Michael Lamport Commons, Ph.D.

Research Associate and Lecturer

Program in Psychiatry and the Law

Department of Psychiatry

Harvard Medical School

Massachusetts Mental Health Center

74 Fenwood Road

Boston, MA 02115-6196

Telephone (617) 497-5270

Facsimile (617) 547-0874

Commons@tiac.net
http://www.tiac.net/users/commons/

57:19:14;27-08-99-20 (Friday, August 27, 1999; 2:19:57 pm)

26:12:14;15-09-99-20 (Wednesday, September 15, 1999; 2:12:26 pm)

50:52:12;28-09-99-20 (Tuesday, September 28, 1999; 12:52:50 pm)

30:52:14;03-10-99-20 (Sunday, October 3, 1999; 2:52:30 pm)

Commons, M. L. & Richards, F. A. Four postformal stages In J. Demick (Ed.), Handbook of adult development. New York: Plenum [or Elsevier?]

Model of Formal Operations 2

Objections to Formal Operations 2

Piaget and Postformal Theory 4

A Review of Some Postformal Research 4

The Model of Hierarchical Complexity 9

Horizontal (Classical Information) Complexity 9

Vertical (Hierarchical) Complexity 9

Postformal Orders of Complexity 10

Metasystematic Order 11

Paradigmatic Order 11

Cross-paradigmatic Order 12

Bringing Simplicity to Multiplicity 14

An Empirical comparison of some measures of postformal behavior 15

Attaining Postformal Stage Performance 16

Implications 17

Acknowledgment 20

The term "postformal" has come to refer to various stage characterizations of behavior that are more complex than those behaviors found in Piaget's last stage--formal operations-and generally seen only in adults. Commons and Richards (1984a, 1894b) and Fischer (1980), among others, posited that such behaviors follow a single sequence, no matter the domain of the task e.g., social, interpersonal, moral, political, scientific, and so on.

Most postformal research was originally directed towards an understanding of development in one domain. The common approach to much of the work on postformal stages has been to specify a performance on tasks that develop out of those described by Piaget (1950, 1952) as formal-operational or out of tasks in related domains (e.g., moral reasoning). The assumption has been made that the predecessor task performances (formal operations), are in some way necessary to the development of their successor performances and proclivities (postformal operations). Unlike many of the other theories, the Model of Hierarchical Complexity (MHC), presented here (Commons, et al., 1998), generates one sequence that addresses all tasks in all domains and is based on a contentless, axiomatic theory.

In any case, the collection of theories form part of the field that is known as Positive Adult Development (Commons, 1999, Sinnott, 1987, personal communication). This field examines ways in which development continues in a positive direction during adulthood.

This chapter will first review evidence supporting the general idea that postformal operations exist. One form of evidence is a discussion of ways in which Piaget's formal operational stage of development cannot adequately describe more complex forms of thought (Piaget, 1954; Piaget & Inhelder with Sinclair-de Zwart, 1973). Specific proposals for how postformal thinking might differ from formal thinking are then briefly reviewed. The history of postformal research and writing indicates convergence between different theories in the types of reasoning described. We will argue that the Model of Hierarchical Complexity provides a framework within which the diversity of other theories can be placed, and illustrate a possible consensus view as to what the postformal stages might look like.

Model of Formal Operations

Piaget (1954, 1976) used propositional logic as a model of formal operations.  Here, he followed a direction developed earlier by Frege (1950) and Peano (1894), who attempted to generalize propositional logic in order to represent other forms of reasoning, most notably arithmetic.  Because propositional logic was developed to reason about other forms of reasoning, it can be used to reason about the logics of classes and relations.  It can represent logical statements about both relations (e.g., p is heavier than q) and classes (e.g., x is a member of the class A).  However, in this form, propositions can be treated as objects in themselves, rather than as the direct reflection of some concrete reality.  Hence, propositions have formal properties that are different from the properties of objects and the actions that organize propositions are different from the actions that organize concrete reality.

Propositions are also statements to which the truth values true (T) or false (F) can be assigned.  Or the propositions may be built out of variables other than truth vales. The actions that organize propositions work under the basic constriction of this bivalent system of truth values.  For example, the truth values impose a restriction on the operation of negation: a proposition and its negation cannot both be true.  To negate a proposition is to change its truth value.

Piaget ties the logic of propositions to the Boole's (1854) system of combination, a system in which nuclear propositions are combined into larger molecular propositions using the of connectives: not, - and, &; or, v (ver = and/or); if, ®; if and only if, « . All these connectives are operations.  The connective not was just discussed in connection with the operation of negation.  The connectives and and or join nuclear propositions into molecular propositions of unlimited length.  If one of the propositions in a string constructed only with the connective and is false, then the entire molecular proposition is also false.  In contrast, only one member of a string connected by or need be true for the molecular proposition to be true.

Objections to Formal Operations

For all its formal and empirical power, objections have been made to Piaget's model of formal operations and the mechanics it implies.  One argument, advanced and expanded by Broughton (1977, 1984) has to do with the nature of the integration of formal and empirical reasoning at this stage.  Simply put, Broughton argues that there is no integration, rather there is domination of the latter by the former. That is, formal operations do not integrate the Boolean logical operations with the empirical manipulations used by participants to answer questions.  The formal structure of reasoning becomes pre-eminent at the formal- operations stage and the empirical structure can no longer function in its negating, and ultimately dialectical role.  As a result, formal operations cannot be used to reason about certain types of phenomena, notably those of a non-Boolean nature.  Perhaps they cannot even be used to observe such phenomena.  Broughton concludes that, if Piaget's developmental sequence leads to such a barren end-point, it ought to be abandoned altogether.

