Image, Diagram, and Metaphor

Peirce asserts a triad of what he calls "hypoicons.

Hypoicons may be roughly divided according to the mode of Firstness of which they partake.  Those which partake of simple qualities, or First Firstnesses, are images; those which represent the relations, mainly dyadic, or so regarded, of the parts of one thing by analogous relations in their own parts, are diagrams; those which represent the representative character of a representamen by representing a parallelism in something else, are metaphors. [CP2.277]

Following this organization then, if there is a diagrammatic thinking, or thinking with diagrams, there must also be a thinking with metaphors and a thinking with images.

Thorstein Veblen ["Why is Economics Not an Evolutionary Science"] brings out the problems of thinking metaphorically, at least when it comes to a science of economics.

But it is precisely in this use of figurative terms for the formulation of theory that the classical normality still lives in its attenuated life in modern economics; and it is this facile recourse to inscrutable figures of speech as the ultimate terms of theory that has saved the economists from being dragooned into the ranks of modern science. [p. 383]

A metaphor works by comparing (setting in "parallel") the system to be known with one that is already known (in the sense we are acquainted with it).  It allows us to understand things we cannot specify in detail, so that while metaphors are effective and satisfying, even exhilarating, and both metaphors and diagrams are human creations (aka "fictions"), the metaphors do not provide the detailed specifications, the "exactitude," of a diagram.

As for imagery, we might compare a sales graph with a map.  The indices and relationships of the map (on the right) allow inferences of new indices and relationships within that map — I can locate my house on it — whereas the abstractions of the graph allow only extrapolations from its fixity.  I can draw any number of conclusions from such a graph, or a photograph or a work of art, but those conclusions will have a subjective inventiveness, external to the image.  Images are also a way of abstracting from experience; of thinking, knowing, even explaining; of drawing consequences, but they are neither diagrammatic nor metaphorical.