Systems

If by 'system' is meant — and this is the minimal sense of the word — a sort of consequence, coherence and insistence — a certain gathering together — there is an injunction to the system that I have never renounced, and never wished to. … 'System ', however, in a philosophical sense that is more rigorous, and perhaps more modern, can also be taken to mean a totalization in the configuration, a continuity of all statements, a form of coherence (not coherence itself), involving syllogicity of logic, a certain syn which is no longer simply that of gathering in general, but rather of the assemblage of ontological propositions.

— Derrida and Ferraris, I Have a Taste for the 

Secret, (Polity Press, 2001), p. 3

Diagrammatic thinking, at least as I envision it, is also an effort to get away from the "system" as an axiomatic, analytically formal, would-be universal "totalization" and to see it as a particular collection of indices and relationships abstracted from experience on the one side and limited in its applications to that kind of experience on the other.

And, such "systems" occur on much simpler levels still. Andrew Whiten's "intervening variable":

Andrew Whiten, "Triangulation, Intervening Variables, and Experience
Projection," Behavioral and Brain Sciences 21 (1) (1998):133

performs the same mediating function in what he calls the "triangulation" of patterns on the one side with consequences on the other.  It really doesn't matter exactly what the intervening variable is — whether it's a word, an image, or a layer of neurons.  What matters is that it's operating diagrammatically with "a sort of consequence, coherence and insistence — a certain gathering together."

Maps, Cameras, and Ideology

Maps as diagrams are judged by how well they function, but that functionality, however it's defined, is guaranteed by the precision and accuracy that goes into the map's making.  A large part of why Captain James Cook rise from below decks to command of three exploratory expeditions to the South Pacific was his mapmaking abilities, and the maps he made were so precise and accurate, I've heard, that they were still being used in some places at the start of WW II.  This emphasis on the accuracy and precision is generally associated with scientific maps.

But there are also persuasive maps.  And with these the accuracy and precision, that is, how much of it is really needed, is measured by the function of the map. Like Marx's metaphor of the camera obscura:

If in all ideology men and their circumstances appear upside own as in a camera obscura, this phenomenon arises just as much for their historical life-process as the inversion of objects on the retina does from their physical life-process. — Karl Marx, The German Ideology, 1844, p.47

the process inverts things.  Instead of the accuracy and precision of the map being the basis for it's functionality, its functionality is the basis for how much accuracy and precision there needs to be.  With science and ideology, or to put it more generally, the inversion is from truth being the basis for acceptance to acceptance being the basis for truth.

And, the camera metaphor also holds up when we consider accuracy and precision in relation to functionless maps hanging on a wall or illustrating a book.  Perhaps the exactness has an aesthetic quality to it, but like the digital accuracy of the universe of photographs now being stored online, it has been rendered inane.

Image or Diagram

The Mercator map developed in 1569 was well-suited for seafaring.  A course plotted anywhere on the map matches up with the bearing the ship needs to take in getting from one place to another.  To be truly useful the Mercator map needed to be supplemented by a marine chronometer and a knowledge of the magnetic versus geographical poles, but as a diagram the consequences drawn from its applications were verified and refined by countless navigators.  However, as a result of its success, the Mercator projection of the world came to represent the world for virtually everyone.  The diagram used by sailors became the image in books and classrooms everywhere.

The basis for accepting or rejecting an image is the connection between it and the object it represents.  The map, as an image, should be a precise and accurate representation of that object.  It can be criticized for distorting what it represents, as the Mercator map has been for distorting distances and sizes.  It can be admonished for embellishing or channelling what it represents with subliminal messages regarding other things.  It can be argued that the connection between a map and its object should be more inclusive and exact like a camera or more exclusive and ambiguous like art.  The map as a diagram is also based on an analogy to the object it represents, and that analogy can also be critically assessed; but it, and its analogy, are accepted or rejected on the basis of their functionality.  Diagrams, unlike images, answer to what can be done with them, to how well they work in subsequent applications of it, not to their derivation from, or representation of, the object.

