Anatomy of Contragrammar

Pieter Wisse


Contragrammar is a design of John D. Haynes who presents it in Meaning As Perspective: The Contragram (1999). He is "concern[ed about] the part attempting to function as the whole." While "inspired by the alarming fact that only very few humans conceive of the need to examine themselves in relation to technology," Haynes proceeds in an even more general vein1 by addressing the need for "assessment of any kind of relationship." Such reflection "entails a sense of perspective." With his "little book [that] is too small to defend itself," Haynes claims for contragrammar that it supports arriving at what his title indicates, i.e. "meaning as perspective."
Let me start with a cursory sketch of contragrammar, yet, of course, without any pretense at substitution. I urge the reader to study Haynes' original design. Short as it is, I've enjoyed it very much.2 Here, what triggers me for my first reconstruction is Haynes' distinction between whole and part. It leads me to think3 about decomposition of a system (whole) into elements (parts). The analytical control of decomposition has traditionally been to keep the system level well distinct apart from the level on which the elements appear. Inescapable contradiction somewhere further along the line of reasoning is then taken more or less for granted, or ignored altogether. If anything, such conceptual difficulties tend to reinforce the system-element differential. Haynes, however, departs to perform his first paradoxical move. Please note that I'm not at all sure whether Haynes himself holds this view. I am recounting my own interpretation which, due to our different perspectives, probably is quite different from his original. So from my perspective, rather than emphasizing the part in its partness, that is, resisting what always seemed the obviously logical orientation, Haynes radically reinforces the part's attempt to function as a whole. He does so by juxtaposition. The original-part-now-turned-whole is also supplied with a part, though. Haynes prepares for a structure supporting interpretative dynamics because this part is the original-whole-now-turned-part.
How Haynes applies symbols is quite helpful for an efficient treatment. He starts from an assertion about X being a part of the whole Y or, in short: The X of Y. Next, part and whole change position as already prescribed, yielding: The Y of X.
By transforming 'X of Y' into 'Y of X,' Haynes has clearly established a difference. However, his second paradoxical move consists of forcing reconciliation by joining these mirror assertions to form an encompassing assertion, or a completed contragram: The X of Y is the Y of X.
In his "little book," Haynes demonstrates contragrammar largely through presenting a small selection of contragrams, and commenting upon them. In addition, he lists 238 contragrams, mostly of his own making, too. They range from "The adaptation of nature is the nature of adaptation" to "You find yourself in you when: the letting go of discovery is the discovery of letting go." With this paper, I would like to contribute to development of structural aspects, thus extending contragrammar's foundation. In particular, I suggest that Haynes' formalization "The X of Y is the Y of X" does not exhaust the anatomy of contragrammar. I recognize opportunities for advancing his intriguing design.



Before whole and part

My own perplexities provide a useful orientation. I find it puzzling, for example, that Haynes doesn't emphasize that from any X and Y it is possible to construct a well-formed contragram. Why not? My guess is that for Haynes whatever 'The X of Y is the Y of X' only qualifies as a contragram when it is true. I would say such a requirement severely hampers the potential of contragrammar. Truth implies closure, actually undermining Haynes' productively paradoxical moves to provide an opening to dynamics of meaning. Could it be that Haynes is actually undecided? My impression from his comments on specific contragrams is indeed that for him they seem to capture, i.e. in the sense of a closure, a 'complete(d)' argument. But, then again, where he abstracts into formalism, Haynes certainly stresses the potential for ongoing dynamics in meaning.
I would like to stay away from the categories of truth and falseness, especially in any absolute sense. Suppose I'm right to recognize two threads with Haynes on his contragrammar, it is the one which opens to meaning that I find intriguing and productive.
Above, in the Introduction, my sketch of contragrammar starts from distinguishing between whole and part. I derived it from Haynes' stated "concern [about] the part attempting to function as the whole." However, the formula arrived at, "The X of Y is the Y of X," makes me wonder at the beginning of the current paragraph why Haynes didn't conclude that from any X and Y it is possible to construct a well-formed contragram.
It is easy to overlook the source of confusion. I believe the condition 'from any X and Y' deserves precedence. It accomplishes the essential recognition that whole and part are secondary, only. Forming a contragram therefore doesn't start from 'the X of Y,' as Haynes seems to suggest. More productively, I would say it starts instead from a 'X' and a 'Y,' subsequently yielding both 'the X of Y' and its contra 'the Y of X,' and finally 'the X of Y is the Y of X.'
From these structural considerations alone, I can already suggest how Haynes' expressed concern may be elaborated upon. Is it really only about one particular part taking over as another particular whole? Or is the more general issue that of the equilibrium in whole-part relationships? And does contragrammar help to realize how a whole is always relative to its part(s), vice versa? Then, does a contragram which Haynes would consider 'true,' suggest how whole and part are optimally balanced, i.e. where it is inessential whether the 'part' of whole or the 'part' of part is occupied?



