Classification System

The main “form of being” of knowledge in systematics is classification, which serves as a cognitive (informational) model of a certain manifestation of TR. In one of the approaches considering the ways of representation of the diversity of Nature, it is aptly designated as the classification system as opposed to the parametric system [Subbotin 2001]. The first reflects the relationships between different objects characterized by the same or different features and represents the categorical structure of these relations by recognizing assemblages of objects (taxa, biogeographical units, syntaxa, etc.) based on their specific features. The second reflects the relationship between different features that characterize the same or different objects and represents quantitative relationships between these features by compact formulas (the van’t Hoff equation in chemistry, the Schrodinger equation in physics, the equation of allometric growth in biology, etc.).

A number of rather formalized definitions of the classification system (= classification in its general sense) was proposed that might be suitable for direct interpretation in terms of systematics [Woodger 1937; Gregg 1954; Jardine 1969; Voronin 1985]. Below is the exposition of a revised version developed earlier by the author [Pavlinov 2011 a, 2018; Pavlinov and Lyubarsky 2011] based on the following notions and definitions.

The classification system CS reflects the general structure of the TR. The latter is decomposed into two basic aspects, taxonomic and partonomic, interrelated in a certain way. The taxonomic system TS is developed for the first aspect, and the partonomic system PS is developed for the second aspect. The general classification system is a union of these two particular classification systems.

The classification system CS is an ordering of the classification units CF by establishing certain relations RCF between them, so it is the relational system. In the simplest case it can be defined as an ordered pair {CF, RCF). If taxonomic system TS is developed, its classification units are taxa T; the relations between them RT are defined as similarity, kinship, rank, etc.; taxa are characterized by taxonomic characters CT, with the respective relations Rc between them being defined (intercorrelations, weights, ranks, etc.); relations RTC between taxa and characters are established by taxon-character correspondence (see Section 6.2). If partonomic system PS is developed, its classification units are partons P with their respective relations Rp (homology, rank, etc.) they are assigned to certain taxa PT, establishing taxon-parton correspondence RTM between them. Partons assigned to taxa PT are operationally representable as taxonomic characters CT, which makes them mutually equivalent: PT C.,.; on this basis, equivalences are established between the corresponding relations: Rp «-> Rc and RTp «-> Rrc. Together, these equivalences can be viewed as a functor connecting systems TS and PS into a single system CS [Shreyder and Sharov 1982]. All these parameters remain formal if they are not interpreted in a meaningful way. For such an interpretation, one more parameter is introduced—basic background theory BT, in which context other parameters acquire a certain meaningful interpretation.

Accordingly, the following general definition of the classification system CS looks as follows:

CS z> (TS) vj {PS}

TS z> BT{T, CT, RT, RTC]

PS z> BT{P, PT. R,„ RT|>}

Position of the parameter BT out of the brackets means that it is not an obligatory part of the definition of either interpretations of CS. Omitting it makes the latter meaningfully undefined and therefore theory-neutral in any respect. If included in the definition of CS, it means the latter is meaningfully interpreted and thus theory-dependent; this is true for all parameters of the above definitions—taxa, partons, characters, and relationships between them. An integrative effect provided by the parameter BT is formalized by the above-mentioned principle of criteria! uniformity’: all parameters enclosed in the brackets {...} must have the same interpretation in all fragments and at all levels of the respective classification system. Thus introduced, the parameter BT fulfills two important functions. First, it serves as the basis for developing both the definition and criteria of naturalness of the classification system within the framework of the respective PTT. Second, it defines an ordering factor (for example, kinship relation), according to which the general structure of the classification system is shaped.

Taking into account the structure of the cognitive situation, two respective basic components can be distinguished in the parameter BT, viz. ontic BT0 and epistemic BTE, according to which two variants of meaningful interpretation of the classification system can be defined. If a PTT is ontology-based, this parameter is defined as BT0: it makes the classification system biologically sound, and its concrete values indicate the properties of TR considered significant according to this PTT. If a PTT is epistemology-based, this parameter is defined as BTE: it outlines the main properties of the method (in the general sense) that generates the respective classification system, which remains with no biologically sound content. Thus, the first option means the dependence of the content and structure of the system CS on a particular substantive background knowledge, whereas the second option means its dependence on a particular classification algorithm.

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