Basic Quasi-Axioms and Principles
The ontic part of the GTT includes quasi-axioms and presumptions describing the TR and answering the question “what?”—what exactly does systematics, in its quite general understanding, investigate? In brief, the answers to this general question define both the objects and their interrelations that systematics explores.
Quasi-axioms and presumptions differ in their conditionality [Rasnitsyn 1996, 2002; Pavlinov 2011a, 2018]. The former are accepted in an “absolute” form; their truth is not questioned and is not verified within particular taxonomic research. The latter are accepted in a softer form; their truth status is accepted not “absolutely” but probabilistically, so their estimates can vary (increase or decrease) as the result of a particular study. It is clear that either the axiomatic or presumptive status of statements about ontology depends on certain background theories. For example, in systematics as natural science, the objective existence of the diversity of organisms is taken for granted as the fundamental quasi-axiom; otherwise all explorations addressed to the TR become meaningless. In contrast, an assumption of evolution as a cause of the diversity of organisms is in general a presumption depending on particular world pictures. With this, it is a quasi-axiom in phylogenetics, while it is excluded from the ontic background in phenetics. A partonomic structuredness of the organisms is expressed by the empirically substantiated quasi-axiom, while particular judgments about the homologies of their parts are always presumptions.
From the very beginning, something like the quasi-axiom of existence is introduced in the GTT. This states that biological organisms with their properties really exist as part of Nature—more precisely, as the elements of the TR. The quasi-axioms/ presumptions of systemity and common cause assert a non-random feature of the TR structure that is caused by an action of certain causes (initial, acting, formal, etc.). According to the quasi-axiom of relations, there are some non-random affinity relations between the diversity patterns of organisms with their properties, which makes sense of representing the TR structure by certain classifications.
The quasi-axiom of aspectedness formalizes the possibility of fixing various aspects of the TR. The most basic is recognition of two fundamental “orthogonal” aspects designated as taxonomic and partonomic ones, corresponding to the diversity of organisms by their features and diversity of features (partons) over all organisms, respectively [Meyen 1977, 1978; Winstonetai. 1987;Tversky 1989; Lyubarsky 1996; Gorska 2002; Keet and Arale 2008]. The interrelations of these basic aspects are fixed by the quasi-axiom oftaxonomic-partonomic complementarity, which means that the taxonomic and partonomic “subrealities” are reflected onto each other in a certain regular way. The following, within each “subreality,” specific forms of relations of their elements (organisms and their features) are introduced as specifications of the general quasi-axiom of relations. Some of them are taxonomic (similarity, kinship, etc.), others partonomic (similarity, homology, etc.), a set of lower-level quasi-axioms specifies interconnections between different categories of relations (say, between similarity and kinship, between similarity and homology).
The most general inference rules (principles) seem to be as follows. First, the correct “translation” of statements (quasi-axioms and principles) of the GTT into those of different PTTs is provided by the principle of interpretability’. According to the principle of classifiability, the diversity of organisms and their features can be more or less adequately reflected by some classifications; it is an explication of the above-mentioned general principle of cognizability. The principle of taxon-character correspondence asserts a certain non-random interrelation between the sets of taxa and characters attributed to them; it follows from the above quasi-axiom of complementarity and ensures the possibility of recognizing non-randomly arranged and characterized classification units. The principle of taxonomic uncertainty’ fixes the impossibility of developing a single PTT and some “omnispective” classification based on it, w'hich would reflect exhaustively the TR in its entirety.
There are several important principles of more practical meaning that regulate the proper arrangement of taxonomic research. According to the principle of taxonomic unity, taxa are delineated in such a way as to reflect the certain unity (affinity) of organisms by specified features and/or relationships. The principle of criteria! uniformity asserts that classification should be elaborated based on some unified system of criteria of recognizing and ranking taxa, choice of characters, etc. It is not always possible to follow this principle for various reasons, so an alternative principle of criteria! non-uniformity is introduced to soften the requirements of uniformity. The principle of representativeness asserts that, for a classification to be adequate to a certain manifestation of the TR, the research sample must be sufficiently representative. The principle of character inequality states that, in order to obtain a sought classification, it is necessary to select (“weight”) characters according to specified criteria.
Along with these basic principles, the GTT develops some lower-order principles connecting the general ones with certain operational rules. Examples are particular specifications of the principle of criterial uniformity for particular classification tasks. Thus, considered together with the principle of ranking, it presumes that, in classification with a ranked hierarchy, the latter should be fixed based on a single ranking scale. The principle (or rule) of progression states that, within an inclusive taxon, its subtaxa of the same rank should be placed in a sequence reflecting some chosen gradient (evolutionary advancement, etc.).
The subject component of the cognitive situation is not considered in the standard axiomatic systems; however, recognition of the three-component structure of this situation obliges this. Perhaps, in order to reflect it more adequately in a quasiaxiomatics, the latter should include certain general categories regulating the very cognitive activity; an example is the axiology developed within the framework of modal logic [Miroshnikov 2010; Ivin 2016].
As follows from the above, the PTTs are such lower-order quasi-axiomatic systems, in which the main provisions (quasi-axioms, presumptions, principles, etc.) of the GTT are filled with different particular contents provided by different interpretations of the original statements. In developing the PTTs focused on ontology, general axioms of existence and relations are first specified by fixing certain aspectsof the TR (phylogenetic, typological, biomorphological, etc.). These interpretations define particular Umwelts, for which the respective aspect-based PTTs are elaborated. If the PTTs are evolutionarily interpreted, their emphases can be on adaptatogenesis or cladogenesis, and parallelisms can be emphasized or ignored. With this, particular relationships between organisms can be taken into account—only similarity or only kinship, or some combination thereof. Based on these ontic assumptions, certain rules for homologization of features, selection of characters, etc. are developed. Relational and object-based PTTs specify the provisions of the GTT for developing particular quasi-axiomatics dealing with the properties of specific relations (similarity, homology, kinship) and the structural units of the TR (species, characters, etc.). In epistemically focused PTTs, particular ways of studying the TR are substantiated: for instance, the principles of taxonomic research can be deduced from certain logical procedures or subordinated to the conditions of certain quantitative methods. Finally, a version of subject-oriented PTT may be based on the predominantly pragmatic principles implementing the above-mentioned axiological consideration.
Another way of the PTTs fragmenting is presumed by the specifics of particular groups of organisms with respect to the structure of their diversity, some basic features of their natural history, etc. An example is the multiplicity of species concepts reflecting, at least in part, the diversity of natural history of certain groups of animals, plants, prokaryotes, etc. (see Section 6.7). Another example is the so-called “horto-taxonomy” of cultivated plants [Datta 2020].