The Transdisciplinary Logic of Transdisciplinarity

Transdisciplinarity is about man, man and the reality of which he is a part. Transdisciplinarity is thus about human successes - progress and creativity, but also failures and regression, or virtue and vice in the traditional expression. In a word, it must account for contradictions and inconsistencies, as well as the appearance of new forms and entities. Classical logic, the binary logic of Aristotle, does not allow contradiction. Designed for propositions, it cannot in principle apply to complex aspects of the real world. However, if all or part of reality does in fact instantiate contradiction, by this definition, reality cannot be logical, if logical means in some way rational and orderly. Despite this potential inadequacy as a picture of reality, this logic has been maintained as a quasi-monolithic doctrine since antiquity. Intuitions that other logical principles may govern existence can be found in both Western and Eastern thought. However, it was not until the development of quantum mechanics in the 20th Century, in particular by Planck, Pauli and Heisenberg, that the failure of classical logic to apply to or describe specific physical systems became evident,1 potentially facilitating the re-evaluation of logic in general.

Despite recent developments in paraconsistent and intuitionist logics, the logic underlying work in all scientific fields, with the possible exception of quantum mechanics, continues to be based on classical or neo-classical notions of truth and/or non-contradiction. This is also true for discussions of ethics or morality and high-level human phenomena such as art and creativity. To the extent that logic is considered at all, it is thought to be in some way in opposition to the essential components of spontaneity, imagination and emotion in normal behavior. Although people value "being logical" as a necessary criterion for socio-economic survival and success, formal logic is considered dry and uninteresting, as well as being essentially inaccessible to the average person - a necessary evil. Logic and epistemology, the philosophy of knowledge, share unfortunately well-deserved reputations for using examples and references that are far removed from daily life and its problems.

The Franco-Romanian philosopher Stéphane Lupasco, who deserves a major, still unrecognized place in the history of Western thought (Nicolescu 1999), provided a theoretical basis for the quasi-universal rejection of contradiction and the maintenance of absolute separation between classical pairs of opposites, especially part and whole, simultaneity and succession, subject and object. Lupasco was able to show that such abstract, idealized concepts are also still present in most of current cosmology that is based on Einstein’s ideas of general and special relativity. The weaknesses of this system are beginning to be recognized, one hundred years after its basic formulation, due to recent demonstrations of quantum non-locality and non-separability. However, these new developments in physics and cosmology have not yet received adequate attention from logicians and philosophers.

1. DEFINING TRANSDISCIPLINARITY

In his Manifesto, Basarab Nicolescu (Nicolescu 1996) describes transdisciplinarity as a new philosophical movement. Transdisciplinarity is not a new discipline, but rather has the task of seeing what all disciplines have in common, what lies in, through and beyond them. What they have in common is a basis for “making sense” of a part of human knowledge and hopefully providing a path to a unified understanding of it.

According to Nicolescu, transdisciplinarity is supported by three major conceptual “pillars”: complexity, levels of reality and the logic of the included middle. On these pillars are based the methodology of transdisciplinarity, as well as the validity of Transdisciplinarity as a rigorous system of thought that is relevant to today’s world. The pillars are, however, different kinds of things, albeit closely related ones:

Complexity is a property which is exemplified or attached in some way to its instances, the things or systems that are complex;

Levels of reality is a categorial concept;

The logic of the included middle is a discipline as such.

These subjects are all currently studied within many philosophical disciplines, of which the most important can be defined as indicated (Smith 2003):

Ontology is the study of being – what is

Epistemology is the study of knowledge – how we know

Logic is the study of valid reasoning – how to reason

Ethics is the study of right and wrong – how we should act

Phenomenology is the study of our experience – how we experience

Metaphysics includes all of the above, as well as science, as it is concerned with the fundamental structure of reality as a whole. Metaphysics is a universal discipline, in which everything, including the status and validity of metaphysics itself, is a proper subject of study (Lowe 2002). One of the interesting consequences of the Lupasco view of reality is that it points toward a convergence of metaphysics and physics and in fact toward the unity of science and of knowledge.

