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A Projection Beyond Piaget's Formal-Operations Stage:

A General System Stage and a Unitary Stage

Herb Koplowitz, Ph.D.
Consultant
The Longwoods Research Group Limited
2161 Yonge Street
Toronto, Canada M4S 3A6

In: Commons, M., Richards, F., & Armon, C. (Eds.) Beyond Formal Operations:
Late Adolescent and Adult Cognitive Development. P4ew York: Praeger, 1984

POST-LOGICAL THINKING

The past five years have witnessed an accelerated awareness that many adults cannot or do not think rigorously. Most of the attention has been paid to problems in the thinking of university students. The purpose of this paper is to outline different stages in development of adult thinking and how these stages affect problem solving and decision making in work organizations.

One major example, concerned with a troubled organisation, will be used throughout to demonstrate thinking characteristic of each stage. I will describe the organisation and then explain how employees at different stages would analyze the problem. The characteristics of thinking at all stages are summarised in Table 1.

The organisation we are concerned with gets its funding from the government. Within the organisation is a department which provides consulting services to organisations in both the public and private sectors.

As I explore this organization and the thinking of its employees, you might reflect on similar individuals and organisations that you are familiar with to see how they fit the patterns I present.

PRE-LOGICAL THOUGHT

Ed is generally a pre-logical thinker. In exploring the cause of problems, he tends to make one-step analyses.

For a pre-logical thinker like Ed, any state of affairs is conceived of as the consequence of the state immediately preceding it, and the analysis ends there.

The absence of logical reasoning in the pre-logical thinker appears in several ways. Pre-logical thinkers tend to respond emotionally to statements rather than to analyze them logically.

Note the syllogism imbedded in Mike's statement.

Major Premise: We should examine inefficient aspects of the department. Minor Premise: The organisation of our work is inefficient. Conclusion: We should examine how we organize our work.

Logically, Ed can disagree with the conclusion only by disagreeing with one or both of the premises. Ed, however takes the statement personally, understanding it only as an attack on himself and his work. Mike never accused the department of not working hard. In defending himself, Ed acts emotionally and, typical of pre-logical thinkers, changes the subject instead of dealing with it rationally.

Pre-logical thinkers tend not to relate effects of one variable to those of another.

Ed lacks the strategy called "separation of variables" (Inhelder and Piaget, 1958). He focusses on only one variable at a time, in this case, skill leveL He does not relate this variable to other variables, such as morale, which also affect the outcome.

Wilma thought that the arrival of a new manager, especially one who is a good listener, might be a good time for department members to meet to discuss the department's problems. When Wilrna convened the meeting, Ed showed another limit to pre-logical thinking, the inability to separate form or method from content.

Pre-logical thinkers like Ed have difficulty setting agendas and sometimes abiding by them. They have trouble separating talk about how they will work on a problem from the problem solving itself.

Ed has also shown two other characteristics of pre-logical thinkers. They tend to locate blame for problems in others, and they tend to believe that it is these others who must be changed if problems are to be solved. It is clear to Ed that management is to blame for the morale problem, and that the solution to the problem lies in management's changing its ways.

Pre-logical thinkers tend not to think abstractly, and the boundaries they draw around parts of the world they know tend to be solid, closed boundaries. It is clear to Ed who is a manager and who is not, and it is clear to him that problems in management can be solved only by helping or forcing managers to change. And when Ed talks about the management of the organisation, he means the people at Mike's level and above (and is likely to use the singular noun "management" as plural as in "We must give management what they want'). Management is not an abstract function within the organization, but a collection of concrete individuals. In Ed's view, the boundary around this collection is closed; any individual in the organization is either inside the boundary or outside of it.

The poor quality of Ed's thinking puts him at a disadvantage in the world, and also disadvantages groups of which he is a member. Because he does not analyze logically, he is open to manipulation by others. Because his causal analyses are one-step and because he does not separate method from content, he is limited in his abilities to understand situations he is in and devise solutions for his problems. He responds illogically and often defensively to criticism and cannot follow agendas, and so is a distraction to groups he works with. His tendency to react emotionally and to not analyze arguments logically leaves him ill-suited to make reasonable choices. He will detract from any democracy, whether on a national or a work-place scale.