From bi- to poly-contragrammar

So far, only well-formed contragrams with two variables have been considered. It seems easy enough to see how contragrammar might be extended when variables are indexed. So, X becomes X1 and Y becomes X2. However, what exactly counts as a contragram when starting from the set {X1, X2, …, Xn}? Where lies the demarcation between whole and part? Is it variable, too? Do all, with 1<f< n,

the {X1, …, Xf} of {Xf+1, …, Xn} is the {Xf+1, …, Xn} of {X1, …, Xf}

count as well-formed contragrams? I don't see any reason why not, especially not because any subset can be transformed to a single variable, resulting in a bi-contragram. All the same, the set { X1, X2, …, Xn} is not ordered. The number of orderings is determined by permutation, which is symbolically given as n! When it doesn't matter which whole/part sequence comes first, n!/2 combinations are relevant. In addition, it is also relevant where the demarcation is drawn. With n variables, there are (n-1) possibilities. Therefore, the sum of poly-contragrams that are configurable from a set of n variables is (n-1)n!/2.
Structurally, a contragram is limited to contra-ing two assertions. Does it make sense to extend contragrammar along this dimension? I don't believe it would produce meaningful results, but at least for discussion's sake it might be worth a try. However, I refrain from it here.
Another idea is to consider other relationships, i.e. different from those between whole and part. Likewise, I leave it to later stages of discussion to attempt such extensions, for example by applying (other) propositions.



Metapattern visualization

My interest in contributing to a discussion of contragrammar was also sparked because I recognized how Haynes' design could be beneficially modeled with the metapattern (Wisse, 2001). What follows here, however, is only a very crude summary of the metapattern, at best. For with my short-cuts explaining it, I directly aim at a discussion of contragrammar.
The thick, horizontal line in figure 1 represents the horizon of the universe of significance. The metapattern stipulates all behavior is situationally determined. An object therefore appears in a model as a collection of situated identities, with specific behavior 'attached' as relevant. As a boundary condition, even generally valid behavior is also situated (the situation of behavior is the behavior of situation). In those cases, the situation equals the universe of significance. For a bi-contragram, figure 1 provides an overview. In figure 1a, it starts with the general objects X1 and X2. Then, in figure 1b, X2 is also identified as an object with relevant behavior in X1 as a situation. Please note, as the dotted, curved line indicates, that the X2-as-part-of- X1 is derived from X2-as-a-whole in its own right. Also note that the actual behavior of X2-in-X1 is not yet modeled. To indicate that such behavior is in order, the metapattern's symbolic language prescribes a text balloon, as added in figure 1c. Figure 1d completes the bi-contragram by including X1 as identifying specific behavior in X2 as a situation, that is, behavior different from X1 in all other relevant situations, and subsequently referring to such behavior itself by another text balloon.

Figure 1a-d: Modeling the bi-contragram.



The explicit emphasis on behavior is what importantly distinguishes figure 1 from a contragram stated as 'The X1 of X2 is the X2 of X1.' It is now possible to indicate compactly both how the X1 of X2 is "united" with the X2 of X1, that is, by contra-ing the relative positions of constituent variables, and what "distinguishes" the one subset of variables from the other (behaviors).
Poly-contragrams require explicit recognition of both permutation of variables and demarcation with the subset. Figure 2 only shows one instance of all possible permutations, but it should make the general idea, and complexity, clear enough.

