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  Hierarchy Theory

Hierarchies are ordinations, as from smaller to larger, or from simpler to more complex. Rank is canonical, not optional. In science related discourses there have been two forms of hierarchy theory -- that based on scale (extension) and that based on descriptive complexity (intension). This delivers two models of the material world; the scalar hierarchy represents extensional complexity (defined as the situation where dynamics of different scale contextualize each other at one locale, resulting in non- linear dynamics), while the specification hierarchy represents intensional complexity (defined as the situation where more than a single discourse can be brought to bear upon a phenomenon).

The scalar hierarchy represents subsystems (or components) nested within supersystems (or wholes). In order not to lose the complexity, models of this kind need to explicitly represent at least three levels simultaneously. The lower level proposes possible dynamics at the focal level, while the higher level regulates or interprets them, as via boundary conditions. In these models small scale dynamics are implicitly assimilated to large scale durations. Therefore, process may be represented at different scalar levels as well as spatial entities, but not change; the system is implicitly synchronic (moments of different scale nest within each other). Signals will not simply transit through scalar levels in amplification, but may be transduced from one level to the next. A transitive downward plunge of signals can be catastrophic. An operational model of the origin of scalar levels is interpolation between primal highest and lowest, protecting lower level organization.

The specification hierarchy too has a synchronic interpretation, as when we overlay a physical description of an organism on a chemical description. Each of these represents a different integrative level. Higher levels here transitively integrate dynamics and phenomena at lower levels, as when biology selects or harnesses a few chemical pathways, or a few physical processes, from the many possible to interact at the biological level. Any two levels are sufficient to explore integration. The polarity of rank here is imposed by the observer, whose level is the highest in the hierarchy, which traditionally is presented as a hierarchy of discourses, as in {physical {chemical { biological }}} -- the specification hierarchy represents levels as nested subclasses. In a diachronic interpretation, the specification hierarchy represents stages of development, as when using the above hierarchy to represent some stages in the development of the earth. Here development is modeled as the accumulation of greater specification (as via growth and/or differentiation). The sequence is then interpreted as having been generated by a concatenation of historical emergences, from the outermost to the innermost class. This sequence is held to be canonical, as when biology is held to be impossible without chemistry. The specification hierarchy is the core of the philosophy of nature as received from the Nineteenth Century.

Stanley N. Salthe


  • The specification hierarchy has similariites to the logician W.E. Johnson's determinable/determinate hierarchy. On this account vermillion is a more determinate form of the determinable red, which in turn is a more determinate form of colour. Computer is a more determinate form of the determinable machine, and PC clone is a more determinate form of both machine and computer.

    John Collier



  • There is an interesting ambiguity in the notion of specification, as Salthe indicates through his distinction between synchronic and diachronic aspects. Both can be mapped into W.E. Johnson's determinable/determinate hierarchy, but the latter has a dynamical interpretation according to which the dynamics of a system generate greater specificity within the system. This occurs, for example, in systems that branch into one or more phases and become hsitorically constrained along the branches. Salthe suggests that both developmental and evolutionary branching is a from of such dynamical specification. This further suggests that there are at least some common and fundamental common principles underlying both development and evolution.

    John Collier