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Fall 1998 On the Insufficiency of Linear Diagrams for Syllogisms
Oliver Lemon, Ian Pratt
Notre Dame J. Formal Logic 39(4): 573-580 (Fall 1998). DOI: 10.1305/ndjfl/1039118871


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.


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Oliver Lemon. Ian Pratt. "On the Insufficiency of Linear Diagrams for Syllogisms." Notre Dame J. Formal Logic 39 (4) 573 - 580, Fall 1998.


Published: Fall 1998
First available in Project Euclid: 5 December 2002

zbMATH: 1002.03517
MathSciNet: MR1776228
Digital Object Identifier: 10.1305/ndjfl/1039118871

Primary: 03B10
Secondary: 03A05 , 03B20

Rights: Copyright © 1998 University of Notre Dame


Vol.39 • No. 4 • Fall 1998
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