Piaget (1971) seems already to have countered Broughton's contention about the closure inherent in formal operations.  Specifically, he discusses the activity of negating key axioms in formal structures as a method of transforming and keeping open hypothetico-deductive structures.  He provides an example of this activity in the negation of axioms in Euclidean geometry that led, during the nineteenth century, to the development of several non-Euclidean geometries.  In addition, he discusses the decomposition of systems into more basic systems, and the subsequent recombination of basic systems into new systems, as activities that keep the formal-operational structure from ossifying.

The argument advanced in the body of research to be reviewed here, however, is that these latter activities are postformal rather than formal.  Their appearance can then be explained as a development necessitated by limitations of a linear formal system. Generally, the argument runs that formal operations, instantiated in propositional operations and employing the system of Boolean connectives mentioned, are adequate to formulate and analyze linear logical and causal relations.  The latter are particularly useful for reasoning about situations in which dependent and independent variables are postulated to exist.  Together, they create a kind of reasoning that will be referred to here as functional analysis. 

In fact, almost all theories, including developmental theories, require, at a minimum, the use of systems to adequately explain the phenomena they address.  Systems are characterized by relations that are not only functional, but transformational as well.  Such transformations require non-linear conceptions of causality.  At this order of complexity, formal operations are not sufficient. For a more detailed discussion of this point, see Commons and Richards, 1978, Commons, Richards, and Kuhn (1982), Richards and Commons (1984), and Commons and Richards (1984a). 

Piaget and Postformal Theory

It is important to distinguish between Piaget's theoretical framework and the products of that framework, in particular formal operations.  While the argument has just been made that formal operations is inadequate as a model for the activities that have most likely been operating in Western thinking for approximately a century, the same claim is not made about Piaget's theoretical framework.  Piaget advanced a complex theory of processes of assimilation, accommodation, and autoregulation that could only be formulated using postformal operations. If Piaget's own explanatory system is explicable in terms of a higher level logic than that of formal operations, then it is the former, but not the latter logic that is of use to psychologists attempting to understand adult stages of development.

A Review of Some Postformal Research

Reasoning such as that shown above, which is characteristic of the reasoning of some adults, is more complex than formal operational reasoning, as defined by Piaget (e.g. Inhelder & Piaget, 1958; Piaget & Inhelder, 1969). In earlier work (Commons & Richards, 1984a, 1984b, Commons et al., 1998) we have argued that this kind of reasoning represents one of several proposed new adult stages. Both empirical and analytic evidence for these stages has been presented. The existence of such reasoning demonstrates that development continues beyond adolescence and into adulthood, into the postformal realm.

A number of different postformal-reasoning theories have been described, including those of Arlin (1975, 1984), Armon (1984), Basseches (1980; 1984) following Riegel (1973)., Benack (1984), Commons and Richards (1978, 1984a; Commons, Richards, & Kuhn, 1982 ), Demetriou (1990; Demetriou & Efklides, 1985), Fischer, Hand, and Russell (1984), Kohlberg (1990), Koplowitz (1984), Labouvie-Vief (1990; 1984), Pascual-Leone (1984), Powell (1984), Sternberg (1984), and Sinnott (1984). All argue in common that postformal behavior involves one or more of the following: perceiving, reasoning, knowing, judging, caring, feeling or communicating in ways that are more complex or more all-encompassing than, formal operations. How the theories have generated their particular form of postformal operations, however, differs.

The most common method of extending stage theory into the postformal area is to locate limitations in formal operations, then describe a kind of thinking, often drawing from other traditions, that enables the individual to transcend these limitations.  Examples of this include: Arlin's (1975, 1977, & 1984), who draws upon creative reflection, Basseches (1980; 1984), who draws on the dialectical tradition; Linn and Siegal (1984), who draw on philosophy of science, Koplowitz (1984) who draws on General Systems Theory and Buddhism, Sinnott (1981; 1984) who draws on relativity theory, or Armon (1984), who draws on moral philosophy. What do some of these conceptions of postformal reasoning look like?

Arlin had the first explicit notion of a stage beyond formal operations. Arlin's (1975, 1977, & 1984) concept of postformal operations is based on the hypothesis that a radical change occurs in the way formal operations are used.  While accepting the idea of formal-operational structure, she proposes that the whole function of that structure changes.  Her argument is that a replacement process takes place whereby problem-solving operations disappear and problem-finding operations appear. To find a problem, requires reflection upon what a problem is. Part of discerning what a problem is requires reflection on how problems are solved. The form of a problem is partially determined by the possibility of some form solvability

Basseches (1980. 1984), for one, argues that postformal thinkers use the idea of form rather than the idea of thing.  Forms are structures whose fundamental function is to change.  As such, forms have system-like properties. Things are structures whose fundamental function is to maintain their stability or identity.  They have the properties of simple, linear, causal models seen in formal operations. In postformal thinkers, structure can never be temporally crystallized, but it can still be used to interpret society, nature, and the self as organizations in constant transformation.

