Louis Althusser writes:
[T]he peculiarity of ideology is that it is endowed with a structure and a functioning such as to make it a non-historical reality, i.e. an omni-historical reality, in the sense in which that structure and functioning are immutable, present in the same form throughout what we can call history, in the sense in which the Communist Manifesto defines history as the history of class struggles, i.e. the history of class societies. [Louis Althusser, "On Ideology"]
A "peculiarity of ideologies," in contrast with other kinds of diagrammatic thinking, is their "non-historical" or "omni-historical reality." What does this mean? How does it work?
Milton Friedman claims that positive economics is, in one part, a "set of tautologies".
Viewed as a language, theory has no substantive content; it is a set of tautologies. Its function is to serve as a filing system for organizing empirical material and facilitating our understanding of it; and the criteria by which it is to be judged are those appropriate to a filing system. [Milton Friedman, "The Methodology of Positive Economics"]
We can certainly see a bid for a "non-historical" status in the use of tautologies; however, in its second part, positive economics consists of "substantive hypotheses".
Viewed as a body of substantive hypotheses, theory is to be judged by its predictive power for the class of phenomena which it is intended to "explain." Only factual evidence can show whether it is "right" or "wrong" or, better, tentatively "accepted" as valid or "rejected." [Ibid.]
These should tie the theory back to the particularity of history by means of specific predictions answering, despite being made in a language of tautologies, to experience.
If the predictions prove correct, they are, subject to certain other considerations, accepted as part of the theory. But what happens if they do not prove correct? The theory, as a a tautologous language and particular hypotheses, is deemed inapplicable to this kind of situation. Friedman uses the example of supply and demand that work well with regard to consumer goods but do not work so well with speculative markets. Apparently, the theory can continue unabated in those areas where it does work while ignoring those where it does not. Althusser's example of communism seems similar. When a hypothesis drawn in terms of the communist theory fails to explain some historical situation, it is not the theory or the hypotheses that is questioned or falsified. The particular historical situation is simply excluded from the ongoing theory's domain.
A key element of a theory being tested by its predictions is that the theory specify up front where and to what it applies. The success of its predictions then reflect back on the theory itself, as both a tautologous language and substantive hypotheses. But an ideology, it would seem, only determines if it applies at all by whether its predictions prove successful or not. In this way, the theory is never questioned, only its applications, and it, as a theory, persists non-historically impervious to its failures.
Diagrammatic thinking is looking at the thing to be understood as a mediating system:
a system in which a multiplicity of factors may weigh in at once, not just in a line and one at a time; a system, then, in which our feeling, for example, that "Robert is prompt," will proceed from our understanding of the totality of his nature, rather than from a coded set of properties pried from his personality; … [William H. Gass, "The Story of the State of Nature," p. 134]
"Robert being prompt" is a consequence "caused" by various particular inputs, as the system sees or defines them, and a system of rules or linkages that produce given consequences from those particular inputs. The key to explaining why Robert is prompt in some particular case is a matter of laying out, as best we can, the system of connections that Robert is such that given certain circumstances we can predict that he would be be prompt.
According to Peirce, however, this is only one of three possibilities. Besides seeing Robert being prompt diagrammatically, we could see it in terms of an image. This is what Gass calls "a coded set of properties" attaching to him as various external characteristics. Such external characteristics could be "pried from his personality;" others could be photographed; the key is that they are external characteristics of Robert. The system of such properties or relationships can be represented diagrammatically, but Robert an opaque node or a dimensionless point, a empty terminus of some and not others of those relationships.
The third possibility, which is historically probably the first and epistemologically the most common, is to understand Robert metaphorically. If we can find a system that is similar to Robert, that as Peirce puts it runs "parallel" with Robert, we can use that to explain things like Robert being prompt. For instance, I might compare Jack to a Prussian officer, or to the Pony Express where promptness was a virtue. The biggest problem with metaphors is a lack of acquaintance with what is supposed to be the known side of the metaphor. Comparing Jack to a Prussian officer does me no good for the simple reason I don't know any Prussian officers. To remedy this, I might even compare him to myself. But to the extent I can discover increasing similarities with something I do know, I come to an increased understanding of Jack.
Gass overall, I think, is lamenting the demise of metaphorical understanding, of art. I, in turn, would lament the demise of diagrammatic thinking. We live, at least publicly, in an age of images, where the system of external relationships is the reality and the human being is no more than an empty point of reference in different images. We can still think diagrammatically and metaphorically in private, through philosophy and art such as it is these days, but then that privacy is increasingly under siege as well.
