Diagrams Gone Bad

This is a route, more or less, that I learned to drive when I was stationed in Japan in the late 60s.  I learned a sequence of turns, marked by different landmarks, to get from the one place to the other.  This diagram could have gone wrong in any or all of three of ways.  

1.  The most obvious problem with the diagram was its lack of flexibility.  If I took a wrong turn at some point, I had no diagrammatic way of a) finding my way back to the route or b) recognizing the route when I did get back to it.  There could also have been other problems like ambiguous or non-unique landmarks.  On a more basic level, the analogy between the physical route and the diagrammed sequence could have been faulty.  Any of these problems in application might have led me to seek a different or more comprehensive diagram.

2.  The diagram itself might have been inconsistent.  This is not too common with something as straight-forward as a map, but it is all too common with more complex diagrams relying on things like logic or authority for their internal consistency — not to mention ideologies which are often intentionally inconsistent.

3.  The diagram could have produced consequences that didn't play out.  If it didn't lead to the proper destination, that would be a biggie, but there could have also been lesser inferences, things like indicating a left turn where none could be made or not clearly indicating which road where more than one veered off in a direction, that would have called for some kind of revision or notes to the diagram.

But if a diagram can be faulted on any of these three levels, it is by means of succeeding on each of these levels that it can, despite being a fiction, be tautly strung between our past and future experience.

An Evolving Fiction

The irony of diagrammatic thinking is that a diagram is a "fiction".

"The work of the poet or novelist is not so utterly different from that of the scientific man.  The artist introduces a fiction; but it is not an arbitrary one; it exhibits affinities to which the mind accords a certain approval in pronouncing them beautiful, which if it is not exactly the same as saying that the synthesis is true, is something of the same general kind. The geometer draws a diagram, which if not exactly a fiction, is at least a creation, and by means of observation of that diagram he is able to synthesize and show relations between elements which before seemed to have no necessary connection." [CP 1.383]

The necessity — which itself can reflect a any kind of "consistency" — used to infer consequences that are taken to apply to that experience is created out of selective abstractions that are merely analogous in some way to experience.  Not only is this fiction deemed capable of inferring truth about experience, the diagram itself tends to become reality for us.

"A diagram, indeed, so far as it has a general signification, is not a pure icon; but in the middle part of our reasonings we forget that abstractness in great measure, and the diagram is for us the very thing." [CP 3.362]

This suggests a Hegelian manner of thinking with diagrams. We accept a diagram as "absolute," as reality, until cracks start to appear in our applications of it, in the inferences made within it, and/or in the consequences being inferred.  Then, at some point, we may just say "next" as Peirce accused Hegel doing, but in one way or another we replace that diagram with one more comprehensive or better-suited to our needs or just different.

Assessing a Diagram

Christopher Sims gave this definition of scientific thought.

"Advances in the natural sciences are discoveries of ways to compress data concerning the natural world — both data that already exists and potential data — with minimal loss of information." [p. 1]

Originally, it seems to me, the goal of the "natural sciences" was explanation, and then at some point that was reduced to "prediction", and now, apparently it's simply a matter of fitting past and future data to data-compressing correlations.  Whether for explanation, prediction, or fit the procedure may be diagrammatic, but assessing the consequences as a measure of diagrammatic thought, especially as the sole measure, seems to get increasingly rickety.  Later Sims laments:

"I think many economists now see themselves as experts in persuasion as much as experts in substantive knowledge.  They are willing to use arguments they know are flawed without explaining the flaws or to cite evidence they know could be shown to be misleading, for the sake of rhetorical effectiveness." [p. 9]

The diagrammatic purpose can only be realized in the motives of individuals users, and the reliance on assessing the consequences by itself is not much of a guarantee.  As Peirce wrote regarding the economics of research:

"It is to be remarked that the theory here given rests on the supposition that
the object of the investigation is the ascertainment of truth.  When an investigation is made for the purpose of attaining personal distinction, the economics of the problem are entirely different.  But that seems to be well enough understood by those engaged in that sort of investigation." [CP 7.157]

The economics of the diagram, the benefit versus the cost of using it, is the second measure, playing off the diagram's adequacy to its purpose.  These considerations determine whether we'll use a diagram or not, but there's a lot of slack in such determinations.  And, I don't think artificially adding the "ascertainment of truth" as a stipulated purpose will take up that slack.  We need to look at the consistency of the diagram itself, the inferences made within it, and the assumptions it makes.  We need to tighten things up between the experience to which it applies and the consequences which it then explains, predicts, and/or fits.

