De Gruyter 2020).

Frederik Stjernfelt is Full Professor of Semiotics, Intellectual History, and Philosophy of Science at Aalborg University Copenhagen. He is the author of Diagrammatology (Springer 2007), Natural Propositions (Docent Press 2014), and Sheets, Diagrams, and Realism in Peirce (De Gruyter 2022).

Ahti-Veikko Pietarinen is Professor of Philosophy at Hong Kong Baptist University, Department of Religion and Philosophy, and associate of Ethical and Theoretical AI Lab and the Centre for Applied Ethics. He is editor of the five-volume series Logic of the Future: Peirce’s Writings on Existential Graphs (De Gruyter 2019–2024).

Workshop Description
The phrase “philosophy of notation” was coined by Charles S. Peirce in 1885 to indicate the investigation of the principles that underlie all notations, diagrammatic and otherwise. Peirce was most interested in a wide range of algebraical and graphical notations for logic, but the phrase can also be applied to his studies on the types of numerical notations, and more generally to his research into formal languages for logic and mathematics and to the norms and principles of scientific notations and nomenclatures. As with its better-known term of “ethics of terminology”, Peirce also extensively wrote on the “ethics of notation” and its applications in science, pedagogy, and scientific communication.

Peirce’s philosophy of notation was largely based on his theory and classification of signs, or semiotics. Semiotics in Peirce is fundamentally a descriptive discipline: it determines which sign types are involved in establishing propositions and arguments, and how these signs relate and combine. The philosophy of notation, by contrast, involves a normative dimension: it determines which sign types should be used in constructing logical and mathematical notations, and how these signs should relate and combine.

Normative assessments, in turn, are based on aims. As far as logic is concerned, it is now sufficiently clear that the aim of Peirce’s investigations into, and experimentations with, logical notations was the achievement of a (nearly) perfectly analytical language, a language that would be an immediate and transparent instrument of logical analysis, or as he also sometimes says, a language that would provide an “icon of logical analysis”. Ethical considerations in notation choice and design are also involved: The person who introduces a conception into science has both the right and the duty of prescribing a terminology and a notation for it; and her/his terminology and notation should be both conservative and to be followed except where disadvantageous.

The workshop’s aim is to provide a forum for an organic and systematic discussion of Peirce’s philosophy of notation. It will cover topics such as the development of Peirce’s unique notations both algebraic and graphical, for both logic and mathematics; his idea of diagrammatic reasoning; his philosophy of mathematics and of mathematical practice; his principle of the “ethics of notation”; his general history and philosophy of science; and the reception, interpretation, and criticisms of his ideas about notations.

Keywords: Analysis in logic; Algebra of logic; Diagram; Diagrammatic reasoning; Ethics of notations; Iconicity; Logic; Logical graphs; Mathematical notations; Notations; Numerical notations; Terminology; Peirce.

Call for Participation
In this workshop, we call for abstracts that address historical, theoretical, and comparative issues in Peirce’s philosophy of notation. Topics of discussion can include, but are not limited to the following research questions:

  • Peirce’s definitions of “diagram”, “notation”, and “icon”
  • Peirce’s algebraical notations for logic and their evolution
  • Peirce’s graphical notations for logic and their evolution
  • Logical notations used by members of Peirce’s group at the Johns Hopkins University (Origins of the ideas)
  • Logical notations used by Peirce’s contemporaries and colleagues in America and Europe (Synchronic perspective – moving from person to person in one moment of time)
  • Contemporary deployment and development of Peirce’s notations (Legacy perspectives – moving through time)
  • Peirce’s notations for numerical and other mathematical systems
  • Peirce’s ethics of notation and terminology
  • Peirce’s diagrammatic reasoning and its alternatives
  • Analysis, iconicity, simplicity, economy, typology etc. in diagrams and other notations
  • Contributions of Peircean notations to scientific progress, pedagogy of mathematics and the sciences, etc.

Abstracts that address historical, theoretical, and comparative issues in Peirce’s philosophy of notation are welcomed. They should be of between 300 and 500 words and should be submitted to by June 1, 2024. Authors will receive notification of acceptance to the workshop before June 7, 2024, when registration for the main conference opens. Participants in the workshop must register for the full conference.

Publication of presented papers is planned in a volume on Peirce’s Philosophy of Notations (De Gruyter) and/or a special issue of a journal.