*2.1. Dialectics in Ancient Greece*

A discourse between several people providing reasoned arguments about the reality common to all of them follows from the multiplicity of the world containing interacting observers. From the logical point of Parmenides that Being is undivided and unmoved, a position which was claimed to be substantiated by the Zeno paradoxes, a search for the explanation of movement in the perceived world led to (1) substantiation of the smallest existing spatio-temporal "quanta" of movement called "atoms", referring to physical reality and (2) the formulation of cognitive pure ideal forms called *eidoi*. This separation into physical and cognitive reality came from the necessity of attributing the property of existence to Being, basically something accessible only to conscious (human) beings. This attribution is analyzed in detail in Plato's dialogue "Parmenides", which is considered as the most outstanding example of antique dialectics and in which Plato, to analyse the notion of existing Being, abandons narrowly interpreted principles of his philosophy of ideas for the goal of explaining the phenomenon of existence. The thesis substantiated in "Parmenides" is formulated in the following way: "The existing One appears as Many". Thus the existing world is present as a multiplicity that corresponds to the principle of multiplicity of primary elements called "seeds" in the philosophy of Anaxagoras. These were later defined by Aristotle as "*homoeomeria*". They include both potential and actual constituents and are harmonized in the *omnium* of their relations by the principle called "*Nous*" by Anaxagoras. A similar philosophical concept was formulated in modern times by Leibniz, who called these elements "monads". Below, we will discuss monad in relation to our definition of an "ontolon" as the element of real existence. The definition of the principle uniting *homoeomeria* as "*Nous*" assumes that a non-physical 'discourse' reasoning between them takes place that results in their harmonization in the Universe. Such harmonization can be either based on the ideal pre-established principles defined by Leibniz as a "pre-established harmony", seen in antiquity in the concept of the Demiurges of Plato's dialogue "Timaeus", or it can be achieved through a kind of a principle of natural selection that was formulated explicitly in the poem "*De rerum natura*" of the Roman poet Lucretius, who followed the atomistic philosophy of Epicurus.

The philosophy of atomism of Leucippus and Democritus initially appeared as a response to Parmenides and Zeno as an attempt to introduce movement in the world. At first glance, it avoided dialectics by claiming atoms as real existing elements, between which was emptiness (the vacuum). In the early versions of atomism, atoms were not considered as ideal essences that could be involved in a kind of discourse, although there is some evidence that Democritus sometimes called atoms "ideas". The strict determinism of the Democritean universe does not leave room for the possibility of a 'discourse'. Later, Epicurus postulated an unpredictable movement (swerve; swerving) of atoms

called by Lucretius "*clinamen*" which introduces potentiality in the universe of atoms and makes it more diverse and variable. These deviations initially appear arbitrary, but they can be controlled resulting in higher levels of organization. In this picture, finally, human consciousness appears which controls them further. The atoms of Epicurus can be viewed as quanta in the process of actualization and the actualized Being is Multiplicity due to the *clinamen*. Without *clinamina* that enlarge the field of potentialities, a strictly deterministic universe would not be able to evolve and generate a multiplicity of events, phenomena and realizations. However, the principle defined by the term *clinamen* cannot be well developed without the more advanced concept of potentiality and actuality introduced in Greek philosophy, by Aristotle despite the fact that Epicurus lived after Aristotle. Aristotle developed his concept of potentiality without reference to atomism, and Epicurus was not influenced by Aristotle's understanding of potentiality.

The most important point here is that atoms possessing *clinamina* escape from the strict determinism of the Democritean world. They can enter into a process that reduces the field of potentialities defined by their *clinamen* and form a kind of discourse or 'communication'. This discourse is not strictly physical as it escapes physical determinism being based on the consistency during interaction. The result of such interaction is a *consistent history* that is produced in it1. The complexification of interaction is associated with generation of predictability of the movement defined as *clinamen* and the possibility of its control. This corresponds to the development of cognition in systems of interaction of atoms possessing *clinamina*.

By the introduction of *clinamina* as the properties of atoms, it becomes apparent that the atoms interact not only via application of deterministic forces but also via the influence of the potential fields of their possible unpredictable deviations, recursively modifying their capacity for such unpredictable movement. Moreover, if atoms unite in organized structures, these capacities become restricted to a certain extent. The interaction via the e ffects of *clinamina* on each other can be described as a mutual measurement process, and when atoms become united into organized structures this measurement appears as an internal measurement within the structure. This kind of measurement can lead to further complexification of the system via reduction of the potential field and self-referential 'memorization' of such reduction.