Conflicting Diagrams

When I was much younger, first
married, and living in a small rural town, I attended a local auction where I was able to purchase a full set of the World Book Encyclopedia for $4.00.  This was the result of two conflicting diagrammatic understandings — one of use-value, the other of exchange-value — as to how this object should be valued.  I found the one more appropriate from my own perspective and snatched up the "bargain".  But how would we say which one was true or false?  Or, assuming the diagrams themselves are not true or false, how would we judge which of the conflicting assertions was true or false?

With exchange-value the answer seems clear.  The auction itself set the value at $4.00.  More generally, someone might have paid that price knowing it was low relative to other markets.  A collection of potential markets would then be the measure.  But use-value is not so clear-cut.  For one thing, it's not quantifiable, not without any number of dubious estimates, and for many that alone is enough to reject it as "unscientific".  For another, even on a personal level, it still requires some fuzzy speculations as to just how useful a thing will be.

Despite their differences, however, both assessments reflect a reliance on purpose.  Garages and backyards of auction junkies are full of objects bought at a "good" price but never subsequently exchanged (or used), and personally, I toted that encyclopedia set around for years without me, or my children, ever actually using it.  Diagrams, first of all, seem to be assessed by whether they do, or do not, serve the purposes of those employing them.

My estimate of the use-value the encyclopedia set failed, and, thereby in a narrow sense, so did my diagram/concept of use-value.  More exactly, though, the failure in this case only showed that  something about my application of that concept was wrong.  I still favor use-value to exchange-value in my capitalistic dealings, but through that application, and others like it, I have learned to be more skeptical about the future uses a thing might have.

Language

In responding to Donald Davidson's confounding of language and conceptual schemes P. M. S. Hacker writes:

"[I]n the metaphorical sense in which a conceptual scheme is said to 'confront reality', it is not a language … but rather the grammar of the language, construed as the rules for the use of expressions that determine what does and what does not make sense.  For it is the grammar of a language thus construed which determines what is logically possible, i.e., what makes sense.  Grammar fixes the 'logical space' which the world (or reality) may or may not occupy.  And assertions couched in the language with that grammar are true or false according to whether things are as they are asserted to be." [Hacker, "On Davidson's Idea of a Conceptual Scheme," p. 298]

The constraints that a language exerts on a "system of generalizations" are constraints on what can be expressed, or more easily expressed, with that language.  These syntactic constraints are to a system of generalizations what the physical constraints of the piece of paper are to a Venn diagram.  One language, or diagrammatic medium, may be more amiable to one conceptual scheme than another, but, in either case, these syntactical constraints are generally taken as being part of the diagram's semantic nature and consistency.

Semantic Consistency

I don't know that we would want assert that all languages are tautological.  Logic certainly is, and perhaps mathematics, to the extent it is not axiomatically related to experience.  But it seems a bit strong to say something like "economic language" is made up of only tautologies.  More generally we might refer to a "semantic consistency" whereby the indices and relationships of a diagram, while they may be inspired by experience, are defined relative to one another within the confines of the diagram itself.  And where the consistency of a diagram is semantic — unlike where it is objective or axiomatic — the application of the diagram becomes a more pressing question.