William H. Gass gives a succinct characterization of analytic statements:
Actually, as Plato argued, analytic judgments refer to an organized system of concepts, and analytic judgments are true when they reflect that system correctly. ["Carrots, Noses, Snow, Rose, Roses," p. 738]
And he goes on to describe literary art as:
In any case, literary language, rather than empty as analytic formulations are sometimes said to be, is so full, so overdetermined, so inevitable in its order, … [Ibid.]
as the most analytic, or the fullest ("thickest" as Gass puts it elsewhere) form of analytic exposition.
First, it makes me ask why art would occur within the diagram itself, like logic or mathematics. Do the artists insist upon the universality of analyticity for themselves and/or their work? Their right to work in the ether of pure language, if not thought. Or, do we, as readers and consumers of that art, demand that the references and consequences be us left to us?
And second, while this analytic approach makes for great writers, logicians, and mathematicians, is it right? Is that the way it should be? Should diagrams, even those of logic and mathematics, be created and understood apart from their references and consequences?
I like to dabble in the stock market. And there is no end to the diagrammatic understandings of the market — from various rules of thumb to intricate and complex mathematical representations — offering me help. Except for occasional flashes, those of divine mathematical complexity and proprietary secrecy, seem to work well enough, but I have never found any within the range of my understanding that are all that helpful. What I need to know is just what all these diagrams seem to methodologically exclude; that is, the subjectivity of who is buying, who is selling, and why.
The single diagram is made up of indices and relationships, analogous to the subject matter, such that certain consequences follow and inferences can be made from them. Being an abstract reduction of the subject matter, the overall purpose of the diagram also has a bearing on its construction and viability. But when more than one diagram is involved the elements needed to represent this kind of situation change. The indices become actors, things to be diagrammatically understood in their own right, and the relationships between them are interactions that touch rather than connect them. It is no longer a question of the overall purpose of one diagram but rather of a number of individual purposes interacting through time.
This is not to say a diagram of the market as a whole, in a mechanistic sense of how it is set up and how it works, is not still not in play. However, much like geography at play in geo-politics, it is the board upon which the game is played. It can force outcomes now and then, and it definitely sets up currents and trends affecting the results, but it is not the game itself. The game is played between the subjects within the situation, subjects who have their own indices and relationships, drawn from their own analogies and based upon their own motives, such that certain consequences follow and they make certain inferences. Not only do these actors change, or evolve, in the course of these interactions; the board itself can change, evolve as it were, as result of what these actors do and how they try to do it. Interacting diagrams require a novelist's narrative that incorporates diagrammatic understandings of all involved. And, while working with a single diagram may be science, or capable of being a science, once more than one diagram are put in motion interacting with each other, understanding what is going to be an art.
Nate Silver has a chapter dealing with the chess match between Gary Kasparov and IBM's chess-playing program Deep Blue in his book The Signal and the Noise: Why So Many Predictions Fail — but Some Don't. The match was billed as a man-versus-machine confrontation. The machine working mechanistically, diagrammatically as it were, was matched against a human whose thought is more general and all-encompassing in a, perhaps, non-diagrammatic kind of way.
But computer chess programs can't always see the bigger picture and think strategically. They are very good at calculating the tactics to achieve some near-term objective but not very strong at determining which of these objectives are most important in the grander scheme of the game. [p. 247]
Kasparov himself felt, after he won Game 1, that Deep Blue had seen only the near-term tactical considerations not longer-term strategic ones.
"Typical computer weakness," Kasparov later said. "I'm sure it was very pleased with the position, but the consequences were too deep for it to judge the position correctly." [p. 249]
But is this really two different kinds of thinking, one diagrammatic and the other not?
Or, is this one kind of diagram, a tactical understanding of atomistic indices in precise relationships, versus another kind of diagram, a strategic understanding with vague indices and less specific kinds of relationships? We could even see the strategic diagram as encompassing and moving beyond the tactical (à la Hegel's aufheben or Kuhn's paradigm shift). But maybe even this is too much. Kasparov began to doubt his assessment of Deep Blue's capabilities during this game when Deep Blue made what was for him and his second an inexplicable move:
To see twenty moves ahead in a game as complex as chess was once thought to be impossible for both human beings and computers. Kasparov’s proudest moment, he once claimed, had come in a match in the Netherlands in 1999, when he had visualized a winning position some fifteen moves in advance. Deep Blue was thought to be limited to a range of six to eight moves ahead in most cases. Kasparov and Friedel were not exactly sure what was going on, but what had seemed to casual observers like a random and inexplicable blunder instead seemed to them to reveal great wisdom. [p. 251]
It was his undoing — "Kasparov would never defeat Deep Blue again" [p. 251] — but the distinction between "tactics" and "strategy" seems to amount to no more than the number of moves ahead being considered. Limits in calculative abilities may require different diagrams, or approaches, but at bottom the diagrams have a quantitative basis. Silver, in fact, refers to what have to be strategic considerations in Game 2 offering a "three-tenths of a pawn" [fn 36, p. 252] advantage.