Sinnott (1981, 1984), using the concept of relativity (Einstein, 1950) proposes relativistic frameworks that contain and co-ordinate more particular frameworks. Each framework can be thought of as a system of relations among elements.  A relativistic framework would then be a more general system for relating systems.  Sinnott uses the concept of system metaphorically, so a system need not be attached to concepts of energy, mass, speed, and so on. It could be a system of relations that co-ordinates people. While a person who thinks in a formal-operational manner could reason within one such system, a person who thinks in a postformal manner deals with the problem of integrating local systems into a framework, and deals successfully with the relativity of the systems.

A variant of this argument appears in Koplowitz's (1984) description of unitary operations.  He argues that, as thinking becomes more developed, the perceived boundaries between people become less useful.  A child, for example, cannot be understood outside of its family.  In a real sense, a child is part of a larger whole, from which that child cannot be disassociated.  Koplowitz's unitary operations are used to comprehend wholes that have internal parts.  Consequently, they organize and bring those parts into relation to one another.

The next group of researchers maintains that postformal cognition attempts to accomplish the same functions as formal cognition, but that the complexity of the patterns of thought, and the complexity posited in the objects of thought, is at a new level. These researchers analyze the

nature of the developmental process, rather than the limitations inherent in formal operations. Instead of concentrating on a demonstration that change does occur, this approach attempts to show how it could and must occur. Piaget (1970) had proposed a general process of equilibrium and a somewhat more specific process of reflective abstraction to account for stages of development.  Commons, Richards, and Kuhn (1982), Sternberg and Downing (1982), Commons and Richards (1984a and 1984b), Fischer, Hand, and Russell (1984), Pascual-Leone (1984), and Sternberg (1984) all focus explicitly on proposing a variety of mechanisms of intellectual development. They attempt not only to clarify proposed mechanisms of development, but also to show that the continued operation of these mechanisms should result in postformal thinking.

One approach, found in Fischer (1980), Fischer, Hand, and Russell (1984), and Sternberg (1984), to describing this new level of complexity is to use the analogy of unfolding dimensionality. The concept of unfolding dimensionality uses dimensions in space to convey the idea of the new size and complexity of postformal cognition. Although size may be thought of as quantitative, dimensional increase in size generates complexities that must be thought of as qualitative. Importantly, different arithmetics, geometries, and algebras are variously possible and impossible in different dimensions. For instance, adding a dimension to two-dimensional space makes it possible for the angles of a triangle to sum to more than 180 degrees and for parallel lines to intersect.  Intuitively, the complexity of geometric systems increases as the size of the space containing them increases.

In a related approach, found in Commons and Richards (1984a and 1984b), Labouvie-Vief (1984), Powell (1984), and Richards and Commons (1984), sets of axioms, or other system properties, are used to describe the increased complexity of postformal reasoning.  Labouvie-Vief (1980, 1984), for instance, uses the properties of different systems of logics.  She describes the limitations of different logics and asserts that these limitations are due to their strength.  A strong logical system is one that has several limiting assumptions.  When a logic contains many restricting assumptions, it seems clear, but causes confusion when applied in areas that do not conform to those assumptions.  Postformal reasoning arrives at an understanding of the inflexibility involved in thinking "overlogically".  It locates the limitations of excessive assumptions and formulates a more flexible, weaker logic containing fewer assumptions.  Although this logic is weaker than the logics it replaces, it retains these assumptions because, with further restrictions, it directs their use in appropriate situations.  By releasing formal thinking from overly restrictively strong logics, a weaker logic allows the development of new kinds of thinking.

Richards and Commons (1984) likewise describe the new complexity of postformal thinking in terms of systems, but attempt to describe systems formally. Their argument for the qualitative nature of change is consequently less tied to the particular nature of either logic or physics. This argument is based on the notion that higher-stage thinking is irreducible to lower-stage thinking.  This means that in the process of stage transformation, new objects of thought appear that cannot be successfully thought about at a lower stage.  Considerable attention is devoted to defining irreducibility in Bickhard (1978), Campbell and Richie (1983), Commons and Richards (1978, 1984b), Commons et al, (1998), Commons, Goodheart and Bresette (1995).

A different perspective on this argument appears in Powell's (1984) description of category operations.  Category operations have been developed in mathematics, partly in response to the Bourbaki (1939) program.  One of the concerns of the Bourbaki program has been to place the various branches of mathematics in relation to one another.  Their approach has been to locate mathematical mother structures that can be transformed and combined to produce the various mathematical disciplines (discussed in Piaget, 1970). Category operations were invented to reach the same goal, but to do so by examining the nature of mathematical operations rather than mathematical structures.  Since category operations characterize the nature of mathematical activity, they model postformal thinking as an understanding of the ways activity can be related.

Both of these general approaches lead to the claim that adult thinking contains the formal-operational framework, but employs at least one more encompassing framework as well.  Some of the more complex adult behavior is characterized by multiple-system models (e.g. Kallio, 1991, 1995).  Some adults are said to develop alternatives to, and perspectives on, formal operations.  They use formal operations within a "higher" system of operations and transcend the limitations of formal operations. In any case, these are all ways in which these theories argue and present converging evidence that adults are using forms of reasoning that are more complex than formal operations. There are also at least two sets of differences between the theories. One is that different theories have different stopping points. Some posit only one postformal stage; others posit up to four.

