*3.6. Dialectical Logic*

The paraconsistent logician Graham Priest [43] has pointed out that Hegel distinguished between dialectics and formal logic—which was for him the Aristotelian logic of his day. The law of non-contradiction holds in formal logic, but it is applicable without modification only in the limited domain of the static and changeless. In what is generally understood as a dialectical logic, which LIR superficially resembles, the law of non-contradiction fails. Subsequent developments of formal logic, starting with Frege and Russell, have forced Hegel's conception of contradiction to be rejected or interpreted non-literally. Neo-Hegelians have attempted to conserve *this* principle of contradiction by emphasizing the factor of time: A is not identical to A, because time has passed in which changes have occurred; contradictions take place one after the other, etc. Articles purporting to describe dialectical logics still appear. In one example, a relation is proposed with non-linear dynamics in which dialectical logic is enhanced by mathematical logic. Nevertheless, the question is not addressed, here and in Hegel, of what drives the change from thesis to antithesis to synthesis, that is, how any term cannot 'stand on its own' but 'goes over' into its opposite or contradiction. Russell demonstrated, before Lupasco, that Hegel's logic could be deconstructed because it still presupposed traditional Aristotelian logic, but not for this more important reason, namely, the absence of a grounding in physical reality.

Piaget, also, did not go beyond the standard Hegelian form of Marxist dialectical materialism. This correctly accords a central role to conflict and contradiction in the transformation of social realities. However as pointed out by Priest [44], and further discussed by Igamberdiev [10] and in this paper, Marxist dialectics fail to give an adequate account of the true contradictions involved in society: an inconsistent or paraconsistent logic is necessary for such an account, albeit in our view not sufficient. A logic of the LIR form seems required to characterize the emergence of new structures from real contradictions.

In the LIR view, cybernetic systems, natural or artificial, *are* dialectical, since each one involves an alteration, a perturbation by an antithetical contradictory process, followed by the return to the (state of) regulation required for the system to be "stable". In other words, a cybernetics alternately actualizes certain phenomena and potentializes the antagonistic, contradictory phenomena in consequence. It is an "oriented dialectical systematization of energetic events, inherent in the nature of energy" [45].

As will be discussed in more detail elsewhere, Logic in Reality differs from standard forms of thought in showing the importance of implication as a process in contrast to reliance on equations. The astrophysicist Stephen Hawking, for whom we have the greatest respect, once asked: "What if the universe and human beings were governed by the same equation?" We ask a somewhat different question: "What if the universe and human beings were governed by the same thing, but it is not an equation?" It is not an *inequality*, which to us a just an equation that does not admit it. It is something like an *inference*, but inferences are associated too strongly with language and its limitations. We have therefore pleaded in this paper for attention to be paid to the strength of *implication* in describing what governs the world. David Bohm [46] had a similar intuition in his proposal of an implicate as well as an explicate order in the universe.

#### *3.7. Dialectics and Logic in Reality in Marx and Engels contra Hegel*

With the basic concepts of Logic in Reality in hand, including its dialectical base, let us how it can be related to some dialectical aspects of the economic theories developed by Marx and Engels, as well as their roots in Hegel. The objectives of this paper do not include in-depth study of dialectics in economical and political theory and practice. In this Section, we simply look at some aspects of this field which can be usefully addressed by combining dialectics, as described in Section 2, with the perspective of Logic in Reality outlined here.

Engels saw dialectics as a fundamental method for gaining knowledge of nature, and as a thought process of involving a real opposition of ontological as well epistemological contraries, similar in appearance to that of Logic in Reality. Arthur [47] points to what we can see are critical weaknesses in Engels' dialectics. One was a tendency to rely on a compilation and classification of examples and another was the presentation of a triadic paradigm as the 'three laws' of dialectics', without a basis in science. To anticipate, we find exactly the same structural weaknesses in the epistemological triads of Charles Sanders Peirce that are considered the foundations of standard semiotics (next Section 4).

The point of departure for knowledge for Engels was the "qualitative aspect of things and phenomena and not their quantitative side". As Brenner has discussed elsewhere [1], for Engels "Dialectics is the science of universal interconnection, of which the main laws are the transformation of quality and quantity—mutual penetration of polar opposites and transformation into each other when carried to extremes—developments through contradiction or negation of negation—spiral form of development." Logic in Reality is a way of giving a physical picture of the transformation of the polar opposites operating in complex systems: it is never complete, and the extremes of 0 and 1 are never reached except in trivial cases. Contradiction or better countervalence inheres in physical processes, and negation of negation remains at the level of linguistic logic. The concept of spiral form of development is an absolutely essential one which Brenner described in detail as a consequence of Deacon's concepts, grounded in developmental biology, of "incomplete nature" [48] (cf. Section 5.1 below).