One difference between man and machine, however, does stand out in Silver's account. Kasparov was clearly assessing Deep Blue's capabilities, the diagram it was employing, and trying to take advantage of any shortcomings he could find. Deep Blue, on the other hand, was not attempting to do anything like that. The programmers, being the humans they are, did design Deep Blue with Kasparov in mind [p. 256], but so far as we know Deep Blue, as a computer program, was not making those kinds of assessments. Considering how an opponent sees the situation, how it draws its inferences, and what purposes might be guiding it does seem to be a peculiarly human characteristic. And, it also seems classically human that such an advantage be ironically rich enough to be their undoing as well.
Peirce delineates his triad of image, diagram, and metaphor in the following passage.
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. [CP 2.277]
And where he goes on in other places to fill out what he meant by images and diagrams, this is pretty much it for metaphors. They run in parallel, a somewhat mystifying metaphor in its own right.
But Giambattista Vico says something interesting about metaphors that might help.
[120] By its nature, the human mind is indeterminate; hence, when man is sunk in ignorance, he makes himself the measure of the universe. [New Science, trans. by David Marsh, Element 1]
In other words, we make a metaphor of one system we know, the "vehicle" of our own selves, with another system, the "tenor" in question. The tenor is seen as working in "parallel" with how things work within us. Although the vehicle is not always ourselves, I think it's fair to say, with Vico, that the initial approach to any unknown thing is metaphorical correlation with something we do know.
But Vico goes on to say, looking at these metaphors marbled into culture as "poetic truth":
[205] … Indeed, if we consider the question carefully, poetic truth is metaphysical truth; and any physical truth which does not conform to it must be judged false. [Ibid., 47]
Human knowledge first turns to metaphor, to poetic truth, and then, only later, fills in the systemic details of the tenor diagrammatically. What's more, according to Vico, that physical truth must "conform to" the poetic truth. This seems questionable in the sense that any metaphorical understanding would surely be undone by different applications and delineations of rendering it diagrammatically. But then the metaphorical understanding could be expected to evolve as well. Perhaps it is a tandem unfolding of concepts in this way that Blumenberg is taking advantage of when he traces the historical evolution of concepts of like "progress" or "truth" metaphorically.
Hans Blumenberg, in "On a Lineage of the Idea of Progress" traces the notion of progress in astronomy back to Hipparchus and his star catalog:
… said to have listed 1,022 stars according to position and brightness, [that] was laid down as an instrument for future comparisons. [p. 9]
This revolutionary notion introduced a "coordinative relation between the quantum of time and the quality of achievement" [p. 6], the idea of postponing or deferring present assertions of knowledge until the necessary data and accuracy could be accumulated and realized in the future.
Copernicus, according to Blumenberg, built on Hipparchus' data but looked at where he fit into this notion of progress differently.
For all the time it takes, the theory of the universe struck him as a finite task ending with him. [p. 18]
And:
While recognizing himself as a beneficiary of the time that had passed since Ptolemy, he gives no sign of sharing the ancient astronomers' sense of a vast future time as a continuing astronomical need. [p. 19]
If this seems a bit hubristic, it is at this point where astronomy, and the sciences more generally, took off. Bruno, following Copernicus, seems to have looked at progress the same way.
Copernicus must not be judged by things whose accomplishment was beyond him; after all, he had been no more than the dawn that precedes the sunrise of true philosophy – by which Bruno meant none other than his own. [p. 24]
The evolution of science seems to have really gotten underway as a Hegelian progression where each new conceptualization, after correcting flaws in previous ones, takes itself as the "absolute," final, consistent and complete encompassing of the matter.
With Galileo, however, this hubris came to be publicly tempered. As Blumenberg puts it:
We must not state that the Copernican doctrine is true, but for this very reason we may continue our intensive research into the objects it refers to. Progress is merely the by-product of this enforced uncertainty, and of the corresponding effort in which we refuse to admit to ourselves that it is as futile as it is declared to be. [p. 26]
This recalls Peirce's insistence on fallibility, and seems common enough today, but what I find interesting is that, despite the professed uncertainty, "we refuse to admit to ourselves that it is as futile as it is declared to be." If concepts are to evolve, perhaps it is essential that each, in its heart of hearts, see itself as absolute.