Figure 2a-b: Modeling the poly-contragram.



Irreducible dimensions in semiosis

It must be realized that figures 1 and 2, as is all of this paper, are 'only' signs. A sign, according to C.S. Peirce (1902), is an irreducible element in semiosis. Pragmatism holds that a sign leads an interpreter to a belief about reality as a basis for his behavior. Semiosis therefore includes dynamics between three elements: sign, interpretant and object. Inspired by the metapattern's articulation of a sign, I have extended Peirce's original semiotic triad into an ennead (Wisse, 2002). The three elements have been developed into dimensions, now each constituted by three more detailed elements. The irreducibility between elements, already emphasized by Peirce, remains. What has been gained is explanatory power. See figure 3.

Figure 3: The semiotic ennead.



I repeat that it is only signs that can be pointed at specifically, and therein lies their important value. Interpretants are beyond reach objectively, as they reside inside subjective cognition. Contrary to what naοve realism holds, whatever object an interpretant 'is about,' is therefore even twice removed from objective analysis. Of course, this shouldn't deter from speculation. Armed with the speculative apparatus of the metapattern and semiotic ennead, I will now return to Haynes and the first part4 of Meaning as Perspective for some additional comments on his "very brief general account of contragrammar."



The presence of focus …

… is the focus of presence. Haynes writes that taking "responsibility for our experiences" involves "contemplative thinking about, or focus upon, our experiences." I don't agree that focus equals self-conscious thought. All cognition proceeds by semiosis. Focus is therefore always active, too, because of the semiotic ennead's irreducible constitution of elements. I would say that dynamics of cognition are especially driven by focal shifts. Intuition amounts to cognitive punctuation (Brouwer, 1907), and referring to intuition suggests how we live by focus largely unconsciously. In terms of the ennead, isn't it more apt to argue that "responsibility for our experiences" requires recognition of motive? Can such recognition only succeed when we are able to maintain a particular focus? And with the motive come one or more concepts as mediated through a particular focus (the consciousness of motive is the motive of consciousness). Then, are we living fully responsibly when we behave on the basis of a recognized and affirmed motive as corresponding concepts indicate?
For all practical purposes, focus and perspective are synonymous to me. Along the interpretative dimension, around focus as the shifting hinge connecting motive and concept, meaning dynamically develops. Focus, or perspective, is irreducibly present in dynamics. I therefore strongly agree with Haynes when he argues for "meaning as perspective." How do I evaluate the claim that a contragram is "a very appropriate vehicle for capturing a sense of perspective […] and thereby offering that perspective to be re-experienced as meaning"? I think what is vital about perspective, or focus, is that it changes. Meaning is not static, not stable. Is a rhythm of focal shifts the engine of meaning dynamics? Could it be that consciousness is always memory, i.e. an interpretative trace marked by past perspectives, or foci? Then, a contragram may help to establish new trails of foci (the perspective of relationship is the relationship of perspective).
I also agree that contragrammar entails a procedure for manipulating signs — from any … — but then there's an infinite variety of procedures imaginable to stimulate semiosis. So at least from my ‘perspective,' "the focus of perspective is the perspective of focus" qualifies as a tautological contragram. I'd like to add that as far as I can judge, what is 'contra' about the 'gram' is reversal of position of elements. I wouldn't say that it necessarily results in a contrafocus, or more or less opposite perspective. Still, as modeling with the metapattern shows, background becomes foreground, etcetera. In some sense, indeed, a contragram might make semiosis 'jump.'
How cognition traverses from one focus to the next doesn't seem to be governed by logic (but by intuition, whatever that is). So, from this own (meta)perspective Haynes makes also sense to me when he "argue[s] that our relationship to meaning is not logical, it is instead non-logical." Without referring to semiosis and therefore regretfully overlooking the sign as an intermediary, irreducible element of dynamics, he nevertheless emphasizes that "meaning always has the quality of perspective." Once again, I agree with the irreducibility of perspective.5 He continues by ascribing to meaning "the quality that emerges between the reflecting subject and the object of reflection, by which I mean that meaning is always perspectival." I still closely follow Haynes in his "view that meaning is not in the object of consideration, nor is it in the subject that enacts the consideration." I believe meaning is in the process, mediated by sign. Is that what Haynes aims at qualifying "the explicit meaning [as] a thing-in-itself […] for the experience between the object of consideration and the subject undergoing the experience of considering"? I prefer the subject taking a more active part, but perhaps on the whole that is just a detail (the whole of the part is the part of the whole).6 Actually, Haynes seems to say that a passive subject "would be doing no more than perceiving the object." How he presents it, perception is a precondition for "treat[ing] the object in a conceptual way," that is, "conceiving of the object in a meaningful way." From — the model of — the semiotic ennead it may be gathered that I abstract from perception, as I do from consciousness, for that matter. As there is irreducible focus involved in cognition, it includes a corresponding concept just as irreducibly. I therefore find Haynes' remark superfluous that a contragram is "essentially concerned with conception." As a sign, of course it is! Enneadic semiosis implies concept, too.



