While classical logic deals with static and unchangeable things, and dialectics stresses the aspects of motion and mutability, the hierarchy of logic, to be complete, must have yet another level, retaining a kind of sameness in any change. I will conventionally refer to this level as diathetical. Obviously, such logic is well suited for discussing (and planning) development; formally, it can be associated with the idea of hierarchy (idiarchy), just like classical logic mainly corresponds to the structural view and dialectics is generally systemic. This is a synthetic way of action combining the features of classical and dialectical logic. The unity of all the three kinds of logic forms the core of hierarchical logic; however, logic in full is wider than this (essentially analytical) triad.
Hegel was the first to consider the synthesis of classical logic, and he called it "speculative logic". The name does not seem entirely appropriate. Though it clearly reflects the active character diathetical logic and its relation to human creativity, it misses the point that logic does not belong to the sphere of thought; it is predominantly manifested in practical activity. In other words, logic is not mere speculation; it is the way of making all kinds of things, the way of action.
In ancient Greek, the word diathesis (and its exact Latin equivalent, dispositio) meant intentional arrangement, or a state of being arranged for something. In particular, it was applicable to various representations or exhibitions, as well as the states of mind or moods. Like the other similar words (analysis, synthesis etc), the term "diathesis" can refer to both the process and the result.
The name of diathetical logic stresses this idea of being properly arranged for definite purpose. That is, while classical logic provides standard means to treat any kind of problem, and dialectics says that there are no universally applicable tools at all, diathetical logic admits the existence of suitable instruments for every task, but it also indicates that one task would probably require different instruments than another, and there is a problem of adequate choice. According to diathetical logic, people need to find appropriate ways of solution for each problem, individually selecting from available means (or inventing new tools, if needed). The same goal can be achieved in different ways; there is no unique path. However, every kind of work requires specific methods, and it cannot be done in an arbitrary way, applying random instruments in a random manner.
In diathetical logic we use certain logical forms and principles, but we are free to develop new logical forms and revise the mode of our reasoning and action. We are never restricted to any predefined (or prescribed) rules, as long as we observe the goal and act purposefully. That is, diathetics implies all-penetrating creativity, including its reflexive application to creativity itself. This is not mere predisposition; rather, it means the active search for the right way of positioning.
In classical logic, we found such fundamental forms as a notion, a statement (proposition) and an inference. The forms of dialectical logic are thesis, antithesis and synthesis. Both classical and dialectical forms are embraced by the primary forms of diathetical logic: categories, categorial schemes and paradigms.
To start with, one could consider a category as a very general (and virtually universally applicable) notion. However, due its universality, a category can represent any logical form at all, becoming a synonym of "a logical form in general", something to convey the idea of a certain mode of action.
To use categories, people do not necessarily need diathetical logic. Quite often, categories are taken in a particular respect, without explicitly stressing their universality—just like any hierarchy can be unfolded in a specific way. For instance, categories delimit various artistic schools; they distinguish one science from another; any philosophy is developed around a central category, thus becoming distinct from a different philosophy.
One can rarely denote a category with a single word. Outside the context, such a designation is meaningless, it has no sense. The same word can represent quite different categories in different situations, and people often dispute in vain, confusing different things of the same name. It is only in action that any abstract words can become saturated with definiteness, referring to real situations rather than mere mental constructions.
Since there is no human activity outside a social context, categories are never usable on themselves, without any reference to other categories. That is, a category becomes meaningful only in a categorial scheme representing the general conditions of the activity reflected in that category. The different hierarchical positions of the categorial scheme provide the possible connotations of the same category, revealing its multiple aspects.
Every logical scheme can be treated as a structure, a system, or a hierarchy. In any case it corresponds to certain (analytical) aspect of human activity, and cognition in particular.
Structurally, a logical scheme contains a number of logical positions (placeholders for categories) linked to each other with logical connectives. The structural aspect of a logical scheme is commonly used in definitions. Every logical position is characterized by a unique collection of properties, and any process of categorization (which is the basis of analytical thought) relates an empirically distinguished object to a position in some logical scheme. Conversely, an object can only be defined by its relations to the other objects, which is reflected in an appropriate logical scheme.
As a system, the same logical scheme may, for instance, describe a number of possible inferences. The systemic aspect of a logical scheme implies splitting it into a number of substructures, and any such substructure is considered as producing the rest of the scheme. Such an "inference" is meaningful only within a particular scheme, and the reliability of the inference depends on the current paradigm. Indeed, the same logical structure can be involved in different categorial systems, thus producing different inferences; when the differences are irrelevant to the practical needs, the categorial schemes can be considered as equivalent. But this is not the absolute equivalence of classical logic, since the differences are still retained somewhere deeper in the hierarchy. A categorial scheme (like any logical derivation at all) is to produce hypotheses, which have yet to be practically tested.
From the hierarchical viewpoint, a scheme represents the levels and directions of development. The scheme is then understood as a number of interrelated structures or interacting systems, forming higher-order integrity. The levels of the resulting hierarchical structure or hierarchical system will represent one of the possible paths of development, from simpler to the more complex schemes. In logical hierarchies, higher levels are usually considered as more general than the lower levels; that is, the hierarchical view of a categorial scheme reflects the levels of generality. However, development can proceed in different ways, which become logically related only within a definite paradigm. The same whole can be made of different constituents, and different organization can lead to the same overall behavior. However, that "sameness" is determined by something wider than a categorial scheme.
Like categorial schemes reflect the levels of generality of categories, paradigms refer to the universality of logical schemes. They distinguish a number of "fundamental" schemes, considering all the others as their specific variants, or representations. Different activities are possible within the same paradigm; also, any activity can develop into a different paradigm.