We look next at the discussion by Arthur [46] of the 'new dialectic'. For example, it is statements like those of Marx that correspond to our view of the ontological priority of real phenomena—the "logic of the body" rather than a "body for the logic", as echoed by the contemporary work of Lakoff [49]. 'Our' dialectics is systematic (with an internal dynamics) rather than historical (demonstrating temporal dynamics). However, it goes beyond the systematic dialectics of Marx in its necessary inclusion of insights from 20th Century physics. We can thus easily dismiss empty concepts in Hegel such the realm of logic being 'timeless'; only standard binary linguistic logics, including that of Hegel, are 'timeless'. Arthur further suggests that Engels applied what was basically a linear logic as he, as the majority of other thinkers, did not have room for the recursive aspects of real processes in the 'sinusoidal' movement from actuality to potentiality and vice versa. Marx's apodictic statements about the 'means of production employing workers' rather than the reverse need not be taken as dialectical contradictions in the LIR sense; the two opposites are in different linguistic domains, turning on two senses of 'employ'.

Logic in Reality thus provides a new, more physically acceptable view of neo-classical concepts in dialectics, for example that a logical progression is at the same time a retrogression. Instead of reading this as a succession of abstract categories, we consider it a description of the dialectical evolution of real processes, for which the simplest model would be graph with two mutually dependent time axes, and which, to quote Arthur, "has nothing in common with a vulgar evolutionism predicated on extrapolating an existent tendency", we add, unidirectional.

A feature of *Das Kapital* [50] is its exposition of the "reciprocal conditions inherent in a whole and not a quasi-historical (linear) development from primitive conditions to advanced ones". Logic in Reality establishes the applicable reciprocity in reality that gives this insight its scientific value. Where we disagree with the dialectical and logical formulations of Marx and Engels is in their essential use of standard categories as constitutive of a systematic dialectic and in their treatment of contradictories. Engels' famous 'three laws of dialectic', referred to earlier, such as the negation of the negation, are restatements of the laws of linguistic Aristotelian logic. The concept of the properties of capitalism as

emergen<sup>t</sup> from such laws is an epistemological one, and bourgeoisie and revolutionary proletariat are terms that lack sociological reality.

In LIR, these are not to be resolved in an eliminative sense, as it is from them that new concepts can emerge without requiring their total disappearance. However, Arthur suggests that one may "draw upon" Hegel's categories to show that anything and everything can become a bearer of value. Our position is no more or less than that anything and everything—that exists—is a bearer of value since it is a bearer of meaning. We discuss further aspects of meaning in Section 5.

It is however, exactly these 'classical' aspects of Hegel's logic that make it relevant to the ontological foundation of the capitalist system. As is becoming more and more obvious, the 'inhuman' aspects of the emergen<sup>t</sup> contradictions in capitalism—the *absolute* dialectic of capital and its quasi-logical primitives (Arthur), are exactly where classical logic gives a reduced, binary picture of the world. It using the principles of LIR that we can accept, by giving a physical dialectical meaning to it, the statement that the separation of "quantity and quality from each other is not absolute".

We will not analyze in detail Hegel's views of Being and Nothing (to which we prefer the 'Nothingness' of Sartre). Heidegger's ontological *Dasein*, while not describing a su fficiently 'full' presence, approaches more closely the physics of LIR. Regarding Hegel's discussion of correlative pairs in thinking, the question cannot be of actualizing an 'inner unity' which does not exist.

Hegel's idealism and absolutism led him to make a further error in respect to necessity and contingency by leaving no place in his Essence-Logic for the latter, while ascribing 'Actuality' to the former [41]. "The sole aim of philosophical inquiry is to eliminate the contingent". What is false here, exactly as in the tychism of Peirce that sees chance as most fundamental, is the absolutism. It is the dialectic between chance and necessity, or determinism and indeterminism that is essential and it is Lupasco who deserves the credit for placing this dialectic on a basis in science.

There are serious limitations in Arthur's analysis of value and form, let alone dynamics and process, by his emphasis on linguistic concepts. In looking for the relation between form and content he mentions as an interesting case the "logical form of a proposition being independent of the variables in it. We speak here then of two sides indi fferently united". We are far here indeed from the real world in which even propositions are not topic-neutral. We thus agree with Arthur that capital has a "certain conceptuality to it" in which a peculiar interpenetration of ideality and materiality is expressed as a contradiction between value and use value. That this leads to a "concrete mediatedness without ever reaching a final resolution" is far from concrete, however.

The Logic of the Concept defined by Hegel shows his struggle with the relations between individual and universal, continuity and identity. Marx used Hegel's terminology for his logic of capital: capital is a universal distinct from its moments (instantiations) while being at the same time continuous and identical with these moments. We will not attempt to discuss the historical validity of Marx's concept but only sugges<sup>t</sup> that the dichotomies only make some sense when considered as partial and interactive in the LIR sense.