The extension of term …

… is the term of extension. Haynes has already dealt with extensions, however limiting himself to three variables. He calls an "extended contragram" when "the structure remains the same." In my terms, whole and part are perfectly mirrored (or contra-ed). "A tri-part contragram" allows for "any internal re-arrangement;" the order of variables may be randomly varied, which is a procedure I haven't included yet, above, for poly-contragrammar.
I have no comments on what Haynes labels a "definitional contragram."7 Or it should be that with possibilities for disjunct multi-situational modeling there is of course no problem "for contradictories [to] co-exist." Every behavior is simply assigned to the situation for which it unambiguously qualifies.
What am I to make from the requirement that "at least one term in the contragram must be a concept"? Applying the semiotic ennead as my frame of reference, it sounds confusing. When a contragram is taken as a sign, I would only apply the 'concepts' of context, signature and intext to it. So, it is not a concept itself.
Of course, this is not what Haynes intends to say. But I cannot follow him in his Platonic orientation, that "a concept is a ‘thing-in-itself'; the essence of the thing." When perspective is always present, as Haynes also emphasizes, there's simply no value in essence other than honoring perspective (the responsibility of essential perspective is the essential perspective of responsibility).
I'd like to translate Haynes' requirement for meaningful dynamics 'signed-off' by a well-formed contragram. The metapattern demonstrates how an object's identity in one situation is derived from its identity in another situation. The boundary condition for an object's identity is where the situation equals the universe of significance. I would say that especially objects thus situated are optimal candidates for contragrams. In terms of the original distinction between whole and part, it is a whole that is still least partitioned that promises productive semiosis through contragrammar. This is confirmed by the extensive list of contragrams Haynes also provides. While acknowledging that my interpretation is essentially subjective, I'm sure that other readers of Haynes' list will also recognize most of the terms he applies as referring to generalizations. For example, nature now is a very popular generalization and therefore lends itself eminently for inclusion in contragrams. Almost any other term may be combined with it without immediately resulting in nonsense.
Indeed, such generalizations offer least resistance for configuration. When one generalization is used to constrain another, chances are optimal for meaningful residue. Another factor contributing to contragrammar's potential for at least not evoking nonsense is that interpretative ordering seems arbitrary to a large extent. Especially when starting from generalizations, it therefore doesn't matter too much which term comes first and which one next. Non-critical, elastic ordering might simply be a consequence of collecting generalizations. As long as short-circuit through nonsense can be avoided, ongoing semiosis may well discover sense, that is, a behaviorally meaningful — according to pragmatism, behaviorally meaningful is of course a pleonasm — configuration of focus with motive and concept.
Starting with generalizations also explains how a contragram exhibits a "play on words." One word may be interpreted very differently when it appears in different contexts. Now even when a contragram doesn't expressly state its generalizations, they are nevertheless clearly implied. It is the interpretation that every term, so to speak, already supports. Haynes: "[B]oth […] terms are initially perceived as separate." I wouldn't have referred to the concept of perception, there. Anyway, another interpretation of each variable is now suggested through the whole of which it now explicitly appears as a part (the history of polysemy is the polysemy of history).8



