Source: Notre Dame J. Formal Logic
Volume 39, Number 4
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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