To repeat, transdisciplinarity is not a new discipline, but the number of important individual disciplines that it is necessary to take into account in order to arrive at a more or less complete initial picture of reality is very large. The logic of the included middle, due to its grounding in physics and exemplification of the principle of dynamic opposition, has an essential role in tying together the various aspects of transdisciplinarity. As I will show, this logic is itself a transdisciplinary system, embodying an ontology and an epistemology applicable to both the theories and subject matter of all disciplines dealing with real entities.

2. THE LOGIC OF/IN REALITY (LIR)

In this paper, I refer to the non-propositional, non-truth-functional logic of and in reality that is emerging from the original work of Lupasco, and extended by Nicolescu (1999) by the principle of levels of reality, as Logic in Reality. The term "Logic in Reality" (LIR) is intended to imply both 1) that the principle of change according to which reality operates is a logical principle embedded in it, the logic in reality; and 2) that what logic really is involves this same real physical-metaphysical but also logical principle.

Based originally on the quantum mechanics of Planck, Pauli and Heisenberg, LIR states that the characteristics of energy - extensive and intensive; continuous and discontinuous; entropic (tendency toward identity or homogeneity – 2nd Law of Thermodynamics) and negentropic (tendency toward diversity or heterogeneity – Pauli Exclusion Principle) - can be formalized as a structural logical principle of dynamic opposition, an antagonistic duality inherent in the nature of energy (or its effective quantum field equivalent) and accordingly of all real physical and non-physical phenomena. The key postulate, formulated by Lupasco, is that every real phenomenon, element or event e is always associated with an anti-phenomenon, anti-element or anti-event non-e, such that the actualization of e entails the potentialization of non-e and vice versa, alternatively, without either ever disappearing completely. The point of equilibrium or semi-actualization and semi-potentialization is a point of maximum antagonism or ‘contradiction’ from which, in the case of complex phenomena, a T-state (T for “tiers inclus”, included third term) emerges, resolving the contradiction (or ‘counter-action’) at a higher level of reality. The overall theory is a metaphysics of energy and LIR is the formal part of that metaphysical theory.

The logic is a logic of an included middle, consisting of axioms and rules of inference for determining the state of the three dynamic elements involved in a phenomenon (‘dynamic’ in the physical sense, related to real rather than to formal change, e.g. of conclusions). In the LIR calculus, the reciprocally determined ‘reality’ values of the degree of actualization A, potentialization P and T-state T replace the truth values in standard truth tables. This logic contains that of the excluded middle as a limiting case, approached asymptotically but only instantiated in simple situations and abstract contexts, e.g., computational aspects of reasoning and mathematical complexity.

As a first step, one may capture these concepts and this postulate by rewriting the three axioms of classical logic as indicated:

LIR1: (Physical) Non-Identity: There is no A at a given time that is identical to A at another time.

LIR2: Conditional Contradiction: A and non-A both exist at the same time, but only in the sense that when A is actual, non-A is potential, reciprocally and alternatively.

LIR3: Included (Emergent) Middle: An included or additional third element or T-state emerges from the point of maximum contradiction at which A and non-A are equally actualized and potentialized, but at a higher level of reality or complexity, at which the contradiction is resolved2.

Additional axioms are required for the proposed application to real-world elements, rather than only to propositional variables, including the essential concept that no real process goes to the idealized, abstract limits of classical logic.

LIR4: Logical Elements: The elements of the logic are all representations of real physical and non-physical entities.

LIR5: Functional Association: Every real logical element e – objects, processes, events – is always associated, 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.

LIR6: Asymptoticity: No process of actualization or potentialization of any element goes to 100% completeness.

In sequence, these axioms express the notion of change; the mechanism of change; the product of change, that is, emergence of a new entity or phenomenon; the locus of change in the elements of reality; the structure of reality and a property of change. The nature of these real-world elements and the basis of the property will be left open for the time being, but the elements can be assumed to be what are commonly termed ‘facts’ or extra-linguistic entities or processes. The term ‘functional’, as used in LIR5. is not intended as part of a functionalist theory of mind, but simply implies that one element cannot exist without the other, or, put positively, that one element depends for its existence on the other.