The point of view …

… is the view of point. From structural aspects of contragrammar — how is a contragram determined as well-formed? — the discussion has shifted to conditions for meaningful dynamics. It is such conditions that Haynes is almost exclusively occupied with. He doesn't allow "any two words representing logically related objects." A neglect for a structural foundation is also evident, for example, where Haynes mentions that a contragram is "only complete (or genuine or successful) when the relatedness of its two (or more) terms emerge as a new point-of-view, that is, the relationship yields (or gives birth to) a basis or (conceptual) essence for the point-of-view." I would argue for interpretative success to be understood pragmatically as establishing a focus connecting a particular motive with concept for useful behavior of the interpreting subject. It is clear that a subject stands to gain from experience applying contragrammar. Dependent on the subject, I suppose that any two, or more, terms may be applied to form a contragram that could set off productive semiosis. Compared to Haynes, I'm of course only a beginner at contragramming and that's precisely why at this stage I'm looking for structural support.
On the other hand, I can contribute several methodical tricks developed in my earlier work. For example, the metapattern and the underlying semiotic ennead are also helpful to position what Haynes calls a contextual contragram. I merely say that it is impossible for a sign not to appear in a context. A universe of significance counts as the ultimate context for a sign. At first sight, then, "a particular context," such as Haynes refers to, could be modeled as a vertical series of separate nodes, rather than the horizon(tal line). The contragram itself can now be easily attached below the lowest of those contextual nodes, as figure 4 shows for a bi-contragram.

Figure 4a-b: Modeling the contextual contragram.



However, it turns out that Haynes' definition might be mistaken. He prescribes that a contextual contragram is a contragram "that only makes sense in a particular context." This doesn't fit his format, though. It reads9 that 'p when: the X of Y is the Y of X.' This way, embedded contragram is the context of Z, rather than the other way around as Haynes maintains. It can be simply repaired, though, by changing it into 'When p: the X of Y is the Y of X.'



The explanation of an ideal …

… is the ideal of explanation. I have already stressed that despite a lack of explicit semiotic perspective, I largely agree with Haynes on meaning. I repeat the quotation that meaning "emerges between the reflecting subject and the object of reflection." How does it fit his view, expressed further on in Meaning as Perspective, that a contragram "(ideally) explains itself." No sign explains itself. Semiosis irreducibly relates all of its elements. The explanation of meaning is the meaning of explanation, by which I 'mean' to say that explanation, too, "emerges between the reflecting subject and the object of reflection." Explanation is a case of semiosis.
Haynes concludes the descriptive part of Meaning as Perspective with some remarks on "contragram notation." I find his visualization actually very suggestive of semiosis, too. His basic shape is an enlarged symbol for infinity, thus also resembling a Mφbius band. Attempting to relate notation to process, Haynes more or less equates the traversal of laps — he also refers to successive scans of a contragram — with cognitive progression, i.e. "the movement from perception to conception: from the perception of content (implicit stage) through to the experience (or re-experience) of forming a conception (explicit stage)."
For myself, I don't feel the need to distinguish such stages on the basis of Kant-like categories, or at least cognitive faculties. Instead, I recognize a foundation in the general anatomy of cognition for which I've designed the semiotic ennead as a theory. Its structural elements are invariant (for interpretation they are always: motive, focus and concept), but punctuated semiosis results in different configurations (the nature of nurture is the nurture of nature). In fact, much of contragrammar's attraction as-I-understand-it lies in its potential for surprise. Given a particular contragram, does semiosis follow a fixed pattern of stages, or scans? I don't believe so. Isn’t there an evolutionary advantage in intuition operating to a degree of randomness? Of course, there are constraints on cognitive dynamics. But just a few of such invariant structural elements constitute infinite variety of configuration. It is a good design that helps to explore and develop configurations, and I believe contragrammar is such a design.




