Abstract
There is growing literature on the employment of diagrams to ease logical reasoning. Less is said about the visual properties of symbolic notations. It is, for instance, no coincidence that most notations offered for implication are asymmetrical to reflect the asymmetry of the operator itself. Hence, the symbol is self-interpreting in that its appearance suggests a property of the object it stands for. In this paper, we discuss a compositional notation, invented by Lewis Carroll in 1884, which suggests relations between propositions. Carroll is known for designing both symbolic and diagrammatic notations for logic. Although his theory was rooted in the “old” logic, he championed a thorough use of notations in the Boolean style that was spreading in his time. In the notation we are considering here, Carroll represents simple propositions, and then their symbols are combined to form compound propositions. An interesting outcome of this design, based on the visualization of the composition of propositions, is that the layout exhibits relations between propositions. For instance, a proposition is shown to be subaltern to another if the symbol of the former is contained by the symbol of the latter. In this paper, we consider the guiding principles for the design of this notation and the extent to which it visually conveys relations between propositions.
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Acknowledgments
In addition to expressing our appreciation to Miles Rind for his help and advice, we want to thank Francine Abeles for her valuable suggestions and critique. Fran has provided us with so many of the fruits of her research over many years, answering our questions while making astute suggestions with generosity and patience. For the second author, this research benefitted from the support of ERC project “Abduction in the age of Uncertainty” (PUT 1305, Principal Investigator: Prof. Ahti-Veikko Pietarinen).
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Englebretsen, G., Moktefi, A. (2022). Lewis Carroll’s Almost Diagrammatic Logic Notation. In: Béziau, JY., Desclés, JP., Moktefi, A., Pascu, A.C. (eds) Logic in Question. Studies in Universal Logic. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-94452-0_8
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