The names and numbers for the most commonly observed skill/lectical levels are shown in the table below, including the approximate ages and educational levels at which they generally become dominant.

Level	Fischer name	Age of onset	Education
0	Single reflexive actions	Birth	n/a
1	Reflexive mappings	6 wks	n/a
2	Reflexive systems	3 mos	n/a
3	Single sensorimotor actions	6 mos	n/a
4	Sensorimotor mappings	10 mos	n/a
5	Sensorimotor systems	15 mos	n/a
6	Single representations	21 mos	n/a
7	Representational mappings	4-5 yrs	0-K
8	Representational systems	7-8 yrs	1-2
9	Single abstractions	10-11 yrs	4-5
10	Abstract mappings	14-15 yrs	8-9
11	Abstract systems	22+ years	15-16
12	Single principles	26+ years	Ph.D.+

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

In texts, hierarchical complexity is reflected in two aspects of performance, the hierarchical order of abstraction of concepts and the logical organization of arguments. Hierarchical Complexity Theory predicts that some increases in hierarchical complexity will take the form of increasing hierarchical order of abstraction. This is because new concepts are formed at each complexity order as the operations of the previous complexity order are "summarized" into single constructs (Fischer, 1980). Burtis (1982) and Halford (1999) suggest that this summarizing or "chunking" makes more complex thought possible by reducing the number of elements that must be simultaneously coordinated, freeing up processing space and making it possible to produce an argument or conceptualization at a higher complexity order. For example, the concept of honor, which appears for the first time at the abstract mappings level, "summarizes" an argument coordinating concepts of reputation, trustworthiness, and kindness constructed at the single abstractions level. Similarly, the concept of personal integrity, which appears for the first time at the abstract systems level, summarizes an argument coordinating concepts of honor, personal responsibility, and personal values constructed at the abstract mappings level.

The figure below illustrates hierarchical integration.

(Complete references for the articles cited in this panel can be found under the references tab.)

Fischer defines 5 tiers, each of which is associated with a primary order of abstraction. These are reflexive actions, sensorimotor actions, representations, abstractions, and principles. Within each tier there are 3 complexity levels. This means there are 13 hierarchical orders of abstraction between single reflexive actions and single principles. These are associated with complexity levels as follows:

Hierarchical order of abstraction

Level	Fischer name	Order of Abstraction	Logical structure
0	Single reflexive actions	1st order actions	Definitional
1	Reflexive mappings	2nd order actions	Linear
2	Reflexive systems	3rd order actions	Multivariate
3	Single sensorimotor actions	1st order schemes	Definitional
4	Sensorimotor mappings	2nd order schemes	Linear
5	Sensorimotor systems	3rd order schemes	Multivariate
6	Single representations	1st order representations	Definitional
7	Representational mappings	2nd order representations	Linear
8	Representational systems	3rd order representations	Multivariate
9	Single abstractions	1st order abstractions	Definitional
10	Abstract mappings	2nd order abstractions	Linear
11	Abstract systems	3rd order abstractions	Multivariate
12	Single principles	1st order principles	Linear

 

First order, 2nd order, and 3rd order concepts are associated with definitional, linear, and multivariate logical structures, respectively.

A definitional logical structure identifies the concept and describes it in terms of a single aspect. For example, at the single representations level (1st order representations), definitional logic allows representations to stand in for persons, objects, simple states, or simple actions—as in, “I not touch that.” At the representational mappings level (2nd order representations), a linear logical structure (referred to as a mapping by Fischer and his colleagues) describes the relationship between representations—as in, “If you're good, your mommy might buy you ice cream,” in which being “good” is coordinated with a particular concrete benefit. At the representational systems level (3rd order representations), the logical structure is multivariate. Multiple outcomes of behavior can be considered—as in, “If I am good, I won't get punished, and I might get to do something fun.” For simplified examples click here.