1st World Congress on Logic, Chance, and Money

Speaker: Reetu Bhattacharjee, University of Műnster

Diagrams have been part of logical reasoning since the 15th century due to their intuitive nature and cognitive advantages. However, with the rise of symbolic logic in the 20th century, diagrams lost their popularity. The criticism against diagrams was that they are ambiguous and lead to misinterpretation.

For example, if we have the premises ‘No M is P’ and ‘Some S are M’ which are represented by the Euler diagrams Fig. 1(a) and (b) respectively. (a) (b) Fig. 1 The premises presented above are from the syllogistic mood Ferio. The valid conclusion derived from these premises is ‘Some S are not P’. This conclusion should be derived by combining the diagrams in Fig. 1. However, upon combining them, we end up with three possible cases. Although ‘Some S are not P’ can be derived from all three diagrams in Fig. 2, the diagrams in Fig. 2(a) and (c) also provide the information ‘No S are P’ and ‘All P are S’, respectively. (a) (b) (c) Fig. 2 This ambiguity is not a fault of the Euler diagram itself but rather the result of a lack of inference rules for combining diagrams.

This problem was successfully addressed when Shin proposed a set of inference rules analogous to those in first-order predicate calculus. However, the visual clarity of Euler diagrams was significantly compromised in Shin’s system. The presentation aims to show how various limitations concerning logical diagrams have been addressed through the inclusion of different inference rules, which have enhanced the diagrams' expressivity.

Additionally, it will discuss how this increased expressivity has come at the cost of visual clarity. J. Lemanski, Periods in the Use of Euler-Type Diagrams, Acta Baltica Historiaeet Philosophiae Scientiarum 5, 50 (2017). M. Giaquinto, Crossing Curves: A Limit to the Use of Diagrams in Proofs, Philosophia Mathematica 19, 281 (2011).  S.-J. Shin, The Logical Status of Diagrams (Cambridge University Press, Cambridge,1994).