The second example is taken from the wash problem (Commons, Miller, & Kuhn, 1982), a task where subjects are asked to predict the outcome of washing a dirty cloth in one or more variable conditions (water temperature, type of soap, etc.) based on previous outcomes for other cloths. The response at the primary stage is like a law ‘‘a cloth washed in hot water comes out clean.’’ Participants act as if they use the syllogism and make a correct prediction. Table 3 gives the action breakdown. Note that the preoperational step is not the consequence of the action, but merely the time ordering of the events.

Since Piaget’s death, few absolute and systematic accounts of stage have been devised, and the notion of stage itself has increasingly come under attack (Brainerd, 1978; Broughton, 1984; Flavell, 1963). The diversity of opinion as to the existence and measure of stage may be grouped into eight broad categories, four of which reject and four of which accept some notion of stage (for detailed reviews of some present stage theories, see for example Alexander & Langer, 1990; Campbell & Bickhard, 1986). ).

First, the concept of stage has been rejected categorically by some behavioral psychologists, most notably Skinner (Skinner & Vaughan, 1983). Behaviorists acknowledge that certain behaviors require the acquisition of others in a chronological sense, but do not characterize these sequences in any definitive way. The emergent property of stage (see Table 4) that Piaget posits is particularly objectionable (Gewirtz, 1991). It assumes automatic generativity rather than the contextualist notion that development is produced by an interaction between actions and the surrounding context.

Second, there are those theorists focusing on maturation and IQ studies (Binet & Simon, 1905/1916; Gesell & Amatruda, 1964; Terman & Merrill, 1937; Wexler, 1982) who work with the notion of sequence rather than stage. To the behaviorists’ notion of chronological acquisition of behaviors, these theorists add a requirement of certain ages for certain acquisitions, thereby charting human development in a normative way that allows for averages and deviancies.

Third, the work of those who characterize development in terms of periods, or ‘‘seasons’’ in human life, rejects the concept of stage. Among some theorists, these periods are quite specialized (Erikson, 1959, 1978, 1982; Levinson, 1986), although among others they form only three or four broad superperiods (Alexander, Druker & Langer, 1990; Flavell, 1963). These periods are seen as sequenced but not hierarchical, and they are not organized in any strictly logical way. Development in terms of periods may be characterized more as socialization, whereas stage development is understood as transformation.

Fourth, there are some who characterize development in terms of levels, reserving the notion of stage to refer to coherence across domains within a chronological period (Case, 1974, 1978, 1982; Fischer, 1980; Pascual-Leone, 1970, 1984). These theorists accept de´calage just as Piaget (1972) did and maintain that functioning at different levels in different domains is normal. These levels are hierarchical, but they may lack a single reflective, generative mechanism, which characterizes a stage. Depending on the level, different kinds of coordinations may take place. These differences are often organized into tiers containing four levels. The first level of one tier parallels the first levels of other tiers. These levels fail to integrate and order lower stage actions in the same way irrespective of level. Additionally, Campbell and Bickhard (1986) claim that level theories (e.g., Case, 1978, 1982; Fischer, 1980) do not build upon a reflective abstraction process of stage change that underlies the whole process of development. Thus, the levels tend to have the qualities of subroutines, so that one cannot be sure that these levels could not be grouped into larger routines or subdivided even further (see Campbell & Bickhard, 1992) because of the lack of inherent hierarchy.

Among those who do accept the notion of stage, a great deal of controversy exists as to the nature and measurement of these stages. First among these is the view, held by many stage theorists, that human beings move through developmental stages, but that this development stops at the stage of formal operations or shortly thereafter (Baltes, 1987). There is also diversity among those who accept the notion of adult stages (for a discussion of these adult stage theories, see Alexander & Langer, 1990; Kohlberg & Armon, 1984; and Richards & Commons, 1990a,b). Piaget made a number of clear statements about postformal operations. Campbell (personal communication) reports Piaget’s statement that constructing axiomatic systems in geometry requires a level of thinking that is a stage beyond formal operations: ‘‘one could say that axiomatic schemas are to formal schemes what the latter are to concrete operations’’ (Piaget, 1950).

[Soft stage theories re ego] A second perspective on stage theory can be identified with the work of Loevinger, Kitchener, and King or others who work with stage in a statistical sense and use psychometric methods to support their theories. Among these theorists (Kitchener & King, 1990; Loevinger & Blasi, 1976; Rest, Turiel, & Kohlberg, 1969) one does not find a clearly delineated a priori logic of stages (Kohlberg, 1984; Kohlberg & Armon, 1984).

A third alternative is found in the work of Armon (1984), Dasen (1977), Kegan (1982), Kohlberg (1984), and Selman (1980), who define clear stages, but whose theories of stage self-admittedly lack a solid foundation in logic.

A fourth alternative has been to extend accounts with organized schemata underlying each stage (Demetriou, 1990; Demetriou & Efklides, 1985; Pascual-Leone, 1984). This fourth alternative has generated a structure and sequence of formal and postformal thought. Kohlberg (1990), Demetriou (1990; Demetriou & Efklides, 1985), and Pascual-Leone (1984) all conceived of two to three postformal stages and saw the necessity of logical analysis to demonstrate and clarify these stages (Commons & Grotzer, 1990). That is, Kohlberg, for example, said that stage is a logical truth and that postformal stages existed (Kohlberg, 1990). This paper continues that one aspect of Kohlberg’s work by formalizing that truth in an analytic model