6 - Diagrammatic versus Linguistic Representation
Published online by Cambridge University Press: 24 November 2009
Summary
I started this work with the following assumption: There is a distinction between diagrammatic and linguistic representation, and Venn diagrams are a nonlinguistic form of representation. By showing that the Venn system is sound and complete, I aimed to provide a legitimate reason why logicians who care about valid reasoning should be interested in nonlinguistic representation systems as well. However, the following objection might undermine the import of my project: How do we know that Venn diagrammatic representation is a nonlinguistic system? After all, it might be another linguistic representation system which is too restricted in its expressiveness to be used in our reasoning. If we accept this criticism, what I have done so far would be reduced to the following: A very limited linguistic system was chosen and proven to be sound and complete. Considering how far symbolic logic has developed, this could not be an interesting or meaningful project at all. Therefore, it seems very important to clarify the assumptions that diagrammatic systems are different from linguistic ones and that the Venn systems are nonlinguistic.
There has been some controversy over how to define diagrams in general, despite the fact that we all seem to have some intuitive understanding of diagrams. For example, all of us seem to make some distinction between Venn diagrams and first-order languages. Everyone would classify Euler circles under the same category as Venn diagrams. Or suppose that both a map and verbal instructions are available for us to locate a certain place.
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- The Logical Status of Diagrams , pp. 153 - 184Publisher: Cambridge University PressPrint publication year: 1995