The following corollaries refer to the notions of contradiction or antagonism and truth:

CLIR1:Contradiction: Contradiction can never be considered as absolute,

because it never takes place between rigorously actual terms, between absolutely contradictory elements, such as those of classical logic and mathematics. Contradiction never occurs except between antagonistic dynamisms. Alternatively, no element, no logical variable or event is rigorously non- contradictory; it always involves some contradiction such that, no matter how much developed, the non-contradiction is always relative and limited.

CLIR2: Truth and Falsity: A truth cannot be absolute, because it can never be rigorously (totally) actualized; a contradictory truth (falsity) can be potentialized as much as one wants theoretically without ever completely disappearing in reality.

Opposing aspects of phenomena that are generally considered independent can thus be understood as being in the dynamic relationship suggested, namely, as one is actualized, the other is potentialized. This is the LIR axiom of Conditional Contradiction. Problems due to the assumption of an absolute independence or separation between opposing dual elements or properties (e.g., local/ global, part/whole, set/member of set, knower/known, rational/irrational, etc.) can be approached from this standpoint. LIR resembles inductive and abductive logics in that truth preservation is not guaranteed, but the elements of LIR are not propositions in the usual sense, but probability-like values as in quantum logics, described by non-Kolmogorovian, non-commutative lattices. Cause and effect, determinism and indeterminism and time and space receive non-standard interpretations in this theory.

3. LIR AS A LOGICAL SYSTEM

It can be shown that LIR is a valid logical system in the sense of consisting of a formal part –the above axioms, a semantics and a calculus (Brenner ?); an interpreted part – a metaphysics, categorial ontology and a contradictorial, two-level framework for analysis; and relevant applications in philosophy and science. I distinguish LIR from standard logics, classical, non-classical, multi-valued, etc. in that all of these employ standard, non-physical concepts of truth and falsity and logical operations. My thesis is that the principles of these binary logics, e.g. the separation of premises and conclusions, underlie the distinctions between the dualities noted above.

Despite its application to the extant domain, LIR is neither a physics nor a cosmology. It is a logic in the sense of enabling stable patterns of inference to be made, albeit not with reference to propositional variables. The three components – formal system, interpreted system, including an appropriate ontology and applications are not independent but are in an interactive relation describable in the system.

3.1 Metaphysics and Ontology

`The domain of LIR in practice is that of phenomena of sufficient complexity so that they instantiate alternate actualization and potentialization together with some form of internal representation. The levels of reality in which this occurs are primarily those of biology and human cognition. There is nothing gained in applying logic in reality to the impact of billiard balls, despite the certain macrophysical changes consequent on it. The balls remain the same ‘to all intents and purposes’. LIR is interested, however, the processes occurring in and between the billiard players.

A major component of LIR is the categorial structure of the ontology (NEO for New Energy Ontology) that fits the above axioms, as follows:

Material

- Energy/Quantum Field

- T-state

Formal

- Process

Emergence, Closure and Downward Causation

- Dynamic Opposition

Separability and Non-separability

- Subject, Object and Subject-Object

The LIR-NEO categorial view provides a formal way of discussing internal and external closure of entities and their coupling in such a way that they, literally, cannot exist without each other. The LIR approach is an attempt to resolve the inevitable problems resulting from the classical concepts of space, time and causality as categories with separable categorial features, including final and effective cause. A discussion of causality and LIR would lead us too far beyond the scope of this paper.

3.2 T-States (Included Middles)

Since the category of a T-state as an emergent included middle is certainly the most unfamiliar one in the ontology, I will provide some further details about the concept.

The concept of an energetic state of phenomena, the T-state, being not only an element of a logic but one that overturns, in certain areas, an axiom of commonsense logic, the law of the excluded middle, is the crucial innovation of my logic of and in reality. It is thus important to first make clear what a T-state is not: it is not an average of two or more elements, a static, scalar result of an arithmetical operation. It is not the result of a physical mixture or fusion; gray is also an ‘average’ of black and white, but this result is inert, without the capacity of change or development. Similarly, a T-state is not the static equilibrium that results from the neutralization of two elements, such as equal quantities of acid and alkali. At a microscopic level, some regions of such substances may depart from equilibrium, but the fluctuations are statistical in nature.

