Between Taxon and Character

As shown in Chapter 4, TR is mentally divided into two “orthogonal” complementary aspects, taxonomic and partonomic (meronomic) [Meyen 1977, 1978; Lyubarsky 1996; Pavlinov 201 la, 2018; Pavlinov and Lyubarsky 2011]. Turning to the first aspect, systematics deals with the diversity of organisms and identifies taxa as units of taxonomic systems representing certain groups of organisms (vertebrate animals, herbaceous plants, etc.). Turning to the second aspect, systematics deals with the diversity of the properties of organisms and recognizes partons (merons) as particular classes of these properties (limbs, body coloration, sexual behavior, etc.). Based on the partons recognized in partonomic systems, classifying characters are fixed, though without a strict (one-to-one) correspondence between them. Organisms are then described by these characters and, based on the results of their comparison by the respective characters, taxa are distinguished in the taxonomic system. The elaboration of the latter constitutes an ultimate goal of systematics, but this aim can be rich only if there is a certain partonomic system with respective characters that have already been developed. On the other hand, the structure of partonomic diversity can only be uncovered after at least some preliminary information has been obtained about the structure of TD in order to differentiate partons not “in general” (which is meaningless enough), but with reference to particular groups of organisms. As a result, we have a kind of dual unity: one aspect of diversity does not exist without another, and the study of one of them is both a prerequisite and a certain result of the study of the other—therefore, the better (more detailed) we know one aspect of TR, the better we know another.

On this basis, the fundamental taxon-character puzzle arises: how to analyze correctly taxa and their characters, if the analyses of the respective aspects of the TR are mutually conditioned. So one part of this puzzle is a hazard of taxonomic research possibly devolving into circular reasoning by the bi-unity of these two aspects: they are involved in the same classification procedure, in which they are mutually interdependent.

In solving this puzzle, it should be clearly understood that both its components— a taxon and a character—are conceptual constructs that cannot be represented outside the conceptual space developed by the general TT. This means that the general solution to this puzzle belongs to the competence of the latter: it defines possible ways to solve the puzzle depending on how the classification units of both taxonomic and partonomic systems and the interrelations between them are defined.

It is to be noted that the frequently declared identity of characters with some observable properties of organisms [Gilmour 1940; Michener and Sokal 1957; Sneath and Sokal 1973; Wagner 2001] is fundamentally incorrect from a conceptualist standpoint. The latter presumes a character to be an information (cognitive) model of the corresponding parton or a certain set thereof, and a sample of characters is an information (cognitive) model of the corresponding partonomic “subspace” [Pavlinov 2018]. Characters are distinguished based on prior recognition of partons, which appear as the result of a certain conceptually motivated cognitive activity involving, among other things, certain concepts of homology (see Section 6.6).

For a general understanding of how this puzzle can be solved, the following formalisms are of use.

To begin with, let us define a character as a variable, with character states (modalities) as variable values arranged by a certain order relation [Sokal and Sneath 1963; Colless 1967, 1985; Estabrook 1971]. This variable serves as a means to compare organisms; in this comparison, the order relation established for the variable is reflected in a set of organisms and establishes a similar order relation between them according to the variable values (character modalities) attributed to them. Based on this order relation between organisms, they can be grouped into taxa.

Let us assume that taxa and characters recognized in respective classifications are related to each other by taxon-character correspondence [Pavlinov 2018]. The latter’s meaning can be thought of as a reflection of a set of taxa on a set of characters, and vice versa. Accordingly, this correspondence establishes a kind of logical sequence of judgments about taxa and characters, which participates in the shaping of the classification algorithm. Taxon-character correspondence is always fulfilled: thanks to this, we can in practice define any taxon by certain characters comprising its specific diagnosis; however, this correspondence can be strict or non-strict.

Strict taxon-character correspondence yields the monothetic taxon definition expressed by the formula “one taxon—one character.” It means that each taxon in classification can be exhaustively delineated by a single character or a single set of completely congruent characters. In such an ideal situation, all subsets of characters would provide completely overlapping classifications of taxa, formalized by the principle of character interchangeability [Meyen 1978]. In systematics dealing with natural aggregates and their features, this formula is never fulfilled because of the incongruence of the characters. This means non-strict taxon-character correspondence yielding the polythetic taxon definition. Accordingly, (a) certain elements (modalities) of any one character can be attributed to different taxa; (b) in any one taxon there is always at least one member that does not possess elements of at least one character in the taxon’s diagnosis; and therefore (c) any taxon in a classification can be comprehensively specified by a combination of several characters only [Sokal and Sneath 1963].