Truth and Facts

When science turned our epistemological world from arguments to explanations, facts, the starting point of those explanations and crucible upon which they are tested, took on a certain  sanctity. They have tended to become truth itself, the only truth we can know directly, and hence all but synonymous with truth for many.  They have come stand on their own, taken as truth apart from all but their bare, literal expression.

Against this view:

"Truth and facts are woven together."

This is a quote attributed Shannon L. Adler, an LDS writer.  I'm not sure where she was going with it — I can't find a reference to the source — but for me it nails that Dragnet mentality of "the facts ma'am, just the facts."

On the one hand, facts are the result of diagrammatically abstracting certain indices and relationships from experience.  If not totally the product of the diagram, these abstractions reduce experience to just what will serve the diagram.  On the other hand, facts are the focal points for testing the consequences inferred from the diagram.  If a general law or principle is used to infer and/or explain a fact, that general law is not itself a fact.  It is a principle defined within and warranted by the diagram.  Those facts on either side of a diagram may be true or false, in a sense, but only within the context of being defined and employed by that diagram.

Facts are abstracted with a resemblance to experience and submitted to the ratification of experience using a "diagram, which if not exactly a fiction, is at least a creation" [CP1.383].  Not only are truth and fact interwoven, it is only in the interweaving of them into one consistent fabric that we have something that, if not true, is at least trustworthy.

Explanations

Basing explanation on deduction, or "covering laws," within the context of formal logical is misleading in several ways.
 

1. The explanans involves a  universal scientific law.  Not only do explanations extend far beyond science, but it's unlikely that any scientific law is universal.  It is better to say that explanations include a "substantive generalization," what Toulmin called a "warrant," where "substantive" means it is generally true.  It is precisely the truth or falsity of the explanatory generalizations that is obscured by limiting them to universals.
    
2. Explanation is a matter of making the explanandum rationally acceptable.  With an explanation we already know the explanandum is true, so there's no need to justify or prove it.  With a plausible explanation the explanans and explanandum are logically consistent, nothing more.
    
3. The logical consistency of an explanation is a matter of deduction.  The premises of a deduction,  'if x then y' and 'x', are actually equivalent to the conjunction, 'x and y'.  It is this conjunction of the explanans and the explanandum (all of them being true) that creates a plausible explanation.  Thus, narratives, absent any generalizations, can constitute explanations on the same logical ground as deductions using generalizations.

Not Mechanistic

A diagrammatic approach to thinking, at first glance, might seem overly mechanistic.  The diagram of a machine is certainly as mechanical as the machine itself.  And many diagrams attempt this kind of rigorous consistency.  Using them is an instrumental matter of making calculations.  Formal logic, holding itself aloof from its applications, is like this.  But while all diagrams, and hence diagrammatic thinking in general, relies on consistency, not all diagrams display the rigor of a mechanical device or formal logic.

In fact, most diagrams just aren't that rigorous.  They employ rules or generalizations with qualifications and exceptions, and they are judged by their functionality, not the mechanistic precision of the diagram itself.  Even the rigorous consistency of formal logic has to be taken with a grain of salt when it comes to actually using it.  Any general assertion we make about experience, scientific laws included, is going to have qualifications and exceptions.

More important, though, applying any kind of diagram, rigorous or less so, is not a mechanical process either.  Take for instance a moral question like pulling the plug:

Illustration and example from Richard Arthur 

Mercadante, "The Persistence of Casuistry" 
 

The question is not the result given by any one of these diagrams — although that can be a question in its own right.  The question is which particular diagram — utilitarian principles, Torah, human compassion, professional ethics, financial concerns, case precedents, Christian scripture, Canon Law , or other unlisted diagram — should be applied or take precedence.  Even if each of these diagrams are as rigorous in their inferences as formal logic, the decision as to which one should be applied is hardly a mechanical process.

Diagrammatic thinking mediates thought with consistency, but it is not limited to a mechanistic approach because of that.

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.