At a single level of reality, the second and third axioms of classical logic are essentially equivalent: there are no contradictions in the same time and place. In my extension of logic, a T-state resolves a contradiction at another level of reality. One example that is frequently given is the apparent unification in the quanton (T) of the apparently contradictory elements of particle (A) and wave (non-A). What is involved at the single, ‘lower’ level of reality are more or less mutually exclusive, antagonistic pairs that can be seen as resulting from the projection of a T-state on it (Nicolescu 1999). The T-state is the included middle or third term in that it is located in the model at an intermediate point in a complex configuration space. In contrast to the Hegelian triad, the three elements here coexist at the same moment of time. It should be re-emphasized that “A and non-A at the same time” does not mean that both are fully actual. One element is more or less actual, and the other is, correspondingly, more or less potential. ‘At the same time’ does not imply an instant of standard clock-time. Process elements deploy their own time and space, or space-time.

LIR is capable of describing a coherent transition between levels of reality. A given T-state (which effects the unification of A and non-A) is associated with another couple of contradictory elements at its higher level (A1, non-A1), which are in turn resolved at another level by T1. The application of the logic of the included middle implies an open, incomplete structure of the set of all possible levels of reality, similar to that defined by Gödel for formal systems. Concatenations of systems and dialectics never have a third term in the sense of a Hegelian or Marxist synthesis. The T-state is not a term, but a state, and emergent T-states, at a higher level of reality, can also enter as elements into contradictory relations.

The purpose of defining T-states as a category is to be able to use the concept to evaluate both philosophical and scientific theories, including patterns of human individual and social behavior. It is in dynamic systems involving feedback in the biological, mental, social and political worlds, in addition to the quantum level, that examples of T-states are to be found. In order to see how two elements in dynamic opposition result in a third, a T-state, one must look closely at the tendencies of each of them toward identity or diversity, homogenization or heterogenization, forces of dissolution or forces of growth.

At the quantum level, a baryon such as the highly stable proton is composed of quarks and anti-quarks of various kinds that are held together by energetic particles called gluons. (Gluons bind the various quarks by ‘exchanging’ energy between them.) It is tempting to see the stability of a proton as due to this dynamic process between two opposing quarks, with the gluon playing the role of an included middle.

In current terms, all living systems supervene on the inorganic level, where the former predominates, and lower levels of organic structure. The latter supervene on lower levels of reality, starting with chemical elements, molecular compounds, e.g., proteins, leading to cell structures, cells and organisms. Each of these stages can be considered a T-state relative to the one below it, but the concept of a T-state resolving energetic oppositions has greater explicatory power than supervenience, which does not describe an interaction between supervenient and subvenient elements, nor the concomitant interaction between the subvenient elements themselves.

It should be noted, however, that each stage of cell division in embyrogenesis is not a T-state, but a system of processes ultimately leading to (relative) non-contradiction, the phenotype. But the phenotype, the individual, is a T-state relative to the genotype, the ‘site’ of the counter-action between the actualized DNA and the residual chemical potentialities of the elements and compounds composing it. These potentialities can be considered as a biological ‘memory’ which can appear as a final cause of development.

In addition to the T-states at the quantum level and in biology, the greatest number of examples is at the mental level. Their structure of these included middles is highly complex. As noted, phenomena at any level of reality can be characterized by differing actualization of primary trends toward non-contradiction (contradictional: identity, homogeneity or diversity, heterogeneity) or toward contradiction (contradictorial: emergence of new entities). Complexification arises because these trends are themselves actualized or potentialized to a different degree, but never completely. In the resulting emergent elements that enter into further contradictorial relations, either homogeneity or heterogeneity is predominant, but the other is also always present. If one looks, for example, at any living system, it is clear that it embodies processes of growth and metabolism and/or decay at the same time. Thus it is not exactly correct to say only that, in living systems, diversity is actualized and identity is potentialized. Rather, the emergence of new forms, heterogeneity, is predominantly actualized and macrophysical processes of degradation, of homogeneity are predominantly potentialized, but at the same time the latter are actualized to a minor extent and the former is potentialized to a minor extent. A similar situation applies to the processes of perception and action. The homogeneous object in my consciousness is only potentialized with respect to the processes of actualization of its heterogeneous aspects actually occurring in my sense organs, of which I am largely unconscious. The inverse situation applies to efferent stimuli. But since actualizations and potentializations are never complete, there is also always some consciousness of heterogeneity in the first case and of homogeneity in the second.