The significance of Aristotle in understanding such a discourse involving potential reality makes him the greatest figure in dialectics. The common opinion is that Aristotle mainly developed formal logic which is the content of his Categories (part of his *Organon*), but he also introduced a kind of logic in reality (see below the logic of/in reality of Lupasco and Brenner). This includes the transition from the potential to the actual, although the opposite transition is not analysed in detail. The grea<sup>t</sup> achievement of Aristotle is the inclusion of *potentia* in his second logic (dialectics). This is seen in his *Metaphysics* and in more detail in *De Anima* (On the Soul). Heredity can be understood in Aristotelian terms as the transfer of information, defined as "entelechy as knowledge" in a seed as compared to the realized "entelechy as the actual exercise of knowledge" of the developed organism (cf. G. Stent's *Molecular Genetics* [11]. Matter in Aristotle's conception is a pure potentiality which is a prerequisite of two types of actuality: one is information ("entelechy as possession of knowledge") and the other is actual realization/presence ("entelechy as the actual exercise of knowledge"): "Now the word actuality has two senses corresponding respectively to the possession of knowledge and the actual exercise of knowledge" [12]. In the latter ("actual exercise"), a selection from two or more possible realizations takes place according to the first type ("possession of knowledge"), and the discourse becomes incorporated in the total reality instead of being a result of interaction of reasoned arguments of conscious subjects. Being in the philosophy of Aristotle includes the unity of potential reality and its realizations, a concept which was developed by him in detail but which had arisen in the concept of

<sup>1</sup> Attempts have been made to make a 'consistent histories' approach to quantum phenomena. We consider these as tautological and ultimately reductionist. As we will see in Section 3, our approach assigns ontological value to *inconsistency.*

the primary substance as *apeiron* outlined more than two centuries earlier by Anaximander. According to Carlo Rovelli [13], Anaximander was the founder of scientific thought in human civilization.

Another important aspect is the understanding of a soul as a *capacity*, inseparable from the body, which we later find in the concept of substance in the philosophy of Spinoza. According to Aristotle, " ... the soul neither exists without a body nor is a body of some sort. For it is not a body, but it belongs to a body, and for this reason is present in a body, and in a body of such-and-such a sort" [12]. On the other hand, di fferent bodies can be animated by the same set of capacities, by the same kind of soul, so soul can be used in a singular, not plural, sense. This was earlier substantiated in Plato's dialogue "Parmenides" formally, while Aristotle presents this as a foundation of a kind of natural science which was later defined as psychology. The discourse of di fferent potential realizations becomes incorporated into the reality that evolves from the inanimate potential matter to the actual realization, bearing form and being capable of an information transfer through the discourse of the substance with itself and in which it appears as a multiplicity of "seeds" sharing the same "soul".

## *2.2. Dialectics in Modern Times*

In modern times, the logic of discourse was incorporated into philosophical thought following the main feature of the new European philosophy that was formulated by Rene Descartes as the distinction between a *res cogitans* and a *res extensa*. Being initially represented as two separate essences, they were unified in di fferent philosophical systems in di fferent ways, and dialectics appeared as the discourse for establishment of such unification. Thus, we can see the development of dialectical principles in the systems of Spinoza, Leibniz and Kant. After Kant, dialectics became associated with Hegelian idealism on the one side and Marxian materialism on the other. In this Section, we will discuss these advances in modern times, their limitations and possible future developments.

Another important aspect here is that if substance is a *causa sui*, it cannot be fully cognizable, since only mechanisms can be fully cognizable in the framework of mechanics. That is why Spinoza ascribed to substance an infinite number of attributes, among which only cognition and spatio-temporality are perceivable by us. In relational terms, only these two attributes can be involved in relations, while other attributes cannot be cognized although they can be involved in some sense in the shaping of the *res potentia*. The statement of the infinite number of attributes by Spinoza has similar meaning to the statement of Leibniz that "monads have no windows" (there is no window through which to see these attributes) and to the statement of Kant about the non-cognizability of the *Ding-an-sich*. The latter also appears as a monad and should not be mixed with the physical object, as it cannot be reduced to its spatio-temporal structure or to its ideal form. Later in this paper, we will call this primary unit "ontolon". The "non-cognizable" attributes shape the potential of monad/Ding-an-sich/ontolon. These attributes correspond to the Epicurean *clinamen* which, as noted above, is beyond shape and form.

