On Middles and Thirds ^†

Abstract

The purpose of this paper is to revisit the concepts of a third in logic and philosophy that have existed since antiquity, widely separated in time and space, but expressing what we consider a higher level of understanding, without going outside the boundaries of science. We claim that the logic applicable to real complex processes combines a non-standard Western “Logic in Reality” and insights from classical Indian and contemporary Japanese logics for which the former provides the necessary grounding.

1. Introduction—The Excluded Middle

The Third Axiom of Aristotle has served logic, science and common sense for over two millennia: there is no term C that is at the same time A and B, its contraries or opposites. The advent of quantum mechanics changed the picture, giving scientific weight to the concept of intermediate or included states, physically or conceptually “between” two others, partially or completely. Wave-particle duality is now an accepted principle in physics, and echoes of the principle can be found in, above all, Asian cosmogonies. Notwithstanding, the default logics in both Eastern and Western standard thought have been bivalent or binary, propositional logics of their mathematical equivalents. So-called fuzzy logics, like most others are still dependent on fulfilling binary criteria of truth and falsity. These logics thus underlie and have the limitations of a standard set and the limitations of a category theory: (1) sets and members of sets are independent of one another and (2) categories are defined as instantiating the properties of exclusivity and exhaustivity.

This paper was presented in part at the online conference of the World Logic Day of UNESCO, 14 January 2023 under the Section heading of Logic and Society. We thank the organizers of the WLD for permission to reproduce this material.

2. Contents of Paper

The two key topics of this talk and their major sources are the following:

• The Logic of the Included Middle: the Franco-Romanian Stéphane Lupasco (1900–1988) [1]; The Logic of Energy, 1951.
• The Law of the Middle: the South Indian Nagarjuna, ca. 300 C.E. [2]; the Japanese Yamauchi Tokuryu (1890–1982): Logos et Lemme, 2020 [3].

Since 1998, Brenner has worked with the theoretical physicist Basarab Nicolescu, a friend and continuator of Lupasco in the field of Transdisciplinarity. Lupasco and Nicolescu and others founded the International Center for Transdisciplinary Studies in Paris in 1984 [4,5]. His update and extension of Lupasco’s work is designated as “Logic in Reality” (LIR) [1], and we start with some general comments and an overview of LIR since it will be the least familiar.

3. Logic in Reality (LIR)

3.1. The Fundamental Principle of Dynamic Opposition

The major components of LIR are its fundamental principle of dynamic opposition (PDO) and its axioms based on it. The principle states that complex phenomena continually but non-cyclically (that is, without perfect circularity—returning to their starting point) move between states of primarily actualization to primarily potentialization of themselves and their opposites or “contradictions”, and vice versa alternately and reciprocally, without going to the ideal limits of 0 and 1. The principle of dynamic opposition (PDO) implies a real physical as well as cognitive linguistic antagonism, including of two theories or ideas. The PDO is a principle of change and movement [1].

The first key axiom—time does not permit listing them all—is that of Functional Association: every real logical element e—objects, processes, events—always exists in association, structurally and functionally, with its anti-element or contradiction, non-e; in physics terms, they are conjugate variables. This axiom applies to the classical pairs of dualities, e.g., identity and diversity, presence and absence referring to real changes, in movement as described by the fundamental postulate. The second key axiom is Asymptoticity: no process of actualization or potentialization of any complex element goes to 100% completeness. This is a restatement of the fundamental postulate, including the essential concept that no real process goes to the idealized, abstract limits of classical logic of 0 or 1.

In LIR, the key logical operator is implication. In standard logic, implication is a linguistic, binary operator resulting in logical consequence. In LIR, it is an ontological operator, which can result in real physical change.

3.2. Science and PDO

The operation of the PDO in science justifies its place in logic. In the areas listed in

Table 1. Areas of Application of the Included Middle.

