History and Philosophy of Logic Notations

Notations are an important aspect of modern logic. Since the time of Leibniz at least, logicians have been keenly interested in the properties of logical notations and symbolic systems. One remarkable attempt to develop a philosophical investigation into logical notations was made by C. S. Peirce, who coined the phrase “philosophy of notation” to denote the principles that govern logical symbolism, both algebraical and graphical. In the works of logicians such as Leibniz, Lambert, Ploucquet, Boole, Frege, Peirce, Schröder, Peano, Russell (and many others), we find important ideas concerning the different modes of representation of logical concepts, and important suggestions regarding the virtues and faults of the different systems.

The aim of the workshop is to update and advance scholarship on the history and philosophy of logic notations, and to explore the present challenges and future developments of the field. Topics that will be addressed include: the history of logical notations; the virtues and the limits of different notations and symbolic 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 and mathematics; cognitive and semiotic dimensions of formal reasoning.

The workshop will take place in Tallinn on 1-2 August 2015, before the 'Logic, Methodology and Philosophy of Science Congress' that takes place on 3-8 August in Helsinki. There is a 2 hour ferry ride between Tallinn and Helsinki.

For more information, please contact: [email protected]

The organisers,

Ahti-Veikko Pietarinen, Francesco Bellucci and Amirouche Moktefi

1. August 2015

Location: Building SOC - Room 414, Tallinn University of Technology

10.00-10.15 Opening

10.15-11.00 Volker Peckhaus, ‘Mathematics as universal reasoning’: On the role of symbols in the algebra of logic

11.00-11.30 Gabriela Besler, Gottlob Frege’s notation in use

11.30-12.00 Coffee break

12.00-12.30 Jens Lemanski, Schemes and notations of Euler-diagrams in the Weigel and Weise circle

12.30-13.00 Anna-Sophie Heinemann, “horrent with mysterious spiculae”: Augustus De Morgan’s notational system of 1850

13.00-14.00 Lunch break

14.00-14.30 Ahti-Veikko Pietarinen, No scope for illation?

14.30-15.00 Francesco Bellucci, Peirce and Wittgenstein on parentheses and other signs

15.00-15.30 Javier Legris, C. S. Peirce’s existential graphs beyond the distinction of logic as calculus vs. logic as language

15.30-16.00 Coffee break

16.00-16.45 Frederik Stjernfelt, Natural kinds and the philosophy of notation

16.45-17.30 Jim Burton, The spontaneous ideology of spider diagrams

2. August 2015

Location: Building SOC - Room 414, Tallinn University of Technology

10.30-11.00 Ofra Rechter, Kant on Notation and Intuition

11.00-11.30 Amirouche Moktefi, On the choice of notations in early symbolic logic

11.30-12.00 Dirk Schlimm, Towards a cognitive and pragmatic account of notations for propositional logic

12.00-13.00 Lunch break

13.00-13.45 Jean-Yves Béziau, Semiotics of modern logic

13.45-14.30 Emily Grosholz, The idioms of logic, arithmetic, and algebraic number theory

14.30-15.00 Coffee break

15.00-15.30 Larisa Gogianu, First-order logic without identity

15.30-16.00 Fabien Schang, If, and only if

16.00-16.30 Reinhard Kahle & Wilfried Keller, Coloured syntax and semantics