The grea<sup>t</sup> progress in philosophical thought made by Immanuel Kant, which he called the Copernican revolution in philosophy, was the revelation [14] that mind is not the basis of Being but only the instrument of human cognition. Real Being is beyond mind and can be defined as a *Ding-an-sich* (thing-in-itself). The later development of German philosophy (Fichte, Schelling and Hegel) abandoned this basic statement and returned to a Mind in its totality that generates the material world as an *Anderssein (Andersheit)* in its dialectical discourse. On the contrary, Arthur Schopenhauer associated the *Ding-an-sich* with the primary energy called *Wille* (will) whose permanent goal is actualization *via* generation of representation (*Vorstellung*). Another trend, which overturned Hegelian idealism, resulted in Marxism in which dialectical discourse is located in an inanimate reality called matter. However, Marxism did not develop the concept of substance in the sense of Spinoza or other earlier philosophers. Dialectical discourse appeared, in particular, in Engels' interpretation, as a vaguely formulated set of "laws of dialectics", which emerge without proper substantiation.

Friedrich Engels, in his unfinished work *Dialectics of Nature*, formulated "three laws of dialectics" [15]. He elucidated these laws as the immanent properties of dynamics of material substance, although his concept is, however, not elaborated well as compared, e.g., to Spinoza. These "laws" are

the following: (1) the law of the unity and conflict of opposites (which arises in Heraclitus); (2) the law of the passage of quantitative changes into qualitative changes (generally based on the ancient paradox of the heap), and (3) the law of the negation of the negation (which may be considered as the invention of Hegel). In fact, in comparison to Hegel's philosophy where dialectics appears as an internal discourse of the Absolute Idea, in Engels interpretation dialectics is positioned far away from any discourse and represents a set of vaguely and rather reductively defined formal laws. This became the basis of "dialectical materialism".

To realize discourse, an element of the world should represent a monad that performs some kind of internal 'computation', which in the more materialistic view can be defined as an "ontolon" (see below the discussion on ontolons in Section 6). In this sense it is more logical to discuss "dialectical organicism"<sup>2</sup> as suggested by Joseph Needham [16] than "dialectical materialism". In the organicism interpretation, the dialectical discourse of simple monads, ontolons in our terms, generates the complex structure of space-time, and, as in Spinoza's philosophy, this discourse rises to the *causa sui* principle. The formulation of "dialectical materialism" without clear definition of the concept of substance as matter that would justify the *deductive necessity* of the "laws of dialectics" resulted in the di fficulties of development of this concept by the next generations of philosophers. We will show later that the concept of an ontolon can resolve the di fficulties in the ontological interpretation of dialectics in nature.

We will turn now to the "post-Marxist" philosophers Merab Mamardashvili [17] and Evald Ilyenkov [18] who performed the most important re-evaluation and development of the Marxian dialectical concept of consciousness. Since the developed concept of substance is lacking in Marx' theory, Merab Mamardashvili refers to Descartes and Kant in its description, while Ilyenkov is grounded mostly in Spinoza. Both Mamardashvili and Ilyenkov refer rather to the logic of *Das Kapital* of Marx than to the *Dialectics of Nature* of Engels. To what extent the newly formulated principles really arise in Marx or are the result of the major reformulation performed by Mamardashvili and Ilyenkov is not so important, but in our view their interpretation goes far beyond the basic formulation of Marx. We will outline first the approach to dialectics as it was formulated by Mamardashvili and then turn to Ilyenkov.

According to Mamardashvili (1930–1990), who significantly contributed to the rationalist theory of perception whose origin was in Descartes and Kant [17], the relation of subjective signifying consciousness to objective reality (the set of signified material bodies) is mediated by the potential set of the whole system of, in particular social and political relations organized hierarchically. This means that Marx, according to Mamardashvili, discovered the phenomenological nature of consciousness via its quasi-objective nature by introducing an abstraction that allows the analysis consciousness as the objective transformation of external objects into quasi-objective patterns, without direct involvement of the processes taking place in internal subjective reality. This means that the nature of consciousness is placed beyond the phenomena that serve for the maintenance of the social system of communication. "Being–consciousness" becomes unified, so that Being and consciousness appear as the di fferent aspects of one continuum in which the object and the subject, the reality and its representation, the real and the imaginary are not strictly separated, while remaining relatively di fferentiated and non-identical to one another. They are connected in the continuum via the relational operator of transformation realized in the course of social dynamics. This is represented as the "dialectical" nature of consciousness in which the discourse between conscious subjects, mediated by the incorporation of the actualized material reality into this discourse, generates the conditions for social dynamics and progressive social evolution. The actualized material reality appears primarily as the result of previous human activity that has formed the signified social memory that represents the basis on which the current social structure is built. This "basis" is not only material but also cultural, and it shapes social structure by providing

<sup>2</sup> The application of the principles of Logic in Reality allows one to cut through the endless discussion of organicism *vs.* realism *vs.* holism *vs.* reductionism. Complex dynamic part-whole relationships are possible, as in the first concept, without the system being 'alive', but which are not reducible to their energetic substrates.

already existing forms or models. In other words, it "geometrizes" the society in the same way as Spinoza's substance geometrizes the world in the course of its self-actualization.