A second difference is that many suggest that there is a "transcendental" stage after the "regular" stages. They also suggest a sequence for the development of "consciousness". The current paper will not deal further with proposal for transcendental stages or levels of consciousness. The tasks that transcendental or consciousness levels address are not claimed to have material of substantive base and are therefore not address by task analysis.

The Model of Hierarchical Complexity (MHC) (Commons et al., 1998; Commons & Richards, 1984a, 1984b) is an across domain or universal system that classifies the task-required hierarchical organization of responses. Every task contains a multitude of subtasks (Overton, 1990). When the subtasks are completed in a required order, they complete the task in question. Tasks vary in complexity in two ways, which are defined next: either as horizontal (involving classical information); or as vertical (involving hierarchical information).

Horizontal (Classical Information) Complexity

Classical information describes the number of "yes-no" questions it takes to do a task. For example, if one asked a person across the room whether a penny came up heads when they flipped it, their saying "heads" would transmit 1 bit of "horizontal" information. If there were 2 pennies, one would have to ask at least two questions, one about each penny. Hence, each additional 1-bit question would add another bit. Let us say they had a four-faced top with the faces numbered 1, 2, 3, or 4. Instead of spinning it, they tossed it against a backboard as one does with dice in a game. Again, there would be 2 bits. One could ask them whether the face had an even number. If it did, one would then ask if it were a 2. Horizontal complexity, then, is the sum of bits required by just such tasks as this.

Vertical (Hierarchical) Complexity

Specifically, hierarchical complexity refers to the number of recursions that the co-ordinating actions must perform on a set of primary elements. Actions at a higher order of hierarchical complexity: a) are defined in terms of actions at the next lower order of hierarchical complexity; b) organize and transform the lower-order actions; c) produce organizations of lower-order actions that are new and not arbitrary, and cannot be accomplished by those lower-order actions alone. Once these conditions have been met, we say the higher-order action co-ordinates the actions of the next lower order. Stage of performance is defined as the highest- order hierarchical complexity of the task solved. Commons, Goodheart, and Dawson (March, 1997; cited in Commons & Miller, 1998; Commons, Richards, Trudeau, Goodheart, & Dawson, March, 1997) found, using Rasch (1980) analysis, that hierarchical complexity of a given task predicts stage of a performance, the correlation being r = .92 (hierarchical complexity of the task that is completed).

Formulating the Postformal Orders of Hierarchical Complexity

Commons et al (Commons, et al, 1998; Commons & Richards, 1978; Commons, Richards & Kuhn, 1982) showed that the postformal stages were true hard stages in the Kohlberg and Armon (1984) sense, but with some small modification. They used a mathematical axiomatic system derived from Duncan Luce's (e.g. Krantz, Atkinson, Luce, & Suppes, 1974; Krantz, Luce, Suppes, & Tversky, 1971) work on measurement. Each proposed stage was checked with the main three axioms. Again, these axiom state that any given higher-stage action has to be defined in terms of an associated lower one and organize those lower-stage actions in an non-arbitrary way.

Commons and Richards' concerns lay with the general specification of any empirical task that possibly could be used to demonstrate either the presence of, or the development into, a postformal stage.  They de-emphasize the reconstruction of the "reality" of a person "at a given stage". Instead, they attempt to develop a general way to specify the organization of tasks in any domain that a person "at a given stage" can do. Other attempts to specify what it means to be at a postformal stage can be found throughout the work reviewed here.

Postformal Orders of Complexity

Four postformal orders of hierarchical complexity have been proposed (Commons & Richards, 1984a, 1984b), beginning with systematic thinking and developing through metasystematic to paradigmatic and cross-paradigmatic thinking. The four postformal orders, according to the GMHC, are displayed in Table 1.

Systematic Order

This stage was introduced by Herb Koplowitz (1982). ⁽¹⁾ At the systematic order, ideal task completers discriminate the frameworks for relationships between variables within an integrated system of tendencies and relationships. The objects of the systematic actions are formal-operational relationships between variables. The actions include determining possible multivariate causes--outcomes that may be determined by many causes; the building of matrix representations of information in the form of tables or matrices; the multidimensional ordering of possibilities, including the acts of preference and prioritization. The actions generate systems. Views of systems generated have a single "true" unifying structure. Other systems of explanation or even other sets of data collected by adherents of other explanatory systems tend to be rejected. Most standard science operates at this order. At this order, science is seen as an interlocking set of relationships, with the truth of each relationship in interaction with embedded, testable relationships. Researchers carry out variations of previous experiments. Behavior of events is seen as governed by multivariate causality. Our estimates are that only 20% of the US population can now function at the systematic order without support.

Metasystematic Order

At the metasystematic order, ideal task completers act on systems; that is, systems are the objects of metasystematic actions. The systems are made up of formal-operational relationships. Metasystematic actions compare, contrast, transform, and synthesize systems. The products of metasystematic actions are metasystems or supersystems. For example, consider treating systems of causal relations as the objects. This allows one to compare and contrast systems in terms of their properties. The focus is placed on the similarities and differences in each system's form, as well as constituent causal relations and actors within them. Philosophers, scientists, and others examine the logical consistency of sets of rules in their respective disciplines. Doctrinal lines are replaced by a more formal understanding of assumptions and methods used by investigators.