It is not just every human's democratic right to be intelligent, to use Machado's (1980) phrase, but also every democracy's need to develop the intelligence of its members.

LOGICAL THINKING

Both Wilma and Chris are logical thinkers. In exploring the cause of problems, they look for linear causal chains.

Wilma's analysis does not stop at the situation immediately preceding the one to be explained, but rather is carried out to the construction of a causal chain (Figure 1) which could, theoretically, be extended back indefinitely.

.Department members keep low profile Department members have no measure of the value of their work
Managers do not know the department's work Department members are not sure if their work is valuable
Managers give no feedback to the department Department members have low morale
a b
FIGURE 1: Logical linear concept of causality

Logic plays an important role in Wilma's and Chris's thinking.

Chris was able to separate out from Mike's syllogism exactly which premise it was that she disagreed with. This is a critical ability of logical thinking.

As was shown before, Wilma, as a logical thinker, was able to relate the effect of department members' skills, as one variable, to the effect of their morale, as another variable. She sees them operating independently to affect the department's performance.

When the meeting began, another ability of logical thinkers appeared.

Ed, as a pre-logical thinker, was unable to separate the content of the meeting from the process by which the content would be addressed. He began talking about the problems before it was settled how those problems would be discussed. Chris, as a logical thinker, knew that the topic was the agenda, and she addressed that topic. She was able to separate content from process.

When the meeting progressed to a discussion of problems and their solutions, two other characteristics of logical thought were manifested.

In analyzing problems, logical thinkers construct a causal chain to discover what the origin of that chain is. That is where they locate the blame for the problem, whether that puts the blame on themselves or on others. The site for intervention, the place where changes should be made in order to solve the problem, is the very place where blame was located. The department's low quality work was seen, ultimately, as being the result of consultants' poor skills, so those skills should be improved. The lack of feedback was seen, ultimately, as being the result of managers' poor communications skills, so those skills should be improved. In this regard, logical thinkers differ from pre-logical thinkers who more rigidly locate blame and intervention sites in others (or in themselves if they have low self-esteem), and from postlogical thinkers who, as will be seen later, take a yet more flexible view.

Logical thinkers are capable of much more abstract thought than are pre-logical thinkers, but they still draw closed boundaries in separating one part of the world they know from another. Wilma and Chris can separate "management", the function, from "managers", the people. However, it is clear to them that management is the job that managers do, that they themselves are not managers, and that Betty and Mike are managers. There is no ambiguity in that distinction. Also, they propose improving management by improving managers.

Wilma and Chris are at a definite advantage over Ed because of their abilities to think logically. They make more sophisticated causal analyses and are capable of correctly analysing situations in which they themselves are at fault. They can run more productive meetings because they can discuss how to structure the meeting before going on to discuss its content. They are less liable than pre-logical thinkers to be verbally manipulated by others because they can analyze arguments logically. In their problem solving they are more flexible than prelogical

thinkers, and better able to consider others' points of view. However, they are not as flexible in their thinking as post-logical thinkers are.

POST-LOGICAL THOUGHT

Mike is a post-logical thinker. A characteristic of post-logical thinkers is that they see cause as happening not only linearly but also cyclically.


Department members keep a low profile
Department members have low morale Managers do not know the department's work
Department members are not sure if their work is valuable Managers give no feedback to the department
Department members have no measure of the value of their work
FIGURE 2: Post-logical cyclical concept of causality


Department has no capacity to handle more clients Lack of demand for more serviceby the department Department has no capacity to handle more clients
Department does not promote its services Department does not expand its capacity Department does not expand its capacity Department does not promote its services
Lack of demand for more serviceby the department
a............................................................................ b
FIGURE 3: Linear causal chains combined into causal cycle
.