A paradigm is the basic mechanism of transferring schemes from one activity to another. It makes people prefer some schemes rather than some others, and reuse them from one activity to another.
Paradigms can also be considered as a mechanism of scheme generation. This process obeys its own logic, which does not fit into the classical or dialectical model, though, of course, any particular instance of scheme generation implies both classical and dialectical reasoning. Resembling logical inference, scheme generation does not, however, assume any predefined logic. Schemes can be empirically found, derived from other schemes, or simply suggested for some general reasons, and these three ways are intertwined in the development of logic. Scheme derivation can be integrative (constructing a new scheme from a number of other schemes) or differentiating (unfolding a scheme). Since any object and its environment are mutually reflected, logical positions and logical junctions are transmutable within the scheme, and this is yet another way of scheme production. All these possibilities co-exist within the same paradigm, which determines the overall balance of the available technologies.
Due to reflectivity and convertibility of hierarchies, there is no absolute distinction between categories, schemes and paradigms. A paradigm can sometimes be represented by a category, or expressed with a categorial scheme (a model).
Up to recently, diathetical logic has never been extensively discussed. The first explicit formulation by Hegel has also become the last. And, of course, one cannot expect any comprehensive exposition of its principal laws.
But diathetical logic is millennia old. Many people have implicitly used it in their practical work, within some special research, or as a part of a different methodology. There are numerous hints scattered in the literature. A preliminary summary of this implicit development reveals at least three ideas that could pass for the logical principles.
The principle of objectivity
Diathetical logic accepts that any reflection of a thing is dependent on that very thing. There is no activity without an object, and no thought without something to think about. People may approach the same thing differently, but all these special views will present the different aspects of the same and hence be mutually coordinated. In other words, people have to account for the objective aspects of the situation in their activity, be adequate and consistent, to achieve anything. This applies both to the definition of the object (the way of separating it out of the integrity of the world) and its treatment (the modes of operation, the associated ideas). If we do something, it necessarily reflects some aspects of the general organization of the world, regardless of the origin of this organization; natural things are as objective as products of human activity, and social processes are as objective as physical motion or life. The principle of objectivity helps to distinguish one activity from another, presenting every activity as the unity of all its structural, systemic or hierarchical aspects. This principle also demands to subordinate one's creativity to real needs, instead of wasting time and effort on something meaningless. No restriction of the human fantasy, but rather a conscious control directing it to the common advantage. Moreover, one can assert that every human fantasy, however weird, does not come from nothing; it will always reflect something in the real world, though that something shouldn't be explicitly indicated, or even emerge to awareness.
Inconsistent and purposeless behavior is not compatible with reason; it brings people down to animals. Conscious people can imitate purposelessness for some reasons (for instance, to loosen the grip of tradition and achieve new logicality); but their behavior remains objective and logical, albeit in a different way. Lack of objectivity is always destructive, and no activity can proceed outside particular culture and specific natural conditions. Understanding human behavior requires reconstruction of the basic traits of the objective situation.
The principle of reflection
Though people pick out distinct things from the integrity of the world, these things still belong to the world, being interconnected with all the other things. In logic, this leads to the possibility of describing one thing through another; exploring one area of activity, we get some understanding of many others. If somebody has mastered one kind of activity, he can cope with many similar activities, or invent, by contrast, adequate modes of action in complementary activities. Human culture forms a whole, with each part depending on each other. This allows scheme transfer between very distant areas of activity, which can produce the impression of logic as a universal basis of activity, though the situation is rather reverse, and it is the all-comprising interrelation of activities that gives birth to general logical schemes and paradigms.
Hegel spoke of reflective categories that can only be defined through each other, one implying the other. However, the realm of reflection in logic is much wider, as any category is necessarily related to any other. Any logical scheme can be applied to any activity. This does not mean that such arbitrariness will take place in real life. Developing cultures select their own sets of preferences, and scheme transfer itself obeys certain logic. However, if something seems to be illogical in one culture, it might well become quite logical in another.
Reflection in logic is related to the self-conformity of hierarchies. Every logical category, or a logical scheme, represents the whole of logic. Where at least some kind of logicality has developed, all the other kinds are implicitly present as well, and they advance to the higher levels of hierarchy in its different positions.
The principle of concreteness
In logic, the general direction of development is from empirical observations to abstract forms, and further, to a variety of their practical implementations. Nothing can be defined entirely within logic; originally, logical categories are mere representations of an intuitively felt commonality of things, together with the human ways of operating with them. It is much later, that such empirical categories become abstract ideas applicable to a wide range of activities and hence irreducible to neither of them. As soon as we arrive at that stage, one is tempted to admit the primary role of logic in human activity, and forget about its true source, the objective necessity. Logical laws seem to be constructed a priori and given us as eternal absolute forms of behavior and thought. But abstract principles are utterly inapplicable to real problems, and one has to adapt general ideas to practical needs before they can become efficient regulators of activity. Such practical interpretations manifest different sides of the same idea; however, on the lower levels of logic, they often seem contradictory and incompatible, producing much controversy and public debate.
The principle of concreteness demands that every abstraction should be complemented by a wide range of interpretations, to unfold its real power. Individual acts originally introduced in human activity in a syncretic way, following the objective logic, will necessarily become reproduced as subjective demand, a consequence of one's world vision and convictions. Being abstracted from reality, any idea must return to it as its unifying principle and the common core of superficially different acts.
In other words, to be consistent, logic must eventually grow into practical work. Until something has been changed in the real world, logical reasoning is essentially incomplete, and the truth of an abstract idea can only be demonstrated by practical action.