Norman, Alexander Jesse; (1999) Diagrammatic reasoning and propositional logic. Masters thesis (M.Phil), UCL (University College London).

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Abstract

It has been the standard view of philosophers in this century that the use of diagrams is incompatible with rigour in logic; and that diagrams are dispensable from logical proof, in the sense that there is no proof of which a diagram is an essential part. This view has come under recent attack by logicians who have proved certain diagrammatic logics—for example, Venn diagrams and Peirce's Existential Graphs—to be sound and complete. This thesis builds on these results. by arguing positively that a diagrammatic logic can have informational resources in virtue of its representational form which are not available to a logically equivalent sentential counterpart: that these resources can facilitate the process of logical inference; and that this implies a view of deductive inference generally which is not straightforwardly "deductivist", but incorporates observational and experimental processes. The strategy followed is to examine the representational features of a particular diagrammatic logic—the alpha Existential Graphs, or EG—and to compare them to those of certain varieties of sentential logic (five-functor two-functor and Polish notation SL). to which EG is extensionally equivalent. In the first half of the thesis, I introduce and situate the standard view; explore the distinctive features of diagrams, and diagrammatic representation; analyse the key idea of perspicuousness; and review current theories of information to determine a compatible background account. In the second half. I introduce EG, and show that it is more perspicuous in the required sense than SL; rebut a well-known claim that EG relies on some special notion of "Peirce provability", and describe how EG can motivate a non-deductivist account of deductive reasoning. Finally, I criticise the standard view of diagrams, and locate EG within Peirce's general theory of signs, underlining the strong motivations for Peirce's late more into diagrammatic logic.

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