**3. Logic in Reality (LIR)**

On many occasions, Brenner has discussed the principles of Logic in Reality and their derivation from the logical system proposed by Lupasco, for example in articles on consciousness [22], ecology [23] and natural philosophy [9]. Underlying this work is a vision of Lupasco's Principle of Dynamic Opposition (PDO) as operative in nature. We reproduce from [1] the best and simplest expression of this principle: "The antagonistic dualities of our world can be formalized as a structural, logical, and metaphysical principle of opposition or contradiction instantiated in complex higher-level phenomena (Principle of Dynamic Opposition—PDO). The fundamental postulate of LIR is that for all energetic phenomena (all phenomena) alternate between degrees of actualization and of potentialization of themselves and their opposites or 'contradictions' but without either going to the absolute limits of 0% or 100%. The point traversed at which a logical element and its opposite are equally actualized and potentialized is one of maximum interaction from which new entities can emerge. It is designated by Lupasco and Basarab Nicolescu, the physicist colleague and major continuator of Lupasco [24], as a 'T'-state, T for included middle or third (*Tiers-inclus*). A relatively simple example of a physical T-state is the transition state in a chemical reaction. This is the point at which the number of molecules of reactants moving toward more thermodynamically favored products and the number moving in the reverse direction is the same. We use the concept of T-states to evaluate both philosophical and scientific theories, including patterns of human individual and social behavior. A dynamic systems view can be used to focus on the feedback or recursion present in all natural processes."

The absence of debate of these concepts of the dynamic general properties of natural phenomena has given them the appearance of a statism when the opposite was intended. The choice of the domains in this paper—dialectics, semiosis and meaning/information, to which the PDO is intended to apply, is in part based on the difficulties of explaining them through the use of standard doctrines, as well as the desire to 'mobilize' the PDO as an explanatory methodology. As Brenner suggested at the 2015 Information Summit Conference of the International Society for Studies of Information in Vienna [25], the concept of scientific method is only one of those meaningful in the contemporary practice of science. Computational methods can be and are applied routinely in all the sciences, but their limitations demand a directed interpretation. In the human domain, it is the application of operative or organizational principles to an individual or social cognitive process to determine its dynamics, what "forces are at work", that we consider essential for the determination of an informational commons.

In a conception discussed at the Vienna Conference, the Information Society is at three crossroads in terms of its future development: we quote from Brenner's paper [26]: (1) a Socio-Political Crossroads where trends toward improvement in the quality of life are offset by a regression and degradation of the mental and social environment, both in part due to the massive role of information in the society; (2) a Transdisciplinary Crossroads, where the science and philosophy of information as disciplines may develop in the direction of integration in an Informational Turn, a new way of Informational Thinking as proposed by Wu Kun [27] that can support efforts toward a Global Sustainable Information Society, in the term of Wolfgang Hofkirchner [28]. Alternatively, they may diverge or regress in the direction of increasingly socially irresponsible specialization and scholasticism; and (3) a Metaphysical Crossroads, inseparable from the first two, involving the direction of development of the science and philosophy of information as a metaphysics, a crossroads that includes a definition of the dynamic relation of man to the universe. Like the other two, there is a positive branch leading toward less dysfunction at the individual and social level. The negative branch implies an on-going blockage of ethical development of the society.

In our view these three domains are also at their own crossroads: they can continue in separation or accept a logic and methodology that places the emphasis on their non-separability and co-evolution. The dialectic logic of/in reality outlined above offers a methodology that provides for linking them dynamically.

#### *3.1. The Philosophical Logic of Stéphane Lupasco*

In the broadest possible sense, this is a paper about change, better about changing and processes in the real world. We are interested primarily in ontological change, about which little has been written from a logical standpoint. The reason is obvious: change is ubiquitous in existence and experience. Theories of change, however, have focused on making it mathematically, computationally and logically tractable, within the framework of standard logic.

Differential equations provide an excellent description of continuous change, but what if the change in question is partly discontinuous, recursive and/or random? In fact, change is contradictory: the most familiar thing about change is that it never occurs in isolation from stability. Change is regular *and* irregular; consistent *and* inconsistent; continuous *and* discontinuous. Since the only logics available have been propositional bivalent logics, incapable of accepting real contradictions, they have been incapable of describing change.

Brenner has written several articles in the last decade which describe the non-standard, non-linguistic logic that we see instantiated in changing processes [29]. It is based on the logical system proposed by the Franco-Romanian thinker Stéphane Lupasco (Bucharest, 1900–Paris, 1988). The extension of Lupasco's system made by Brenner is called Logic in Reality (LIR), and it has been applied most recently to the fields of information [30] and the philosophies of information and ecology, as noted above.

Despite its publication in some fifteen books in his lifetime and its continuation by his associate Basarab Nicolescu [24], Lupasco's system of thought has remained unknown outside France, where it had been rejected by the academic community. With a few notable exceptions, Brenner's publications have suffered the same fate. The reason here is less obvious, but in our opinion it has to do with the fact that acceptance of our logic of and in reality requires the acceptance of a new, scientifically grounded concept of the dynamics of change in all complex, interactive phenomena at biological, cognitive and social levels of reality.

