Edwina, Alex, and Doug F,

In my note to Alex, I said that every diagram is a structure, and every structure is a diagram.  But I was too hasty in saying that.  I should have said that a diagram is a kind of structure that may be used to represent the significant aspects of something else. 

A diagram could be isomorphic to the structure it represents, but more often than not, a diagram represents only some aspect of a structure that is considered significant for some purpose.  That significance is the Thirdness. 

For example, an architect's blueprint for a building only represents a small, but important part -- namely a map of the major parts and how they fit together.  As a simplified outline, it would be Secondness.  But as an intentional plan, it would beThirdness.

In any case, it's safe to say that every diagram is a structure.  Its relationship to some other structure could be secondness if it if just happens to resemble it.  But the relationship would be thirdness if the person who drew the diagram had intended some purpose for it, such as a plan for building something, for teaching something, for selling something, for repairing something, or for destroying something.

And for Doug F, I would emphasize that the purpose of the diagram might be conscious in the mind of the person who draws it, but the reasoning methods in the cerebellum for constructing the diagram would not be conscious.  An expert painter freely uses techniques that may have required years of conscious thought to learn.

John