Causes and Forces

In "How to Makes Our Ideas Clear" spends most his time clarifying the concept of force by working on what seem like an a priori explication of the a diagram,  a "parallelogram of forces."  However, concept of force is tied to our existential experiences of acceleration.  This "purpose" guides the applications of the diagram to experience, the structuring of the diagram itself, and the testing of inferred consequences from it.

He then goes on to say, given his understanding of the concept of force, that:

Whether we ought to say that a force is an acceleration, or that it causes an acceleration, is a mere question of propriety of language, which has no more to do with our real meaning than the difference between the French idiom "Il fait froid" and its English equivalent "It is cold."

But this is doesn't ring true.  A mathematical diagram of forces is one thing, and a categorical diagram of causes is another.  In fact, it would seem that modern science, among other things, was precisely this turning away from the Aristotelian causes for a mathematical renditions of forces. It was, thus, not a major shift when modern science shifted from causal explanations to statistical ones.  It was simply a continuation of the mathematical manipulations of a very different concept, namely force.

Peirce describes this concept functioning as the basis for modern science:

This leads us to undertake an account of the idea of Force in general. This is the great conception which, developed in the early part of the seventeenth century from the rude idea of a cause, and constantly improved upon since, has shown us how to explain all the changes of motion which bodies experience, and how to think about all physical phenomena; which has given birth to modern science, and changed the face of the globe; and which, aside from its more special uses, has played a principal part in directing the course of modern thought, and in furthering modern social development.

The rudeness of "idea of a cause" is apparently it's more rudimentary diagrammatic representation as Aristotle's four kinds of causes and what can be done with it compared to the mathematical representation of forces.

Logic of Lying

Stephen Toulmin wrote:

Frege, Bertrand Russell, and their colleagues confined logic to the study of formally valid arguments, as discussed in Aristotle's Analytics, and, by the same decision, expelled from logic all consideration of substantively sound arguments, as discussed, for example, in the Topics. ["The Construal of Reality," p. 109]

And Toulmin, like Aristotle, would like to leave room for both, formal logic and "substantive" or "dialectical" reasoning when it comes to knowledge.  However, Aristotle is clear about how formal logic should work in this context.

It is a 'demonstration', when the premisses from which the reasoning starts are true and primary, or are such that our knowledge of them has originally come through premisses which are primary and true …. Things are 'true' and 'primary' which are believed on the strength not of anything else but of themselves: for in regard to the first principles of science it is improper to ask any further for the why and wherefore of them; each of the first principles should command belief in and by itself. [Topics, Book 1, §1 translated by W. A. Pickard]

If we begin with a first principle, something true in and of itself, then the rigorous consistency of formal logic insures what follows is true.  But if we reject the very idea of first principles, that there can be anything in and of itself known to be true, formal logic can only claim consistency.  The first rule of lying is to keep it consistent, and formal logic, without first principles, is an unquestioning accomplice in such efforts.

Denotation and Reference

Professor Ian Dove gave a talk at UNLV entitled 

"Doing Philosophy through Painting? On Danto and Taylor on Tansey on Art" in which he discussed Mark Tansey's picture "Derrida Queries de Man".  I was reminded of a quote from Peirce:

A man's portrait with a man's name written under it is strictly a proposition, although its syntax is not that of speech, and although the portrait itself not only represents, but is, a Hypoicon.  But the proper name so nearly approximates to the nature of an Index, that this might suffice to give an idea of an informational Index. [CP 2.320]

Perhaps, being more complex, Tansey's painting could provide a better example than the portrait for exploring the nature of propositions and indices.

On the one side, there is a predicate, a Hypoicon, in this case the picture itself.  It is a metaphor, based on Sydney Paget's illustration, "The Death of Sherlock Holmes".  The illustration shows Holmes and Moriarty fighting at the Reichenbach Falls, and in the story, "The Final Problem," both of them plunge to their deaths. There are no doubt similarities and contrasts I'm unaware of, but there's at least the cliffs which are more prominent, they seem built out of text, and and the two figures appear to be dancing more than struggling in Tansey's painting. 

One point that doesn't come out so clearly in Peirce's example of the portrait, is that there are already indices of a sort within the painting.  The two figures, if seen closely, look like Derrida and DeMan.  The text-filled cliffs perhaps indicate the texts of the two men, or of Deconstruction in general, and perhaps their steepness portrays their rigor or uncompromising nature.  But all this is an analytic kind of thought, Peirce's a priori method, contained within the context of the painting.

On the other side, the subject, the title of the work, "Derrida Queries de Man," creates a substantial index.  This subject-index works in two ways.

1. It puts the focus on the two figures in the painting, and it identifies the one, Derrida, as ostensibly questioning de Man.  This I would refer to as the denotative aspect, a definition of the indices from within, or in terms of, the predicate-icon.

2. But this subject-index of the title also brings forth information drawn from sources other than the predicate-icon itself.  In this case it is the controversy surrounding de Man's collaboration with the Nazis in Belgium from 1940 to 1942, and Derrida's article, "Like the Sound of the Sea Deep within a Shell: Paul de Man's War" (Critical Inquiry 14 [Spring 1988]: 590-652) trying to minimize those actions.  He was "questioning" de Man in a way that was more like dancing with him.  Deconstructive methods, what would be the poison to any and all forms of totalitarianism, are being used to justify a collaboration with one the worst of them.  This "collateral" information I would refer to as the reference of the subject-index.

Subject-index and the predicate-icon thereby produce this proposition that these two men are dancing under the guise of one questioning the other in a very precarious place, that their own texts put them in danger of falling, of both of them being discredited.

Truth in Diagrams

Diagrams are fictions:

"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, …" [CP 1.383]

So how is it that these fictions can be true or false?  To answer that question I think we have to look Peirce's notion of a metaphor which he defined as "representing a parallelism in something else" [CP 2.277].

The diagram is built on an analogy with its object.  The diagram runs from that analogy and its applications to the consequences that can be inferred from it; and as a metaphor, if it runs "parallel" to the object and its interactions, the diagram would be true.  The parallelism must be maintained in three respects: (1) a realistic analogy, (2) consistent inferences, and (3) corresponding consequences.  Something similar, I would venture, is going on with art as well.

Anyway, the catch in all this is the object.  Is it the object in all the obscurity of it’s secondness?  Or, is it an object constructed, more or less articulated, in thirdness?  This is a problem with metaphors in general.  If we say “this person’s a wolf” what’s the object we have in mind?  The animal in the wild?  Or, have we seen one staring blankly at us in a zoo?  Or, perhaps, it's a conglomeration of encyclopedia entries, school courses, or fairy tales?  We have these denotations and connotations for “wolf,” but most of us have no referent, no direct acquaintance with the animal itself.  Thus, the thirdness of those denotations and connotations become the referent, the object, on which our understanding and use of “wolf” is based, and the whole thing becomes an exercise in analytic viruosity.  The virtue of science, but not all that calls itself “science”, is that it demands a direct contact with the secondess of the object, both in applying the diagram and in testing its consequences.

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.