The comparison of the Lupasco logic with standard logics is rendered difficult due to the limitation of the latter to the linguistic domain. These semantic logics, bivalent or multivalent and their most recent epistemic, paraconsistent and paracomplete versions still require absolute separation of, for example, continuity and discontinuity, space-time and matter, chance and necessity, etc. and lead in linguistics to the paradoxes with which we are all familiar. Paraconsistent logics, which accept contradiction, capture only the linguistic as opposed to the physical aspects of processes, although some real inconsistencies in simple change (Sorites problems) are accepted. Logics of epistemic change are based on linguistic abstractions. No logical characteristics are ascribed to the physical processes of change. It is thus not surprising that no generally applicable theory of change has been developed for the extant domain of macroscopic, complex and interactive processes.

#### *3.2. Logic in Reality: Axioms and Categories*

As noted in Section 2, Aristotle outlines his fundamental concept of potentiality and actuality in the "*De Anima*", ("*On the Soul*"). In this already metaphysical context, he writes that potentiality is matter and actuality is form. Thus, we need to know what matter and form are, but we can assume they are di fferent. Why, to use a more modern term, potentiality should be instantiated in matter and actuality in form is not clear. What is more important for this study, however, is the relation that *Aristotle* sees between potentiality and actuality. In *De Anima* there is no direct indication that one can be transformed or transform itself into the other, but this is implied by his concept of life as an internal transformation of the body. If it is implied by Aristotle's view of the movement of energy, there is certainly no indication of the possibility of movement from actuality to potentiality.

As discussed by Brenner in [1], Lupasco's definition of the two terms in terms of energy has place for this contrary forward movement. It is implied by the fact, observable in part, that no complex process goes to the absolute limits of 100% potentiality or 100% actuality, except in trivial cases or those in which there is no real interaction. The entire literature around Schrödinger cat fails as 'alive' and 'dead' are not interacting states. Given this interpretation, why is not more attention paid to it in philosophy when it fits modern physics?

#### *3.3. Toward a New Non-Boolean Logic*

Since George Boole published his *Laws of Thought* [4] in 1854, Boolean logic has been the canonical logic of science and philosophy. Boole demonstrated that classical, bivalent propositional logic could receive an algebraic formulation and proposed a general symbolic method for logical inference. His algebra contains terms for both quality and quantity and provides the basis for standard probability theory. However, his terms for *quality* are strictly limited to formalizable, binary properties of phenomena. Non-Boolean logics and algebras [31] have been shown, relatively recently, to be really necessary in the area of quantum mechanics, with a few interesting but constructed exceptions in the work of Diederik Aerts [32], Elio Conte [33] and others.

However, as should be more widely appreciated, Boole himself was aware of the limitations of his own system and was completely open to others, sometimes of a striking modernity: "we sometimes find more just conceptions of the unity, the vital connexion and the subordination to a moral purpose, of the di fferent parts of truth, among those who acknowledge nothing higher than *the changing aspect of collective humanity* (italics ours), than among those who profess an intellectual allegiance to the Father of Lights". Further in a key Appendix to [4] he writes that the central role of mathematics as derived from his Laws of Thought, it is not a su fficient basis either of knowledge or of discipline, "As truly, therefore, as the cultivation of the mathematical or deductive faculty is a part of intellectual discipline, so truly it is only a part."

Balance is necessary in any view of the operation of the human mind: "I would especially direct attention to that view of the constitution of the intellect which represents it as subject to laws determinate in their character, but not operating by the power of necessity; which exhibit it as redeemed from the dominion of fate, without being abandoned to the lawlessness of chance," Boole's logical laws of thought can manifest their presence "otherwise than by merely prescribing the conditions of formal inference." The distinctions between true and false, between correct and incorrect, are cornerstones for his and all other standard logics. But this distinction "exists in the processes of the intellect, not in the region of physical necessity".

Boole is honest in admitting not to have found a *construens* to accompany his *destruens*, but several of his remarks sugges<sup>t</sup> that some aspects of Logic in Reality would have been congenial to him. One was to the e ffect that his Laws of Thought (logic) were capable of precise scientific expression, but were invested with a lower 'authority' than the laws of nature in general. "Were the correspondence between the forms of thought and the actual constitution of Nature proved to exist, whatsoever connexion or relation it might be supposed to establish between the two systems, it would in no degree a ffect the question of their mutual independence." "Wherever the phenomena of life are manifested, the

dominion of rigid law in some degree yields to that mysterious principle of activity", a teleology accomplished "not, apparently, by the fateful power of external circumstances, but by the calling forth of an energy from within." We quote Boole *in extenso* [4], because we have seen no references to these passages elsewhere. It has been left to Lupasco to continue and talk about the 'laws of energy' and their deployment and to show that some real macroscopic processes follow a logic whose terms do not commute or distribute and are accordingly non-Boolean. This extension of logic, as noted, has not been widely accepted in the literature.