Logical thinkers, with their concept of causality, tend to see themselves as reacting to given aspects of their realities. In this case, Wilma saw her low morale as a reaction to managers' lack of appreciation of her work. She saw the department's not expanding its capacity as a reaction to a low level of demand for its services. Post logical thinkers with a cyclical concept of causality, understand that we often produce those "givens" in our reality to which we react. Mike could see that Wilma not only reacted to the managers' lack of appreciation of her work but also, through her low profile, eaused it. He could see that the department not only reacted to low demand but also, through its lack of promotion, caused it. 3

The cyclical view of causality enables post-logical thinkers to view things in context, and one thing they tend to view in context is logical argument. Wilma made implicit use of two syllogisms:

1. We should not promote our services if we have no capacity to serve more clients than we have now. We have no capacity to serve more clients than we have now. Therefore, we should not promote our services.

2. We should not expand our capacity if there is no excess demand for our services. There is no excess demand for our services. Therefore, we should not expand our capacity.

To Wilma, both major premises and minor premises are true, and the conclusions are valid. Mike, however, looks not only at Wilma's arguments, but also at the context in which they are made. Looking at the arguments alone (Figure 3a), he
would agree with all premises and both conclusions. When he looks at them in context (Figure 3b), however, his opinion changes. He now disagrees with the first major premise. He now feels it is appropriate to promote services when the premise that his department has no excess capacity since he recognises that an increase in demand will stimulate his staff to become more efficient. He also disagrees with the minor premise of the second argument. He believes there is excess demand for the department's services, but that the department has not yet tapped it.

Note that Mike can still make logical arguments and is still convinced by others' logical arguments. The difference between him as a post-logical thinker and Wilma as a logical thinker is that Mike, unlike Wilma, looks at the context in which a logical argument is made in order to see whether the context changes the judgement of the truth of the premises.

We have seen how Wilma, as a logical thinker, was able to relate the effects of one variable, e.g. staff members' skills, to the effects of another variable, e.g. staff members' morale. While logical thinkers see that there is a relation between variables, they tend to think of them as acting independently of each other. Postlogical thinkers see variables as interdependent.
.

Wilma, as a logical thinker, understands morale and skill to operate independently of each other. She therefore believes it must be possible to separate the effects of morale from the effects of skill. Mike, as a post-logical thinker, understands morale and skill to operate interdependently. Each provides the context in which the other operates and neither can be varied without affecting the other.

Because post-logical thinkers look not only at objects and events but also at their contexts, and because they view causality as cyclical rather than linear, they conceptualise problems differently and intervene to solve them differently from how logical thinkers do.
.

Mike, as a post-logical thinker, put the blame for problems in the dynamics of systems rather than in individuals or in events which initiate the problems. A circle has no beginning. Because he views cause as being cyclical, Mike sees no beginning to the causal process which results in the problem. He understands his staff's morale problem to be the result of an unfortunate dynamic in the system. He does not blame top management for his staff's morale problem. Post-logical thinkers do not find the concept of blame, in the sense of blaming individuals, to be useful at all in understanding how situations arise or how problems can be solved.

As a post-logical thinker, Mike is not restricted to intervening at the site of the cause of the problem for three inter-related reasons. First, as we have just seen, he does not see a problem as having a cause. Second, a causal cycle has no beginning, but it can be broken at any point. Third, post-logical thinkers understand any action as a reaction to a context; if they decide to change a particular action, they have the choice of changing the action directly or changing the context to which it is a reaction. Instead of intervening at "the cause" of a problem, post-logical thinkers intervene where they have leverage, that is, where they can effect the greatest change with the application of the least effort.

Wilma wanted to change top managers' behaviour of not giving feedback about the department's performance. As a logical thinker, she chose to consider the cause of the problem to be management's behaviour, and so she decided to intervene there. Mike, as a post-logical thinker, understood that there was no one cause of the problem, that the causal cycle underlying the problem could be broken at any point, and that managers' behaviour could be changed by altering the context to which they were reacting. His point of greatest leverage was his staffs behaviour. By altering his staff's visibility, which he could control, he could change the managers' behavioural context. They would now have to respond to a highly visibility group instead of to a low visibility group, and they would likely respond to it by noticing it and giving it attention and feedback.