The principle of taxon-character correspondence presumes the possibility of relating taxa and characters by a kind of precedence, according to which their logical and procedural relations can be represented as either “taxon-► character” or “character->taxon.” Based on this, the following stepwise classification algorithm of taxonomic research can be construed. The latter begins with a selection of particular sets of organisms and their characters based on certain previous results. At the next step, an analysis of the data may be conducted in two ways depending on a particular taxon-character precedence. In one case, it may start with a more detailed partonomic ordering, which results in the recognition of characters used to identify the respective taxa intensionally. In another case, it may start with an extensional delineation of taxa, to which particular characters are then attributed. Thus, in the first case, character recognition precedes taxa recognition, while in the second case the precedence is the opposite. The first option is most consistently implemented by scholastic genus-species scheme, by typology, and by biomorphics: most significant characters are first identified following certain criteria, and then taxa are recognized on their basis. The second option in its “pure form” may occur, when certain new (e.g., molecular) characters are selected to see what might be the outcome of employing them for the classification of organisms. Some of its elements are implemented by numerical taxonomy: taxa are first distinguished based on an analysis of the entire set of characters employed, and then particular diagnostic characters are attributed to each particular taxon.

A rigid dichotomy of these two schemes with opposite “precedences” represents the general classification procedure in a simplified and scarcely realistic form. In fact, practical systematic research is organized more complexly, in such a way that the precedences “taxon-xharacter” and “character->taxon” alternate within a single sequential iterative procedure [Meyen 1984; Lyubarsky 1996; Pavlinov and Lyubarsky 2011; Pavlinov 2018]. In this algorithm, taxon-character correspondence is manifested dynamically as an interleaving of opposite “precedences” at different iteration steps. Suppose a certain group of organisms is first selected for which both taxonomic and partonomic order relations are preliminary, given by preceding research. As a result of its taxonomic analysis, particular characters are specified, on the basis of which taxonomic classification is carried out, with taxa being more precisely outlined and diagnosed. In the context of this taxonomic classification, the characters are studied in more detail, with their homology, weight, etc. being specified and changed by necessity. Then, based on specified characters, taxonomic analysis is again carried out, with parameters of taxa (composition, ranks, etc.) being specified in their turn, etc. As a result, in particular taxonomic research with a sufficient number of characters and taxa included, taxon-character correspondence, being less strict at its beginning, can be expected to become stricter at its end due to the action of the principle of convergence.

An idea of the successive iterative procedure of taxonomic research solves the puzzle in question in a rather general form. It “breaks” a closed logical circle of reasoning by replacing it with a sequence of internested hermeneutic circles. The latter means that, at each iteration step, a particular classification task does not “mirror” a previous one but rather is specified and solved in a less fuzzy context than the previous one.

Because of the non-strict nature of the taxon-character correspondence, employing different sets of weakly correlated characters yields unavoidably different classifications with various degrees of naturalness. Since the characters constitute the only basis for any classifications elaborated by a comparative method, the question of “naturalness” of both classifications and methods yielding them is thus largely a question of the choice of “natural” characters. This fact was recognized at the very beginning of rational classification activity, and it is formalized by the fundamental principle of character inequality. The choice of due characters for elaborating due classifications is routinely termed character weighting, so the principle just mentioned is specified as the principle of differential character weighting. It presumes the elaboration and application of a certain weighting function, by which specific weights

are ascribed to characters; they are directly proportional to the contribution of the characters to the resulting classification. This function is operationalized by a set of weighing criteria which allows characters to be arranged according to a certain weighting scale by ascribing them particular weights.

Therefore, character weighting is a very important part of any version of the natural method: without much exaggeration, one may say that the latter is designed largely to interpret properly the general weighting function to make its particular interpretation most adequate to a particular understanding of what the natural classification should be. Its “adequacy” is provided in that it is developed by the PTT as part of its methodology based on its onto-epistemic premises, so the character weighting is theorydependent. The latter means that there cannot be a single universal weighting function with the respective universal weighting scale: what is considered important for the character weighting in one PTT will not necessarily be so in the others. Thus, in typological systematics, characters should characterize archetypes, body plans, or ontogenetic patterns; in phylogenetic theory, they should indicate kinship relations; and in biomorphics they are selected so as to characterize biomorphs (life forms); and so on.

It follows from the above that, in order to elaborate natural classification with naturally defined taxa according to a certain system of criteria of naturalness, characters should be weighted “naturally” according to the respective weighting criteria. Therefore, proper application of the weighting function constitutes an important part of the above iterative classification algorithm, and its “partonomic step” includes proper character weighting. For instance, an iterative procedure is implemented in numerical phyletics by the method of successive character weighting [Farris 1969] and by Bayesian inference [Chen et al. 2014]. Thus, the development of the weighting function with respective weighting scales and criteria and its implementation in classification algorithms is a prerequisite for solving the taxon-character puzzle at an operational level.

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