As an example, we would suggest that almost all professors at top research universities function at this stage in their line of work.

Paradigmatic Order

At the paradigmatic order, people create new fields out of multiple metasystems. The objects of paradigmatic acts are metasystems. When there are metasystems that are incomplete and adding to them would create inconsistences, quite often a new paradigm is developed. Usually, the paradigm develops out of a recognition of a poorly understood phenomenon. The actions in paradigmatic thought form new paradigms from supersystems (metasystems).

Paradigmatic actions often affect fields of knowledge that appear unrelated to the original field of the thinkers. Individuals reasoning at the paradigmatic order have to see the relationship between very large and often disparate bodies of knowledge, and co-ordinate the metasystematic supersystems. Paradigmatic action requires a tremendous degree of decentration. One has to transcend tradition and recognize one's actions as distinct and possible troubling to those in one's environment. But at the same time one has to understand that the laws of nature operate both on oneself and one's environment--a unity. This suggests that learning in one realm can be generalized to others.

Examples of paradigmatic order thinkers are perhaps best drawn from the history of science. For example, the nineteenth-century physicist, Clark Maxwell, constructed a fields paradigm from the existing metasystems of electricity and magnetism of Faraday, Ohm, Volta, Ampere, and Oersted using the mathematics of fields and waves. Maxwell's (1871) equations, showing that electricity and magnetism are united, formed a new paradigm. The wave fields can be easily seen as the rings that form when a rock is dropped in the water or a magnet is placed under paper that holds iron filings. This paradigm made it possible for Einstein to use notions of curved space to describe space-time to replace Euclidean geometry. The waves were bent by the mass of objects so that the rings no longer fit in a flat plane. From there modern particle theory has been able to add two more forces to the electromagnetic forces.

Cross-paradigmatic Order

The fourth postformal order is the cross-paradigmatic. The objects of cross-paradigmatic actions are paradigms. Cross-paradigmatic actions integrate paradigms into a new field or profoundly transform an old one. A field contains more than one paradigm and cannot be reduced to a single paradigm. One might ask whether all interdisciplinary studies are therefore cross-paradigmatic? Is psychobiology cross-paradigmatic? The answer to both questions is 'no'. Such interdisciplinary studies might create new paradigms, such as psychophysics, but not new fields.

This order has not been examined in much detail because there are very few people who can solve tasks of this complexity. It may also take a certain amount of time and perspective to realize that behavior or findings were cross-paradigmatic. All that can be done at this time is to identify and analyze historical examples.

Copernicus (1543/1992) co-ordinated geometry of ellipses that represented the geometric paradigm and the sun-centered perspectives. This co-ordination formed the new field of celestial mechanics. The creation of this field transformed society--a scientific revolution that spread throughout world and totally altered our understanding of people's place in the cosmos. It directly led to what many would now call true empirical science with its mathematical exposition. This in turn paved the way for Isaac Newton (1687/1999) to co-ordinate mathematics and physics forming the new field of classic mathematical physics. The field was formed out of the new mathematical paradigm of the calculus (independent of Leibniz, 1768, 1875) and the paradigm of physics, which consisted of disjointed physical laws.

Rene Descartes (1637/1954) first created the paradigm of analysis and used it to co-ordinate the paradigms of geometry, proof theory, algebra, and teleology. He thereby created the field of analytical geometry and analytic proofs. Charles Darwin (1855, 1877, 1987) co-ordinated paleontology, geology, biology, and ecology to form the field of evolution which, in its turn, paved the way for chaos theory, evolutionary biology, evolutionary psychology. Albert Einstein (1950) co-ordinated the paradigm of non-Euclidian geometry with the paradigms of classical physics to form the field of relativity. This gave rise to modern cosmology. He also co-invented quantum mechanics. Max Planck (1922) co-ordinated the paradigm of wave theory (energy with probability) forming the field of quantum mechanics. This has led to modern particle physics. Lastly, Gödel (1931), co-ordinated epistemology and mathematics into the field of limits on knowing. Along with Darwin, Einstein, and Planck, he founded modern science and epistemology.

Bringing Simplicity to Multiplicity

Reviewing his career, Piaget (1952) remarked:

"My one idea… has been that intellectual operations proceed in terms of structures-of-the-whole. These structures denote the kinds of equilibrium toward which evolution in its entirety is striving; at once organic, psychological and social" (p. 256).

In part, the work of all the researchers mentioned here is a response to this one idea. Their work represents part of an broad attempt to grow out of the form Piaget gave to a wide variety of nineteenth-century thought. The question remains whether the growth of postformal theories is itself proceeding in terms of some sort of structure-of-the-whole.  Broughton (1984) argues that this is not the case and suggests abandonment rather than revision.  Another approach to this question is to assume that postformal research does not talk about many different stage sequences, but about many different manifestations of the same stage sequence.