Similarly, Mike found it difficult to get his staff to increase the department's efficiency when he tried to do it directly. He had more leverage in getting the staff to promote the department's services. His staff was then working in the context of high demand for services. and it reacted to that context by increasing the department's capacity.

Post-logical thinkers are capable of more abstract thought than are logical thinkers. While logical thinkers locate cause in concrete objects and their actions, post-logical thinkers locate cause in such abstract entities as "systems dynamics". And while logical thinkers must directly intervene exactly where they want change to happen, post-logical thinkers, with their more abstract understanding of causality, can change a pattern by changing its context. Post-logical thinkers draw open boundaries around entities and events.
.

The boundaries drawn by post-logical thinkers are open in two senses. First, they do not clearly separate inside from outside but allow leakage. Second, they allow energy and information to pass across them. As a result, problems inside a boundary can be solved by intervening outside of the boundary.

Mike, as a post- logical thinker, is at an advantage over logical thinkers like Wilma and Chris. While he can make and analyze logical arguments as well as they can, he can also look at their contexts and see whether that affects his judgement of the truth of their premises. He understands the interdependence of roles and can therefore analyze events more clearly. And he is more flexible in his solution of problems, directing his interventions not only at situations he wants to change but also at their contexts and at linked events where he has leverage. However, he still lacks the freedom of unitary thinkers. 4
.

UNITARY APPROACH

The unitary approachS knows and acts on the world as a unit. In the unitary approach, one understands that while it is possible and often useful to draw boundaries which break the world into separate entities and events, the world itself is undifferentiated.

Unitary concepts are most commonly found in modern physics and in spiritual disciplines. While very few individuals are capable of sustaining a unitary consciousness, there are more who are able to achieve momentary unitary perspectives of situations. Such a person is Wilma's Aunt Maude.
.

Maude's unitary concept of causality differs in two important ways from the logical and post-logical concepts. First, to logical thinkers, the causes and effects of a given event are confined to a line. To post-logical thinkers, they are confined to a cycle. To Maude, they have no boundary; causality is all-pervading. Wilma's low morale is caused not only by management's lack of feedback and Wilma's own low profile, but also by events in her own family, events in others' families, and so on. Her low profile has effects not only on her own morale but also on her childrens' habits as they watch and learn from their mother's behaviour.

Second, Maude understands cause and effect not to be different events but different manifestations of one underlying phenomenon. It is like the way the existence of the north pole of a magnet implies the existence of a south pole, even if the south pole is not visible. The occurrence of the cause implies the occurence of the effect, even if it has has not yet manifested. As north and south poles are different aspects of one phenomenon, neither existing in isolation of the other, so too cause and effect are different aspects of one dynamic and not separately existing events.

It is important to note that Maude can draw a boundary line and call what is inside

of it a causal event. She can focus on a line or on a cycle of causality. She can also draw a separation between cause and effect. She can talk with Mike at his level and to Wilma at her leveL But she understands that the boundary is not one which she has noticed out in the world, but one which she herself constructed.

Like logical thinkers, Maude is able to reason making use of syllogisms. Like postlogical thinkers, she understands that in applying logical reasoning, one must consider the context in which one reasons. But Maude's use of logic is tempered by more considerations.
.

Maude did not restrict herself to using logic to convince Wilma. If Wilma could learn her lesson indirectly, that would suffice. And Maude did not confine herself to changing Wilma's belief in order to change her behavior and solve her problem. If she could raise Wilma's profile subtly, without convincing her of the need to raise her profile, that also would suffice.

As a reserve strategy, Maude might have taken what would appear to be an illogical approach. She might have devised an argument to convince Wilma to keep her profile even lower, if in so doing Wilma would realize how she prevents management from getting the information it needs.

Maude can think logically, but she uses logic as only one of a number of a communication tools to change others' ideas and behaviors.

