The Architecture of Logic: Diagrammatic Reasoning and Spatial Syntax in Lewis Carroll’s The Game of Logic

Abstract Mathematics has long relied on diagrammatic devices to render abstract structures perceptible and cognitively accessible. In the nineteenth century, visual pedagogy and playful learning converged in experimental didactic models grounded in spatial organization and rule-based manipulation. Within this context, Lewis Carroll’s The Game of Logic (Carroll in The game of logic. MacMillan & co, London, New York, 1887) introduced a grid-based system for teaching Aristotelian syllogism through movable counters arranged within a square diagram. This article interprets Carroll’s logical grid not merely as a pedagogical tool, but as a structured spatial matrix analogous to architectural compositional systems. The red-grey binary scheme of occupied and empty sectors is read in parallel with the solid-void dialectic underlying modular design practices from Durand to Froebel. By framing diagrammatic reasoning as a shared operative structure between logic and architectural design, the study positions the diagram as a cognitive and spatial interface between mathematics and architecture.