The problem of specifying what is meant by a stage and by a stage sequence remains a critical issue in developmental theory.  Elsewhere, Piaget (1972), Flavell and Wohlwill (1969), Kohlberg (1969, 1981, 1984), Flavell (1971, 1972, 1977, 1982), Bickhard (1978, 1979), and Campbell and Richie (1983) have devoted considerable attention to it. This specification is centrally important in Kohlberg and Armon (1984), and Commons and Richards (1984a, 1984b). Kohlberg and Armon's concern is to distinguish functional, soft, and hard stages.  Functional stage refers to the Eriksonian (1959, 1978) model in which each stage develops in order to perform a new task or function.  Soft stage refers to development that is conditioned by particular experiences.  These experiences could arise from differences in personality characteristics, education, class, age, and so on.  Hard stage refers to developmental sequences that occur universally, arising out of the overall reorganization of an underlying intellectual framework.

Table 2 presents one way that the stage sequences presented here can be aligned across a common developmental space. The harmony in the alignment shown in Table 2 suggests a possible part of a reconciliation of Kohlberg and Armon's (1984) hard- and soft-stage distinction. Hard stages were to have some logical basis whereas soft stages might be based on some functional ordering based solely on empirical findings. Although each of these stages may be soft stages individually, taken as a whole, they indicate the development of some hard stages. The General Model of Hierarchical Complexity provides a proposal for what the logic may be underlying the sequences reported in Table 2.

The nature of these various postformal stages or levels cannot be determined from Table 2. Their extent may range beyond the developmental areas so far described.  Their empirical nature has been emerging with a clearer understanding of the similarities and differences of the various stage conceptions.  For this to have happened, the nature of elements and operations have been communicated among the researchers studying the various developmental sequences that appear in Table 2.  Part of what this suggests is that the proposed postformal stages have been adequately formalized in a way that has facilitated comparison. Similarly, theories of stage transition must be formalized.

An Empirical comparison of some measures of postformal behavior

One way to test whether there might be an necessary ordinal sequence underlying all of the separate postformal theories, is to empirically compare performances across instruments developed within each theory. Although this has not yet been done for all of the theories, some preliminary work has been done comparing a few of the instruments. In Commons et al. (1989) scores on the Multisystems Task, developed to assess the General Model of Hierarchical Complexity, were correlated to tasks from a few postformal theories, including Armon's Good Life Interview, Kohlberg's Moral Judgment Interview, and Loevinger's Sentence Completion Task. As Table 3 shows, only Loevinger's scores were not related to the other measures of postformal stages. Scores from the instruments were also factor analyzed, using principal components analysis. All of the instruments, except for Loevinger's Sentence Completion task, showed significant positive loadings on the first factor, which was termed the structural factor.

Sentence Completion Task is related to is the inverse of education. King and Kitchener (1989; also see Kitchener & King, 1990) have obtained similar results for the SCL.

These results provide some beginning empirical support that there might be a common underlying variable, they do not suggest what that variable might be that underlies these different postformal conceptions they.

Because the model of hierarchical complexity is based upon sequencing the order of hierarchical complexity of tasks, the model logically contains all the stage systems. The sequence of stages and levels generally lines up across theorists. At this date, we would be surprised by an error in the sequence after infancy. If there were such it would be in infancy. The Model of Hierarchical Complexity does not address interest, as Carol Gilligan (1982) does. Nor does it address domain, content, or the conditions under which performance is obtained.

Commons et al (1998) present Theorem 3: A linear order of development may exist only within a single domain, on single sequences of tasks. This theorem shows inconsistences in development across tasks and domains. The corresponding Model of Hierarchical Complexity Scoring Scheme discusses many systematic ways of producing variation in performance.

Attaining Postformal Stage Performance

Commons and Miller (1998) and Commons and Richards (1997) have described both stage transition and reasons why transition takes place or fails to take place. The first three steps (deconstruction) start with initially high loss of perceived reinforcement opportunity. But, during the advance through these initial steps, more reinforcement is obtained. Psychologically, the results are consistent with Jesus Rosales and Donald Baer's (1996) work on behavioral cusps. They posit more cusps than there are stages, however. Most of the proposed psychological mechanism of transition seems to be consistent with these theories. Despite this, most theories do not operationalize clearly the steps in transitions or the empirical basis for transition.

Both within many neo-Piagetian accounts (e.g. Case, 1974, 1978, 1982, 1985) and Precision Teaching (e.g. Binder, 1995) accounts, automatization of previous stage behavior is predicted to improve the rate of obtaining next-stage performance. From the data from Precision Teaching, fluency in lower-stage tasks greatly enhances the acquisition of the new stage tasks. As a task is completed near the maximum rate and errors almost disappears, the actions are said to become automatized. With Hence such over learning leads to automatization. The task stimuli are said to become "chunked". That is, each individual stimulus in the task has to be discriminated individually but they are discriminated as a whole.

Although all tasks must have an order of hierarchal complexity, performance on such tasks depends on many other task characteristics. They include: level of support (Fischer, Hand, & Russell, 1984); Commons & Richards (1995), horizontal complexity, fluency of performance on the component tasks, "talent", interest, etc. Hence, one expects complex interrelationships between measures of performance on tasks and conditions of measurement. The stage of performance should be curvilinear when plotted against age (Armon & Dawson, 1997; Dawson, 1998) and linear when plotted against. Any variability should increase with age, and it does. Yet, there is some evidence that at the higher stages there is less spread. The proclivity to integrate relationships and systems and even paradigm from many domains probably increases with postformal stage.

