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Graphical representations of intersection of sets as logical combinations are much older than Venn. Euler and Leibniz are often quoted and the current Wikipedia article also quotes Ramon Llull but I do not really find the illustrations provided in the Wiki Commons for Llull very compelling.

I expect that these kind of ideas can be found in many other places and even older times, perhaps in disguise.

In this context I find the heraldic uses of theological diagrams such as shown here quite fascinating as a kind of medieval fashion statement.

Do you know of older examples of graphical representation of logical and/or set relations, for instance of Chinese, Arabic and Greek origin ?

(ps: at least one of the tags is a joke)

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+1 for a diagram chase through history. Very nice. – Cam McLeman May 5 '10 at 17:39
up vote 2 down vote accepted

You may already be familiar with Ruskey and Weston's "A Survey of Venn Diagrams," which includes a discussion of Borromean rings. Such rings are similar to the valknut and the triskelion, of which the gankyil is a type. All of these figures are quite old.

Of course these observations don't answer your question about the use of graphical representations of logical and/or set relations in antiquity.

Plato refers to diagrams, for example, in his discussion of the double-divided line in Book 6 of Republic and in Meno when Socrates questions Meno's slave about a problem in geometry -- how to find a square double in area to any given square. I imagine more examples can be found.

An interesting project would be to find examples of "visual" language in the works of Plato, Aristotle, and Euclid.

While writing this post I came across the following two references:

Edwards, Anthony W. F. Cogwheels of the Mind: The Story of Venn Diagrams. Baltimore, Maryland: The John Hopkins University Press, (2004).

Kuehni, Rolf. "On the Source of d’Aguilon’s Arc Color Mixture Diagram." Unpublished manuscript, 2003.

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Thanks a lot Mr Shutt. I did not know about Edwards' book. I think this contributions gives sufficient sources of study, research and reflexion to be considered a good answer to my original question. As this is community wiki (because there is not a clear cut answer to it), please feel free to add other tidbits about logical diagrams. I am particularly interested by hints of prehistorical graphical representation of ideas and constraints. – ogerard May 9 '10 at 7:04

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