The originality of this picture does not reside in its identification of a consciousness, a consciousness of consciousness (sometimes designated as awareness) and an unconscious. Rather, it is in its emphasis on the logical character of the origin of these higher-level structures in a principle of dynamic opposition at the level of basic physics, the mechanisms for their emergence and the subsequent complexification of their interactions.

T-states in the socio-political arena can correspond, among other things, to new laws. Unlike compromise or ‘centrist’ positions, T-states are radically new structures that are sometimes developed to reconcile oppositions between groups that have been unable to succeed in suppressing or eliminating each other. One example of this is the situation of segregationists and anti-segregationists in the Southern United States before 1956, which led to the passage of laws against racial discrimination and acceptance, albeit slow, partial and grudging, of racial equality.

The existence of an included middle T-state that is both a logical and physical element at these different levels of reality is, for me, an indication of the transdisciplinary character of the system as a whole.

3.3 A Two-Tier Structure of Reality

The most general description of reality is that it consists of entities and the physical and relational structure in which they find themselves, at different levels. A set of levels that is widely used consists of quantum, macrophysical, biological, cognitive (individual and social) and cosmological (Poli 2001).

At all levels of reality, I will assume that there is a conflict or opposition between but also within epistemological elements and the energetic processes to which they correspond. I may and in fact always will focus on one or the other aspect, but there is present a contradictional relation, one aspect is actualized while the other is potentialized. In other words, I apply the category of Dynamic Opposition to entities at the two levels. I then find in the physical domain, the same division of entities into Separable and Non-Separable; with and without the equivalent of an energetic relationship. In the latter, the actualization of one entity potentializes the other, in the former not. It is not that such two-tier systems of phenomena (of perception, reality, meaning, etc) have not been proposed. But my thesis is that only the antagonism within and between levels that is capable of explaining or rationalizing their existence and non-epiphenomenality. LIR mediates the relations of both horizontal and vertical transitions, and the relations themselves can be seen to be at different levels of reality.

In linguistic terms, one looks at semantics and syntax, in philosophy at parts and wholes and so on. This division brings with it what is often referred to as a tension between the structure and its elements, and I see in this ‘tension’ an expression of the instantiation of the principle of dynamic opposition outlined in this book, namely, that elements and structures share, to a more or less actual or potential extent, one another’s properties, both physically and also epistemologically, in the sense of alternating perspectives.

LIR can thus be seen as applying to a reality of dualities or dichotomies, between either classes of entities or two individual terms. Examples of some of these are the following, presented with the caveat that my division into physical and linguistic is also open to debate:

PhysicalLinguistic

Data of Theories Theories

Truth-makers Truth-bearers

Becoming Being

Element Set

Matter (-energy) Symbol

Facts Meaning

Presentations (external) Representations (internal)

Individual Group

Semantics Syntax

One can make ananalogy with relational structures in set theory, membership of elements in sets and inclusion of sets in one another; relations between elements, relations between sets or classes of elements, events, etc. and the descriptions or explanations of those events

4. LIR AND OTHER LOGICS

I will not discuss other logics in detail, but just refer to three relevant relatively recent groups of logics in order to emphasize the major differences between LIR and all other logical systems:

4.1 Paraconsistent Logics

LIR extends the meaning of contradiction in paraconsistent logics (PCL). PCL are defined such that contradiction does not entail triviality. In some, such as those of Priest (Priest 1987), an ontological commitment is made and real contradictions are allowed. In others, such as the logics of formal inconsistency of Carnielli (Carnielli 2005), they are not. LIR captures the logical structure of the dynamics involved in the contradictory aspects of real phenomena, in particular of thought, some of which are mirrored in paraconsistent logic. However, the ‘contradiction’ in LIR is conditional, in contrast to that in PCL: propositions are ‘true’ and ‘false’ at the same time, but only in the sense that when one sense is actual, the other is potential. If a principle of logical inconsistency can be shown to be present in physical reality, then an extension of Gödel’s theorems to selected aspects of macroscopic reality may be possible and desirable.