Physics	Pendulum: actual <> potential energy
Chemistry	Transition States; Oxidation/Reduction Potential
Biology	Activation/Passivation of Nerves; Mitosis
Psychology	Doubt; Memory; Consciousness; Creativity; Ambivalence; Anticipation
Sociology	Altruism; Common Good; Democracy

, one or both of the key concepts of Logic in Reality are instantiated. These are (1) the movement from potentiality to actuality and vice versa and (2) the presence of an included middle state through which a process passes in an asymmetric, sinusoidal movement. Entropy and global irreversibility characterize the world as a whole, but negentropy and reversibility emerge locally at higher physical levels and in cognition in human beings. Higher levels of order are possible in physics due to the operation of the Pauli exclusion principle for electrons, which is a principle of difference.

3.3. Other Logics

Starting in the 20th century, new groups of logics were developed, as it became apparent that the strict limits of the Aristotelian system were inapplicable, especially in quantum physics: paraconsistent; paracomplete; quantum; probabilistic.

Of these, in principle, only quantum logics limited to quantum phenomena discuss real physical change. Nicolescu has suggested, however, that some aspects of quantum mechanics apply in the macroscopic world as well, especially to cognitive phenomena, as in the previous list.

Other Buddhist and Western logics can be interpreted as linguistic systems of predicates or propositions. The terms “gaps” and “gluts” apply to the lack of or excess of true statements possible according to the Aristotelian laws of the excluded middle (LEM) and non-contradiction (LNC), respectively. The corresponding logical systems are referred to as paracomplete and paraconsistent. Paraconsistent logic includes what Graham Priest has called “true contradictions” [6], which from the strict classical perspective is an oxymoron.

To our knowledge, LIR is the only theory in which the three major axioms of classical logic are modified at once. Standard propositional or predicate logics, (classical or non-classical) involve rules of inference for determining the truth of propositions and linguistic formulations of beliefs, etc. LIR involves rules for inferring the actual/potential state of the changing real-world elements involved in a phenomenon.

In some cases, an algorithm exists which such a logic can follow; however, this is not a necessary property. There is a great deal of existence, real within science, for which algorithms cannot be written. One example is the set of equations for quantum systems which do not commute or distribute.

LIR is concerned with reality as directly as possible and not with statements or propositions about reality. LIR follows the laws of theoretical physics but does not have the same underlying mathematical structure. The emphasis is on real change as it is and could be experienced by human beings. It is thus an “ontology with a human face” [7], without the features of exclusivity and exhaustivity of standard category theory.

4. Information, Philosophy of Information and LIR

Major recent developments first in science and technology and later in philosophy have been made in the field of information. Information is unique, appearing to “combine” both epistemic elements and ontological processes. We introduce it here to justify the need for some new paradigm for logic. The features of information have made this key concept extremely difficult to characterize in standard logical terms. Logic in Reality accepts that both features co-exist and change, and we consider if these features of reality require a corresponding logic. For example, Terrence Deacon [8] has suggested absence as a significant feature of information, a rare recognition of the ontological importance of a “negative”, always in a dynamic relation with its positive—that is, its here presence.

In relating logic to information, we emphasize that LIR and the Lupasco theory on which it is based is a logic of energy, which is a better of energetic change. The scientific grounding is in the movement of energy from higher to lower levels, from greater to lesser complexity, following the 2nd law of thermodynamics which applies globally. Local reversal to more complex ordered states can take place but requires an input of energy in some form.

The cybernetician Norbert Wiener stated that information is neither matter nor energy but “information”. Recent interpretations support rather the physical nature of information via the concept of an energy-information equivalence principle [9]. The concept that information is a physical system obeying physical laws is at the core of Logic in Reality. Our own best definition of information is as a bundle or sheaf of processes and meanings, all of which are operators in the real world. These process elements follow the principles of logical movement from actuality to potentiality. In some cases, an algorithm exists which such a logic can follow; however, this is not a necessary property. There is a great deal of existence, real within science, for which algorithms cannot be written. One example is the set of equations for quantum systems which do not commute or distribute. It is important to recognize Wiener’s underlying insight that there is “something else going on”, something like a middle (?) between energy-as-physics and energy-as-information that is also a carrier of meaning.

The contemporary Chinese information philosopher Kun Wu has a very similar view on information, which is critical of Floridi’s semantic understanding of information. It is interesting that Wu’s understanding on information derives from his creative approach to bridging the gap between matter and mind. Information is thus a middle or median in Wu’s conception.