Implications

There are a number of reasons that postformal stages are important. Without giving the order of importance by the order of presentation here are some of the reason. Postformal stages may account for part of unequal accomplishment. They might account for part of the differences among individual within a social group as to things like income and schools performance. Stage of performance might be used to evaluate the effect of a culture on social, political and educational development (Bowman, 1966; Commons & Goodheart, 1999; Commons, Krause, Fayer & Meaney, 1993; Commons & Rodriguez, 1990; 1993). They might make clear the evolutionary implications of attaining postformal performance (Commons & Bresette, in press). Because education is a strong predicator of stage of performance, we might be better at finding out why, if we understand the postformal stages and their measurement better. Society might be organized to produce and pay-off the acquisition of postformal performance. Individually , the benefits and costs of postformal development in the wide domains investigate could be understood.

There are clear social benefits, including improved moral and ethical atmosphere to the attainment of increased postformal development. As social perspective skill increase with these stages, the plight of the under classes improve. Dialogical mans are used to have real discussion in the process of making policy. The abuse of power is decreased.

Another and important social benefit is that postformal development is associated with increased innovation. Innovators functioning at each of the four stages do tasks of different hierarchical complexity that do not overlap with one another. They do the different tasks using skills that are increasingly rare. The end results are entirely different for society. People have been known to buy the expertise of people functioning at the systematic and metasystematic stage, however, we posit that a person must function in the area of innovation at least at the metasystematic order of hierarchical complexity or higher to produce truly creative innovations. That means that at least two multivariate systems must be co-ordinated.

The results of innovation become much more expensive at the paradigmatic and cross-paradigmatic stages. In fact, at the cross-paradigmatic stage, so few people exist that societies have no mechanisms to encourage such activity as far as I know. Yet it is the cross-paradigmatic skills that change the course of civilization.

The development of complexity in human societies depends upon innovations by single individuals. The innovator has the tendency to discern and discriminate relationships among elements that are extremely complicated. Making an innovation is much more difficult than learning about it after it is made. Major cultural innovations require paradigmatic complexity (Commons & Richards, 1995) at least because there is no support whatever from within the cultures themselves. The difficulty of an action depends on level of support in addition to the horizontal information demanded in bits, and the order of hierarchical complexity. The level of support (Fischer, Hand & Russell, 1984) represents the degree of independence of the performing person's action and thinking from environmental control provided by others in the situation.

There is little support for major innovations in culture because the history of the necessary hierarchical complexity surrounding the task is absent. Nor is there a history of reinforcement that would induce the subject to detect new phenomena. "Finding" a given question increases complexity demand by one order of complexity over solving a posed problem with no assistance. Finding the question allows for finding a problem to address that question, which increases the complexity demanded by one further order (Arlin, 1975, 1977, 1984). Finding and identifying the underlying phenomenon requires still a third additional order of complexity.

Lastly, there are interpersonal and personal benefits to moving through the postformal stages. Relationships are seen more in equitable terms. The struggle for independence and dependence is integrated into a more function interdependence in which contribution to the needs and preferences of others is part of non-strategic interaction. Unresolved conflicts are dealt within a larger framework of co-constructing a workable dialogs

Some of this material comes from three sources: a) Commons, M. L., & Goodheart, E. A. (1999), The philosophical origins of behavior analysis. In B. A. Thyer (Ed.). The philosophical foundations of behaviorism. Kluwer. b) Commons, M. L., & Bresette, L. M. (In press). Major creative innovators as viewed through the lens of the general model of hierarchical complexity and evolution, M. E. Miller & S. Cook-Greuter (Eds.), creativity, spirituality, and transcendence: paths to integrity and wisdom in the mature self. Stamford, CT: Ablex Publishing Corporation. c) Richards, F. A., & Commons, M. L.  (1990).  Postformal cognitive-developmental research: Some of its historical antecedents and a review of its current status.  In C. N. Alexander, & E. J. Langer.  Higher stages of human development: Perspectives on adult growth, New York: Oxford University Press. Leroy Brockman and Patrice Marie Miller have edited the manuscript and made major suggestions.

The standard stage sequence was constructed by Commons and Richards working many people. Most importantly, from 1981 on, Pascual-Leone discussed with Commons half stages. Fischer and Commons also talked about them. Richards and Commons had most of the stages by 1978, although they missed the systematic and paradigmatic stages and were unsure of how to define the abstract stages as mentioned above. By 1983, they had them all. Most important to this process/accomplishment was the input of Fischer. He supplied the arguments for abstract stage, as well as his four levels per tier (but did not have empirical evidence for performance at the higher two levels). Koplowitz suggested the systematic stage at my office while we were editing his chapter. He said if there is to be a general system or metasystem, it must be about some system, that is it must consist of simpler systems. Elena Jomar (1984) suggested the paradigmatic stage at a lecture held at Harvard School of Education by Carol Gilligan. She said that if there were a cross-paradigmatic stage there had also to be a paradigmatic stage to cross.

Sonnert and Commons (1994), after scoring a number of protocols, using both the Colby & Kohlberg (1987a, 1987b) manual and the Model of Hierarchical Complexity, came to see Kohlberg's moral judgment stage 4/5 as a transition. At Dorothy Danaher's wedding party, Kohlberg, Higgins, Miller, and Danaher discussed with him why he did not see his stage 4 as systematic and stage 5 as metasystematic postformal stages. He said that although his stages were postformal, he had not thought to relate them to the post-Piagetian postformal work. Later, Kohlberg (1990) wrote a chapter relating them.