4.2 Intuitionist (Paracomplete) Logics

This group of logics was developed in the mid-20th Century by Brouwer and his followers to handle problems arising from the presence of, better, intuitions about the presence of, infinities in mathematics. While their discussion is outside the scope of this paper, I still want to indicate that they remain classical from my point of view: the Axiom of the Excluded Middle is stated not to hold in certain cases, but the Axiom of Non-Contradiction does hold, and no axiom of an Included Middle is suggested. Applications to reality, perhaps by way of category theory, have been suggested by Roberto Poli (Poli 2003), but the absence of dynamic interaction terms makes this a less useful tool than LIR.

4.3 Universal and Quantum Logics

The approach of universal logic is to try to insure that any logical system has a proper mathematical expression. This is certainly desirable, and it is possible that the key principles of LIR could be mathematized. I do not believe, however, that it is a necessary strategy once the domain of logic has been expanded to include the representations of reality that I have suggested.

More appropriate schemes can be found in the logical concepts of quantum physics, starting with the idea of superposition of states of quantum entities before the ‘collapse’ of the system toward one or the other as a classical limit. We have here a picture that is similar to our familiar A and non-A and their interaction at an intermediate included middle T-state. In our picture, phenomena at the classical limit can be described by classical logic.

The physicist Diederik Aerts (Aerts 2003) has shown how some of these concepts may be expanded to apply to non-quantum phenomena. In other words, there is a “meso-” domain in which neither quantum nor classical mechanics apply integrally. This is exactly the domain that LIR can handle logically. This grounding in physics is one of the things that support my claim that LIR is transdisciplinary

5. LIR AND TRANSDISCIPLINARITY

I have restated the definition of Transdisciplinarity at he beginning of this paper, and I have defined LIR as the logic of Transdisciplinarity. From a formal standpoint, I also need to define in respect of how this transdisciplinary logic applies to transdisciplinarity itself, apart from the normal semantic overlap between the nominal and adjectival forms.

I will assume that ‘Transdisciplinarity’ is composed, not of a set of disciplines, but of a set of attributes or relations such as the transdisciplinary attitude, which is in a sense a meta-principle, describing people who are open to and use the principles and methodology of Transdisciplinarity, especially in its humanistic and moral aspects. Other major elements, discussed elsewhere at this Conference, are transdisciplinary education,

Transdisciplinary logic, then, is one which governs the dynamics of the entities, processes and theories of the many individual disciplines. However, is also applicable to the relations pertaining to Transdisciplinarity itself, that is, to the set of relations located between and among the disciplines, leading to epistemological emergence to something ‘beyond’ the disciplines as a T-state or included middle. This is because the relations between any pair of disciplines, with their different approaches and subjects, are in opposition or have elements which are in opposition. We have all had the experience of such conflicts in the context of multi- or inter-disciplinary collaborative effort. One observes the same kind of alternating actualization and potentialization of the respective viewpoints as well as, hopefully, the emergence of consensus as in arguments within individual disciplines.

There is one distinction which it will be essential to keep in mind as we discuss application of this transdisciplinary logic of transdisciplinarity - LIR. This logic is in one sense a theory and, to the extent that its physical postulates or underpinnings can be disproved, it meets Popper’s criterion for a scientific theory of falsifiability. There are problems with the Popper approach, but the idea is still useful in many cases.

Transdisciplinarity is not a theory, and as noted, there are several statements possible of what transdisciplinarity is, in other words, how the definition I gave above of what lies in through and beyond the individual disciplines is to be interpreted. I like to look at transdisciplinarity as an attitude both to people and to science and knowledge, although there is, also, a transdisciplinary ontology of Subject and Object and their interaction – the ontological included middle.

In another sense, however, logic in reality is more than a theory: it is also a set of tools for analyzing the extent to which other theories conform to or adequately represent the non-separable properties of real phenomena. In this regard, LIR provides what is in fact a new criterion of falsehood. Any theory whose argument depends on the absolute independence of the entities or interpretations under discussion is likely to be biased in favor of one other. LIR avoids this trap because it assumes the existence of a counter-theory with which it is necessarily in a dialectical relationship. Reality, for LIR, includes the existence both of LIR and anti-LIR and their conjunction. This is a statement in somewhat more formal terms of what Nicolescu has called the open, Gödelian structure of knowledge, which insures the avoidance of all dogmatism and fundamentalism.

