Notre Dame Journal of Formal Logic

On the Insufficiency of Linear Diagrams for Syllogisms

Oliver Lemon and Ian Pratt


In Volume 33:1 of the Notre Dame Journal of Formal Logic, a system for diagramming syllogistic inferences using straight line segments is presented by Englebretsen. In light of recent research on the representational power of diagrammatic representation systems by the authors, we point out some problems with the proposal, and indeed, with any proposal for representing logically possible situations diagrammatically. We shall first outline the proposed linear diagrammatic system of Englebretsen, and then show by means of counterexamples that it is inadequate as a representation scheme for general logical inferences (the task for which the system is intended). We also show that modifications to the system fail to remedy the problems. The considerations we present are not limited to the particular proposal of Englebretsen; we thus draw a more general moral about the use of spatial relations in representation systems.

Article information

Notre Dame J. Formal Logic Volume 39, Number 4 (1998), 573-580.

First available in Project Euclid: 5 December 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03B10: Classical first-order logic
Secondary: 03A05: Philosophical and critical {For philosophy of mathematics, see also 00A30} 03B20: Subsystems of classical logic (including intuitionistic logic)


Lemon, Oliver; Pratt, Ian. On the Insufficiency of Linear Diagrams for Syllogisms. Notre Dame J. Formal Logic 39 (1998), no. 4, 573--580. doi:10.1305/ndjfl/1039118871.

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