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Article ID: CBB001550610

Was Lewis Carroll an Amazing Oppositional Geometer? (2014)

Moretti, Alessio (Author)

History and Philosophy of Logic
Volume: 35, no. 4
Issue: 4
Pages: 383-409

DOI: 10.1080/01445340.2014.981022

Publication Date: 2014
Edition Details: Part of a Series: “The Square of Opposition”
Language: English

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Science and literature Geometry Mathematics Logic Models and modeling in science 19th century Great Britain Carroll, Lewis

Some Carrollian posthumous manuscripts reveal, in addition to his famous `logical diagrams', two mysterious `logical charts'. The first chart, a strange network making out of fourteen logical sentences a large 2D `triangle' containing three smaller ones, has been shown (by Richards, in 1986) equivalent---modulo the rediscovery of a fourth smaller triangle implicit in Carroll's global picture---to a 3D tetrahedron, the four triangular faces of which are the 3+1 Carrollian complex triangles. As it happens, such an until now very mysterious 3D logical shape---slightly deformed---has been rediscovered, independently from Carroll and much later, by a logician (Sauriol), a mathematician (Angot-Pellissier) and a linguist (Smessaert) studying the geometry of the `opposition relations', that is, the mathematical generalisations of the `logical square'. We show that inside what is called equivalently `n-opposition theory', `oppositional geometry' or `logical geometry', Carroll's first chart corresponds exactly, duly reshaped by a logic-preserving geometrical transformation, to the `oppositional tetrahexahedron', which is a very powerful `oppositional closure', the elegant 3D entanglement of a `logical cube' and six `logical hexagons' (and therefore eighteen `logical squares'). The temptation is therefore high to consider the author of Alice's Adventures in Wonderland as a forerunner of oppositional geometry

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Article Beziau, Jean-Yves; Read, Stephen (2014) Square of Opposition: A Diagram and a Theory in Historical Perspective. History and Philosophy of Logic (pp. 315-316). unapi

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