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Table 1

Postformal Stages, as described in the General Model of Hierarchical Complexity

Table 2

Comparative Table of Concorded Theories of Formal Stage

Table 3

Empirical Comparison of Individuals' Scores on Different Measures of Postformal Reasoning

Ms GL MJ Loev Structural Loading

Multisystems .44** .31** .13 .75

Good Life .41** .00 .85

Moral Judgment .22 .64

Sentence Completion .26

Arlin (1975, 1984 4

Arlin, 1975, 1977, 1984 19

Arlin's (1975, 1977, & 1984) 5

Arlin's (1975, 1977, & 1984) 5

Armon (1984 4

Armon (1984) 5

Armon & Dawson, 1997 17

Basseches (1980. 1984) 5

Basseches (1980; 4

Benack (1984 4

Bickhard (1978, 1979 14

Bickhard (1978) 8

Binder, 1995 16

Boole's (1854) 2

Bourbaki (1939) 8

Bowman, 1966 17

Broughton (1977, 1984 3

Broughton (1984 14

Campbell and Richie (1983) 8, 14

Case, 1974, 1978, 1982, 1985 16

Clark Maxwell 12

Colby & Kohlberg (1987a, 1987b 20

Commons & Bresette, in press 17

Commons & Goodheart, 1999 17

Commons & Miller, 1998 10

Commons & Richards (1995 17

Commons & Richards 1984a 1984b 4

Commons & Richards, 1978 10

Commons & Richards, 1984a, 1894b 1

Commons & Richards, 1984a, 1984b) 9, 10

Commons & Richards, 1995) 18

Commons & Rodriguez, 1990; 1993 17

Commons and Miller (1998 16

Commons and Richards (1978, 1984b) 8

Commons and Richards (1984a 4

Commons and Richards (1984a and 1984b 6

Commons and Richards (1984a and 1984b) 7

Commons and Richards (1997 16

Commons and Richards, 1978 4

Commons et al (1998) 10

Commons et al. (1989 15

Commons et al, (1998) 8

Commons et al, 1998 4, 9

Commons, 1999 1

Commons, et al., 1998 1

Commons, et al, 1998 10

Commons, Goodheart and Bresette (1995). 8

Commons, Goodheart, and Dawson (March, 1997 9

Commons, Krause, Fayer & Meaney, 1993) 17

Commons, M. L., & Bresette, L. (in press 20

Commons, M. L., & Goodheart, E. A. (1999 20, 24

Commons, Richards & Kuhn, 1982 10

Commons, Richards and Kuhn (1982 4

Commons, Richards and Kuhn (1982) 6

Commons, Richards, Trudeau, Goodheart, & Dawson, March, 1997 10

Darwin (1855, 1877, 1987 13

Dawson, 1998 17

Demetriou (1990; Demetriou & Efklides, 1985 4

Descartes (1637/1954) 13

Einstein (1950) 13

Einstein, 1950 6

Eriksonian (1959, 1978) 14

Fischer (1980 7

Fischer, Hand, & Russell, 1984 17

Fischer, Hand, and Russell (1984 6, 7

Flavell (1971, 1972, 1977, 1982) 14

Flavell and Wohlwill (1969) 14

Frege (1950) 2

Gilligan (1982) 16

Gödel (1931) 13

Inhelder & Piaget, 1958 4

Jesus Rosales and Donald Baer's (1996) 16

Kallio, 1991, 1995 8

King and Kitchener (1989 15

Kitchener & King, 1990 15

Kohlberg (1969, 1981, 1984 14

Kohlberg (1990 21

Kohlberg and Armon (1984) 10

Kohlberg and Armon's (1984) 14

Koplowitz (1984 7

Koplowitz's (1984) 6

Krantz, Atkinson, Luce, & Suppes, 1974 10

Krantz, Atkinson, Luce, & Suppes, P., 1974 10

Krantz, Luce, Suppes, & Tversky,1971 10

Labouvie-Vief (1980, 1984 7

Labouvie-Vief (1984 7

Labouvie-Vief (1989; 1984 4

Labouvie-Vief (1990; 1984 4

Leibniz, 1768, 1875 13

Linn and Siegal (1984) 5

Maxwell's (1871) 12

Overton, 1990 9

Pascual-Leone (1984 4, 6

Peano (1894 2

Piaget (1950, 1952 1

Piaget (1952 1, 14

Piaget (1963, 1972 14

Piaget (1970) 6

Piaget (1971 3

Piaget & Inhelder, 1969 4

Piaget, 1970 8

Planck (1922) 13

Powell (1984 4

Powell (1984) 7

Powell's (1984 8

Rasch (1980 10

Richards and Commons (1984 7

Richards, F. A., & Commons, M. L. (1990) 20

Riegel (1973) 4

Sinnott (1981, 1984 6

Sinnott (1981; 1984) 5

Sinnott (1984 5

Sinnott (1984), 7

Sonnert and Commons (1994 20

Sternberg (1984 6, 7

Sternberg (1984) 5

Sternberg and Downing (1982 6

1. He suggested that meta-systems and general system must operate upon systems while we were working on his chapter at Dare Institute.

2. ²As modified by Commons (19 ).