Zhensong Wang believes that Wu’s theory is stuck in a dilemma, which is that it advocates a rebellion on the modern philosophy but actually still follows the Cartesian philosophical model of mind–body dualism. So, Wang insists a reformation on Wu’s conception. If information surely belongs to the material world according to Vopson’s study, the debate between materialism and idealism will finally become an obsolete topic that is the Cartesian legacy, because the mind does not logically go beyond the physical world. The only existence is nature itself. Therefore, semantic information, meaning and mind logically can be naturalized as well, because as philosophy it is a part of natural philosophy [10].

The studies on information, energy and matter are just different ways for us to investigate nature. All of them are ontologically adequate and epistemologically necessary. Wang believes that it is the way of naturalistic study on the philosophy of information. The evolution of the informational world thus clarifies the nature of meaning and mind, from omnipresent interaction, to systematic exchanges, to perception, to sense, to thinking, to rationality and to reflection. A new way of studying philosophy, combining with science, is inevitable. Consequently, new logic is needed as well to describe the feature and movement of information.

The Catalan sociologist Manuel Castells [11] suggested in 2000 that unique relationships are developing between the classical disciplines of science and philosophy as a consequence of new understandings of the science and philosophy of information. As stated by Wu [12,13], the overall movement is that of a philosophization of science and a scientification of philosophy, leading to their convergence—a Unified Science-Philosophy of Information (USPI). What is essential is the clear joint operation of scientific and philosophical aspects of information in communication and human social interactions.

5. Revolution in Information

In 2017, Wu and Brenner published “Philosophy of Information, Revolution in Philosophy”, suggesting that understanding philosophy in informational terms could lead to new understandings of the role of information in science. In this paper, we suggest the converse is also valid: that the application of some neglected concepts of existence and logic as they appear in, primarily, Eastern (China, India, Japan) philosophies would constitute a “revolution” in information, adding another dimension to it.

The so-called Tetralemma of Nagarjuna occupies a central place in this logic. Nagarjuna (see above) developed the concept of lemmas in opposition to logical axioms as better reflecting non-linguistic reality. One of many existing versions is as follows [2]: there is; there is not; there neither is nor is not; there both is and is not.

This classic Eastern logic of the middle was reformulated by Yamauchi (see above) as follows: being a middle is not only being between two terms but also being neither one nor the other and accordingly being one and the other. Classic bivalent logic is a logic of exclusion, of either/or, a “worldly” logic; lemmic logic resembles concepts in Buddhism such as the Great Vehicle and Supreme Truth. For Yamauchi, we have arrived at logic, not as a synthesis derived from the relation between affirmation and negation but via an immediate direct experience, an intuitive reality. To repeat, the joint operation of double negation and double affirmation is antithetic to standard logic but results in the compatibility of opposing terms such as being and non-being and grounds them. The need for a grounding of the Tetralemma itself was perceived by Yamauchi; however, he and his followers have admitted that they have not found an epistemic or ontic ground for their logic except in human intuition [14]. This could disqualify lemmic logic for serious consideration, let alone scientific validity. The lemmas cannot be “proved” in any classical, semantic sense. Taken by itself, any statement of belief that their grounding is intuitive is inadequate as a basis for science and natural philosophy. From our standpoint of mental processes as following physical laws, we suggest that the complex mental processes corresponding to knowledge—in Lupasco’s terminology Knowledge-as-Such and Intuition—are not separated or separable, constituting another real duality, and we conclude that the missing grounding for the “middle way” of Nagarjuna and Yamauchi can be found in the principle of dynamic opposition (PDO).

6. Emergent Information and Conclusions

Finally, we should mention the relevance of the work on emergent information and the environment by the systems and information scientist Wolfgang Hofkirchner. This link determines that the apparently most abstract and theoretical concepts from Eastern philosophy are in fact essential to progress in society.

The exemplification of what amounts to a new theory of knowledge within the philosophy of information complements the original insights of Wu Kun. Extensions to meaning on the theoretical side and to sustainability and ethics on the practical side are both necessary and possible.