#### *2.3. Dialectics in Ilyenkov's Conception and Beyond*

The concept of dialectics as a metalogic based on reasoning and discourse was developed by Evald Ilyenkov (1924–1979), who incorporated its principles into basic substance understood in the sense of Spinoza and having the basic property of a *causa sui*. Despite his close association with Marxist dialectic materialism and apparent rethinking of Hegelian idealism, Ilyenkov su ffered from the attacks of both orthodox Marxists and anti-Marxists, which resulted in his premature death. According to Ilyenkov, substance perpetually generates objective forms of subjective activity which follow a logic external to a material body. In this regard, the process of cognition which includes discourse and reasoning is not transcendent to the being, but immanent to it. Before Ilyenkov, such a point of view was formulated in the Marxist psychology of Lev Vygotsky and Leontiev in the 1930s, later substituted by a reflexology grounded in the works of Ivan Pavlov. The main idea on which Ilyenkov's concept of dialectics is based is the unity of cognition and space-time, of a *res cogitans* and a *res extensa*, which are linked via a *res potentia* (see below). The unity of *res cogitans* and *res extensa*, which is the central point of Spinoza's philosophy, is attributed to substance from the lowest levels of its organization and becomes highly expressed at the highest levels such as human civilization. The basic property of cognition, following Spinoza, is a capacity of a body to build a trajectory of its movement across other bodies according to a logic of arrangemen<sup>t</sup> of these bodies in the space external to that body. The idea of a thing in this regard becomes fully coincident with the way of its being, which is its generation based on this idea. In other words, the idea as *eidos* turns to be the idea as *technos* as defined by Mamardashvili [17], and these two aspects of idea (eidos/technos) are inseparable in the generating activity. As an example, a geometric shape is ideal because it represents a way of formation/generation of all material bodies possessing this shape.

The basic function of intellect, according to Spinoza and Ilyenkov, is to move and arrange external objects. Humans perceive the world only because they move and arrange external bodies in their activity. This activity is not based on the mechanic causality but on the causality which immanent to the primary substance which is *causa sui*. Mechanical causality is always external to the body, while substance possesses causality in itself realizing self-movement via establishing relation to external bodies by its abstracting capacity which generates pure (ideal) forms of reality. In this activity, the *ordo et connexio idearum* coincides with the *ordo et connexio rerum*, in other words, ideal activity results in valid practical implementations. At the level of social organization, intellect is involved in establishing relations not only to external material objects but to other intellectual beings, which becomes the basis of morality and successful social communication.

The unity of cognition and space-time needs to be incorporated not only in philosophical thought but also into the foundations of mathematics. This has been realized only recently in the concept of meta-mathematics developed by Voevodsky [19] who included geometrical foundations of mathematics in its basis. The intrinsic logic of meta-mathematics corresponds in this approach to the spatio-temporal structure that is generated internally on the basis of this logic. When geometry is introduced into the foundations of mathematics, the world becomes shaped in a particular way fitting its habitability, which resembles the anthropic principle in physics. The limits of geometry become associated with the limits of computation of the particular world, and in the theory of homotopic types developed by Voevodsky the basic foundations of mathematics can be verified computationally [19]. The grounding of Ilyenkov's dialectics in Spinoza's concept of substance represents its major advance, but it has certain limitations due to the apparent disregard of relational principles in the operation of cognitive activity. In fact, Spinoza's substance is a manifestation of the 'One', while Plato, in the dialogue "Parmenides", had already substantiated that the existing One appears as Many. In the universe of the forms of existence or "ontolons", the spatio-temporal order appears as a relation between objects established in their interaction. The intrinsic limits of computation shape the spatio-temporal order

and also pose limitations on cognitive activity. They represent the principles that are inherent to our world and may result from the transcendent action of the establishment of the actualized physical world from the pure logical principles that are insufficient for its appearance. To what extent this transcendent action is similar to our cognitive activity remains open, but in this paper we present what amounts to an 'immanent' alternative in the work of Lupasco. David Hume [20] indicated a possibility of such similarity. If the basic property of consciousness, according to Spinoza and Ilyenkov, is the establishment of space-time, then the introduction of fundamental constants at the birth of the Universe is a 'conscious' act that sets the limits of (and for) actualization of the *res extensa* from the *res potentia*. The assumption of a *res cogitans* here seems apparent, otherwise we need to introduce the principle of natural selection between universes, as in the multiverse of Smolin [21] which assumes the unsubstantiated actual pre-existence of them all. The anthropomorphic 'bootstrapping' by a basic 'intelligence' that determined the limiting conditions of the physical world is, however, beyond scientific reasoning and cannot be discussed in this paper.