Marx's *critical* systematic dialectic is also closer to LIR than Hegel's *a*ffi*rmative* systematic dialectic in that the contradictions inherent in capital are not eliminated or sublated but deepened or developed as it evolves. In the same Compendium, Carrera [51] cites Marx's aphorism that "philosophers (such as Hegel) have only interpreted the world in various ways; the point is to change it". Here Marx is being too classical: serious interpretations can also 'change the world', given a favorable terrain.

Both Hegel and Marx and their commentators su ffered from reliance on epistemological readings of dialectics. Bellofiore [52] mentions the "inner connections of objects and concepts"; "capital as an invisible subject in a kind of perennial movement in a circle", moving<sup>6</sup> (?) from simple and abstract categories to more complex and concrete notions", with 'redefinition' of the categories." The problem in our terms is that both authors defined a category as a principle unifying di fferent particulars, reconciling

<sup>6</sup> The term 'moving' here raises many questions which it would be otiose to follow.

the universal and individuals by the principle of the complex unity of identity in di fference. This fails (in LIR) by the impossibility of *complete* unity, when it incorporates the moment of di fference. Stating that this demonstrates a *negation of the negation* has no meaning in an ontological sense. Although we thus have problems with the stages of Bellofiore's argument, we can agree with his conclusion, namely that we are dealing with two antagonistic ontologies, and a proper reading of *Capital* implies that Hegelian circular views about capitalism are false in practice.

In contrast to the heavily ideologically loaded and hence largely incorrect tenets of the economics of Hegel and Marx, the work of the Japanese economist Kôzô Uno [53] and his colleague and translator Thomas Sekine [54] illustrate the kinds of balanced, non-dogmatic positions that are possible in approach similar to ours. Uno argued that capitalism, throughout the 20th Century, must be studied at three distinct<sup>7</sup> levels of abstraction: (1) pure theory in the form of Hegelian dialectics; (2) concrete capitalist history, "which must be recounted with full empirical detail; and (3) at a mid-range level between the two, focused on capitalism's developmental stages". Obviously, it is this mid-range level that is most adequate for the understanding of complex real processes such as capitalism.

In his Appendix 2 to [54], Sekine characterizes the "true teaching of Uno's economics, which lies in his grasp of capitalism as something that exceeds the confines of formal (i.e., tautological logic)". Uno assigns proper ontological value to a capitalism whose nature cannot be concealed, and it thus can be seen to follow a logic that is independent of any ideology, Marxist or bourgeois supported by mathematical myths. A rational dialogue about the problems generated for both the society and the environment becomes possible.

Our approach remains beyond the criticism of dialectics because the dialectical concept in the form of a Lupascian synthesis avoids final truths that were claimed by Hegel, Marx and which, in their application to social reconstruction, resulted in totalitarian societies. In fact, Engels in his later years was ready to support the idea that social progress can be achieved by peaceful means, which include incremental legislative reforms in democratic societies as was further developed by his disciple Eduard Bernstein. The dialectical approach developed here is in concordance with the humanistic trend that can be dated back to a 1795 essay by Immanuel Kant "Perpetual Peace: A Philosophical Sketch". The main statement of Kant, which is truly dialectical, is that permanent peace is a goal which mankind can approach gradually in the course of its improvement. A conscious ethics commits us to act such that perpetual peace can be reached; this represents an example of the categorical imperative. With our new formulations of both dialectics and logic in hand, we now turn to their applications to aspects of meaning and its instantiation in the areas of semiotics, information and communication.

#### **4. Semiotics and Semiosis: The Dialectics of Meaning**

The views of dialectics and logic that we have developed can be used as tools to reconceptualize the areas of semiotics and semiosis. The key concept in semiotics has been the introduction of an ontological and epistemological role for the sign. Signs are elements or units of language that are assumed to convey meaning to living beings capable of receiving and interpreting them, that is, of evaluating their relevance to the on-going processes of survival and growth, physical and intellectual. Two names in the thought of the last 150 years are associated with semiotics as a discipline, Charles Sanders Peirce and Ferdinand de Saussure. The problem with these authors and their countless followers is that their theories are non- or anti-dialectic. Simply, contradiction is given a purely negative interpretation.

As soon as living beings appear in the universe, meaning appears as process aspects essential to their survival and reproduction. With the arrival of self-awareness of existence, say, at the level of human beings and cats, semiosis describes the active, ontological process of the *discovery* of meaning in

<sup>7</sup> As usual in our critique, calling appealing to some abstract concept of distinctness adds nothing to the argument. It is neither necessary nor desirable to make absolute separations between dialectical theory and the necessarily historical developmental stages of a social phenomenon.

and as existence-as-process. It is creative, participatory and relational; semiosis carries an emotional stance or feeling toward existence and the self as part of that existence, which includes the capacity for its perception. It is a phenomenon within the scope of natural philosophy, with its own dynamic 'logic' of processes.
