Alex,

The words 'structure' and 'diagram' have multiple informal meanings in dictionaries of English. They also have multiple formal meanings in different theories of engineering, science, architecture, mathematics, ...

Alex> Diagram is just a picture. Rotate it on 180 grads or delete labels, nothing to think about structure :-)

From ancient times to the present, the angles and sizes of many kinds of diagrams have been very significant -- but there is usually some fixed ratio of the size of the diagram to the structure it represents:  diagrams in geometry, architectural plans, maps of the earth, moon, stars, and designs of engineering systems (a car,  a pump,  or a violin, for example).

But I agree that some diagrams of linguistics or logic can be moved or rotated without changing the meaning.

But the beauty of Peirce's existential graphs is that they can be used for multiple purposes.  For representing logic, an EG can be mapped to and from a linear notation without any change in meaning.

But in 1911, he wanted to generalize his graphs to represent "stereoscopic moving images" or "moving pictures of thought".  For those purposes, he could generalize EGs to map pictures, even moving pictures, to graphs that have two kinds of information:  abstract logic that has no implicit physical information and representations of physical structures where the relative positions and angles are significant.

This is a very important reason why Peirce's diagrammatic reasoning is far more expressive than predicate calculus *and* LLMs.  I'm writing another article about Peirce's Delta Graphs, which appear to be going in that direction (just before Peirce had a serious accident and left the document incomplete).  But he left enough hints and requirements to indicate the direction he intended.  In 2018, I published an article about generalizing existential graphs (see the references in the PDF I sent).

John