Peirce’s inclusion diagrams, with application to syllogisms

Reetu Bhattacharjee and Amirouche Moktefi


While developing his system of Existential graphs which he viewed as the logic of the future, Charles S. Peirce continued working on variations of past diagrams. In particular, he introduced in the period 1896-1901 an original variation of Eulerian diagrams where the shape of the curves indicated the sign of the classes that were contained in them. These diagrams recently attracted attention for their ability to represent negative terms more directly than earlier schemes. Yet, we offer here a more general rationale: we argue that Peirce conceived these diagrams by making inclusion the main operator, a practice that is found in his other logical systems, both algebraic and diagrammatic. This is achieved by expressing universal propositions in an inclusional form. This shift allows him to classify syllogisms under just three diagrammatic forms in a style that is found in some of his contemporaries.

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