In her unitary moments, Maude differs from both logical and post-logical thinkers in her understanding of how variables relate to each other.
.

While Maude, as a logical thinker, understands variables to operate independently of each other and Mike, as a post-logical thinker, understands them to operate interdependently, Maude understands that the very boundary between variables to be constructed. When she needs to in conversation, Maude can talk of 'morale' as separate from 'skills', but she understands that to be an artificial construction of two separate variables from what is essentially undifferentiated.
.

To the unitary mind, problems are not problematic. Both Wilma and Mike saw in the low morale a problem to be solved, a situation which needed correction. To Maude, however, a "problem" is an opportunity to develop one's potential rather than a situation that is somehow mistaken or in need of correction. A problem occurs when the approach of an individual or an organization meets the limits of its applicability, and this provides the opportunity to improve the approach.
Also, to the unitary mind, a problem is not bounded. To a logical thinker like Wilma, the problem began with the lack of measure for the value of the department's work, and ended with low morale. To a post-logical thinker like

Mike, there is a problematic dynamic in the system bounded by a casual cycle. Maude, however, understands the lack of feedback and the low morale in the department to be essentially inseparable from dynamics in other systems.

For purposes of conversation she can separate "the problem event" from its context, but she understands that separation as an action committed by her.

Finally, to the unitary mind, there is usually no problem solver sitting outside of a problem situation. Therefore, there can be no intervention. Maude understood herself to be a part of her niece's situation. She therefore did not necessarily understand herself to be deliberately "solving" a problem or "intervening" in a situation, but rather, simply to be hanging out.

It should be clear by now that the unitary mind operates at a high level of abstraction. The world is understood to be essentially continuous and without boundaries. An individual constructs boundaries, breaking the world into entities and events in order to talk about them and manipulate them. In its most developed phase, the unitary mind is concerned with a non-material reality.

In the unitary leveL one develops a depth of understanding that allows one to both accept situations as they are given, and to bring about the most appropriate changes with the least disturbance.7

TABLE 1
STAGES IN ADULT COGNITIVE DEVELOPMENT
PRE-LOGICAL LOGICAL   POST-LOGICAL UNITARY 
Cause  One-step Linear  Cyclical   All-pervading/ Cause and effect as manifestations 
of one dynamic
Logic  Emotion over  logic/Process not separate from content  Logical context  Logic in  One communications tool 
out of many
Relation among variables  Unrelated  Independent  Interdependent  Constructed 
Blame/problem location Others  Where problem starts  In the system  Problems as opportunities/Boundary constructed
Intervention site  Others  Where the problem is Where there is leverage Where appropriate
Ability todeal with the abstract Concrete  Abstract  Relationships  Spiritual/Nonmaterial 
Boundaries  Closed  Closed  Open  Constructed 
 

SUMMARY

Pre-logical thinkers are liable to be manipulated by others who use arguments that would not stand up to logical analysis. They are liable to make illogical choices and to detract from the effectiveness of groups they are members of. In matters of verbal argument and analysis they are not able to serve themselves or others skillfully.

Post-logical thinkers have a flexibility in their thinking that enables them to intervene in situations in a most powerful way. They tend not to get stuck in situations that trap less sophisticated thinkers. However, there is an incompleteness in their approach that is resolved only in unitary thought.

Knowing what stage an individual's thinking is at can help you:

NOTES

1. Excerpted from "Post-Logical Thinking" in Bishop et aL (In Press).

2. What I am here calling "post-logical thought" follows the structure of general system theory. General system theory (G.S.T.) is usually defined as a discipline "whose subject matter is the formulation and derivation of those principles which are valid for 'systems' in general" (Von Bertalanffy 1968, p. 32). I find it unsatisfactory to consider G.S.T. a study of something externaL Such a definition leads to arguments as to whether a particular entity such as an automobile engine is or is not a system, when G.S.T. itself holds that anything can be regarded as a system. It is more useful to consider G.S.T. to be a way of thinking, or as a stage in the development of thinking.