Friedman's answer to this question is:

"[T]here inevitably will remain room for judgment in applying the rules.  Each occurrence has some features peculiarly its own, not covered by the explicit rules.  The capacity to judge that these are or are not to be disregarded, that they should or should not affect what observable phenomena are to be identified with what entities in the model, is something that cannot be taught; it can be learned but only by experience and exposure in the "right" scientific atmosphere, not by rote. It is at this point that the "amateur" is separated from the "professional" in all sciences and that the thin line is drawn which distinguishes the "crackpot" from the scientist." ["The Methodology of Positive Economics," p. 25]

This is no more than "common sense," what Deleuze called the "process of
recognition" that precedes "good sense", "the process of prediction" [Difference and Repetition, p. 285] deployed on a scientific level.  It is based upon an education in "the 'right' scientific atmosphere;" in particular, it is based on the specialization of "professional" schooling where an instrumental confinement to the diagram is embedded as a way of life. [see, "Re-Imagining the Academy: Louis Menand"] The problem is that it blinds its adherents to alternative diagrams, to there even being alternative diagrams, to different interpretations of the same situation, and it allows the importation of diagrams, with often tragic results, into situations where they do not apply.  Any diagram is a selective abstraction, one among several, and there is always the question whether it applies or not.

Tautological Consistency

Milton Friedman ["The Methodology of Positive Economics"] describes economic science as:

"[A] system of generalizations that can be used to make correct predictions about the consequences of any change in circumstances." [p. 4]

And, he notes this system has two components.

"In part, it is a 'language' designed to promote systematic and organized methods of reasoning. In part, it is a body of substantive hypotheses designed to abstract essential features of complex reality." [p. 7]

He goes on to say:

"Viewed as a language, theory has no substantive content; it is a set of tautologies." [p. 7]

In one sense the economic language, like any other language and modern logic for that matter, is a set of tautologies.  Concepts such as supply and demand, perfect monopolies and perfect competition are defined relative to one another within the diagram.  The relationships between them are true, by definition, in all instances.

However, consider the accounting assumption, at least it was an assumption when I took accounting, that businesses are "on-going concerns."  Much of accounting, but especially the valuing of assets at cost, was based on this assumption.  It was part of defining what a "business" was, part of the accounting language, but it was not a tautology. The corporate raiders of, what was it, the 1980s, made a great deal of money, even went to jail, questioning that assumption.  There was a large and profitable difference between assets valued at cost in an ongoing concern and those same assets if the "business" was not to be an ongoing concern.

A language or logic does not sever its connection with experience by being tautologically consistent.  X = X is always true, but there remains the question of just what can and cannot be an X.  That tautology, and the diagrammatic inferences made employing it, will not work for something like Philip, who can be drunk or sober.

Assessing the Consequences

Peirce describes working with diagrams as follows:

"It is by manipulating on paper, or in the fancy, formulæ or other diagrams — experimenting on them, experiencing the thing. Such experience alone evolves the reason hidden within us and as utterly hidden as gold ten feet below ground — and this experience only differs from what usually carries that name in that it brings out the reason hidden within and not the reason of Nature, as do the chemist's or physicist's experiments." [CP 4.86]

He seems to have in mind the self-contained axiomatic diagrams, such as geometry or logic, and the "experimentation" he describes occurs within the diagram itself. It does not involve experience outside the diagram.  We might add new indices or relations to a map, to a steamboat pilot's knowledge, or to the sciences of chemistry and physics, but that would not be done working only within those diagrams.  It would be done by applying them to experience and measuring the inferences made against experience.  The diagram would be tied to experience both fore and aft as it were, and it is a peculiarity of axiomatic diagrams, not diagrammatic thinking in general, that they can cast off those lines and set sail.  And even having set sail, those axiomatic diagrams must be able to dock again, to measure their results against experience now and then.  Where there is an objective or axiomatic consistency on the input-side of diagrams, there is a consistency derived from assessing their inferences on the output-side.

This not to say diagrammatic thinking is necessarily experimental.  Any of Peirce's means of fixing beliefs — tenacity, authority, discussion, and/or experimentation — can be used to measure the consequences being inferred from a diagram, and thereby assess the diagram itself.  Even within the experimental means there are any number of criteria — truth, utility, beauty, goodness — that can be and have been applied.  This is just to say there is a measure in using the diagram that has a bearing on the structuring of the diagram itself.