1. More specifically on technology, Haynes adds in his Preface that "there is nothing wrong with it" as supplying "partial solutions to living our lives as humans. They are remedies or supplements to our lives." Yet, "the human condition is considerably more than the sum of its supplements." Haynes warns against "the unreflected use of technology [as it] will consume some of our critical abilities as human beings, in particular, our ability for appreciating conceptual meaning." The quality of efficiency is the efficiency of quality. But doesn't the problem originate from too limited a view of technology? The nature of technology is the technology of nature.
2. I am very grateful to John Haynes for sending me a personal copy: the pleasure of reading is the reading of pleasure. It's easy to experience the author's joy at writing such a book.
3. Of course, I'm aware of diverging from Haynes' approach. Rather than avoiding it, for the aim of constructive discussion I'm emphasizing differences as I experience them.
4. As already indicated, part two contains Haynes' list of 238 contragrams.
5. I have earlier written on a synthesis between Haynes' perspectival phenomenology and my own subjective situationism (Wisse, 2003).
6. I'm sure that especially an aphorism such as 'the whole of the part is the part of the whole' is not at all my original invention. As I couldn't discover that this particular sentence has been expressed earlier, though, any plagiarism on my part is therefore far from intentional. Anyway, the point I want to add here is that Haynes' contragrammar first of all provides a procedure for increased productivity by trial and error. Often, in hindsight a particular contragram leads to the obvious, i.e. an insight that the subject is surprised about it still needed discovering. The second benefit of contragrammar is that it supports each and every single contragram. With the growth of both case experience and structural expertise, the practice of the master is the master of practice. Semiosis inspired by one contragram contributes to semiosis started by another, and so on. Therefore, recognizing 'the whole of the part is the part of the whole,' not merely as a clever aphorism, but as a contragram, too, immediately increases intensity of interpretation.
7. In note 1, above, I've added the contragram 'the quality of efficiency is the efficiency of quality.' But it might be better to state that the 'the quality of efficiency is the inefficiency of quality.' More or less following the format of Haynes' examples, would 'the quality of efficiency both is and is not the efficiency of quality' qualify as a "definitional contragram"? It seems well-formed enough, but I'm still left with my lack of understanding of how Haynes defines "definitional."
8. When names, or generally signs, are not confused with what they are supposed to identify, the metapattern supports awareness of, say, possible superficial differences. One and the same overall object, an individual person, for example, may be known by different names in different situations (and/or different 'subjects,' hence subjective situationism; see also note 5, above). This is almost the opposite of the play of contragrammar, with its invitation to break through the superficiality of the repetition of identical names/signs in order to appreciate a different order of meaning.
9. Haynes doesn't supply the formula for contextual contragrams. I designed it to clarify my point.




Brouwer, L.E.J., 1907, Over de grondslagen der wiskunde, Mathematisch Centrum (Netherlands, reprint, 1981).
Haynes, J.D., 1999, Meaning As Perspective: The Contragram, Thisone (New Zealand).
Peirce, C.S., 1902, Logic as semiotic: the theory of signs, in: Philosophical writings of Peirce, edited by J. Buchler, Dover (reprint, 1955, pp. 98-119).
Wisse, P.E., 2001, Metapattern: context and time in information models, Addison-Wesley (USA).
————, 2002, Semiosis & Sign Exchange: design for a subjective situationism, including conceptual grounds for business information modeling, Information Dynamics (Netherlands).
————, 2003, The constitutional force of perspectival phenomenology: philosophical unification in information systems, in: Proceedings of the Ninth Americas Conference on Information Systems, Association for Information Systems, pp 2766-2774.



Pieter Wisse ( is founder and president of Information Dynamics, an independent company operating from the Netherlands and involved in research & development of complex information systems. He holds an engineering degree (mathematics and information management) from Delft University of Technology and a PhD (information management) from Amsterdam University.



August 2003, web edition 2003 © Pieter Wisse