3. The post-logical view of causality differs from the logical view in another important way. The logical thinker believes that if applying a small force will result in a small effect, then applying a large force will result in a large effect, and that the effect will be in the same direction as that of the force applied. The post-logical thinker understands that a small force can also result in a large effect if a positive feedback cycle is involved, a large force can result in a small effect if a negative feedback cycle is involved, and, in paradoxical interventions, a force can result in an effect in the opposite direction. For further exploration of the post-logical concept of causation, see Koplowitz 1976, Watzlawick, Beavin, and Jackson 1967, and Watzlawick, Weakland, and Fish 1972.

4. For a more detailed view of post-logical thinking, see Koplowitz 1976, 1978 and 1984, Watzlawick, Beavin, and Jackson 1967, and Commons et al. 1984.

5. Thought is a mental process of working out how different things relate to each other and how mental images are affected by transformations. I believe that individuals who operate at a unitary level do not work out their answers but rather have a direct or obervational access to them, and that there is, therefore, no "unitary thought". There are, however, unitary concepts and unitary consciousness.

6. The concept of variable as construct appears in modern physics in the Heisenberg uncertainty principle. The physicist cannot measure both position and momentum with total accuracy. The process of measuring a variable such as momentum is more akin to creating the variable than it is to discovering or noticing it.

7. For a further look at the unitary stage see Koplowitz 1978 and 1984 and Wilber 1981.

BIBLIOGRAPHY

Baron, J. What is good thinking Paper presented at Conference on Thinking. Harvard University, 21 August 1984.

Bateson, M. Our own metaphor. New York: Alfred A. Knopf, 1972.

Commons, M., Richards, F., and Armon, C. (Eds.). Beyond formal operations late adolescent and adult cognitive development. New York: Praeger, 1984.

Inhelder, B., and Piaget, J. The growth of logical thinking from childhood to adolescence. New York: Basic Books, 1958.

Isenberg, D. How senior managers think. Harvard Business Review, November 1984.

Koplowitz, H. The college classroom as organism: a general system theory approach to understanding and changing the college classroo m. Doctoral thesis, University of Massachusetts, Amherst, 1976.

Unitary thought: a projection beyond Piaget's for mat operations stage. Unpublished manuscript, 1978. Available from the author at The Longwoods Research Group Limited, Suite 200, 2161 Yonge Street, Toronto, Ontario, Canada M4S 3A6.

A projection beyond Piaget's formal operations stage: a general system stage and a unitary stage. In Commons, M., Richards, F., an Armon, C. (Eds.). Beyond Formal Operations: late adolescent and adult cognitive development. New York: Praeger, 1984.

Lochhead, J. A profile of the cognitive development of freshman engineering students. Paper presented at American Psychological Associates Convention, San Francisco, 30 August 1977.*

On learning to balance perceptions by conception: a dialogue between two science students in Lochhead, J. and Clements, J. (Eds.). Cognitive Process Instruction. Philadelphia Franklin Institute Press, 1979

The confounding of cause and effect, change and quantity. 1980.*

Machado, L. The right to be intelligent. Elmsford, N.Y.: Pergamon, 1980.

Perry, W. Forms of intellectual and ethical development in the college years. Cambridge: Harvard University, 1968.

Piaget, J. The child and reality: problems of genetic epistemology. New York: Viking, 1973.
Renner, J. and Paske, W. Quantitative competence of college students. Scientific American, May 1977, p.p. 283-292.

Von Bertalanffy, L. General system theory. New York: George Brasiller, 1968.

Watzlawick, P., Beavin, J., and Jackson, D. The pragmatics of human communication. New York: W.W. Norton, 1967.

Watzlawick, P., Weakland, J., and Fisch, R. Change: principles of problem formation and problem resolution. New York: W.W. Norton, 1974

Wertime, R. Slowing language down: a heuristic for systematically getting at the issue. Paper presented at Conference on Thinking, Harvard University, 22 August 1984.

Wilber, F. No boundary. Boulder: Shambala, 1981.
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