Since the advent of systems science and complexity science, other frameworks have been available for analysis of how science is done, that is, by inclusion of the subjective observer-agent as part of the objective experimental system. Feedback interactions provide for the changes that working scientists make in their working hypotheses. The problem with most of these theories is that they lack grounding in the physics of the systems under study, and are often forced to refer to absolute chance or indeterminism as the most fundamental principle in the universe.

6. THE TRANSDISCIPLINARY APPLICATIONS OF LIR

The LIR system I have outlined briefly transcends the usual boundaries of logic as supporting a linguistic domain and the limited aspects of reality that are subsumed under that domain. LIR thus has the characteristics of a metatheory and/or a metaphilosophy. LIR provides a picture of the emergence of new phenomena and forms that focuses on the sequence of oppositional or contradictorial processes involved that supplements their quantum mechanical description by Aerts. Relationships between the logic of Lupasco and the logical concepts of significant philosophical precursors such as Hegel, Peirce, and Whitehead and current thinkers (Dummett, Derrida) can also be established (Brenner 2005).

6.1 Philosophy and Metaphysics. The Themes of the Conference

LIR permits new logical interpretations of issues in areas such as continuity and discontinuity; causality and the analytic/synthetic distinction; aspects of the foundations of mathematics including set theory and the Axiom of Choice; and perception and cognition, etc. LIR has potential consequences for the study of the meta- and nexus-themes of this Conference and the relations between them. LIR provides a picture of the emergence of new phenomena and forms that focuses on the sequence of oppositional or contradictional processes involved. The process metaphysics of LIR supports the openness of the transdisciplinary approach by providing alternatives to inadequate but unfortunately quite prevalent expressions such as ‘spontaneous emergence’ and reified structural concepts (e.g. of ‘consciousness’) without reduction to naïve mechanistic physicalism.

6.2 Complementarity - Somehow

The 2006 Metanexus Conference dealt more specifically than this one with the relationship between concepts of continuity and change and their relation to science and religion, and the issue of complementarity in quantum physics was one of those discussed which is very relevant to this year’s subjects (Von Stillfried and Walach 2006).

In 1947 Nobel Price laureate Niels Bohr was awarded the Danish Order of the Elephant, normally given only to members of royal families and presidents of foreign states, to honor his discovery of the fundamental principles of quantum mechanics. For his coat of arms Bohr chose the Taoist yin-yang symbol. The Latin motto reads: "Opposites are complementary." Here Bohr not only expressed his conviction that complementarity is the most fundamental principle underlying physical reality; he also considered a religious symbol to best represent this principle. This is an illustration of his belief that complementarity is evident not only in the strictly physical world. In fact, Bohr believed complementarity to be the most fundamental principle of existence as a whole.

Bohr asked physicists, essentially, to accept A and non-A (wave and particle characteristics) at the same time, or, better, or A or non-A depending on what theoretical or experimental questions were being asked. But what could this mean? Complementarity becomes something like a simple juxtaposition. Apart from providing no explanation or description of how one aspect insured the continuous existence of the other, this picture does not seem adequate where A and non-A appear to have such a drastically different character. If the Bohr picture were true, and science and religion are complementary, and complementarity is as Bohr described it, then science and religion would be opposites. The LIR principle of dynamic (that is, interactive opposition) avoids this unwelcome separation.

If the fundamental nature of dynamic antagonism is accepted, a true contradiction in quantum phenomena is neither physically nor logically unacceptable. It is not physically unacceptable because wave and particle properties are not fully instantiated at the same time; the measurement of one potentializes the other. It is not logically unacceptable for exactly the same reason. Two answers can be given to the objection that this formulation simply restates the result of experiment: 1) if the particle aspects are actualized, the wave aspects must be present as potential, otherwise it is difficult to explain how they could reappear; 2) it is not in the LIR view that there is any problem with the observed duality of quantum entities in the first place.

By allowing quantum mechanics and logic to inform one another in a transdisciplinary fashion, appropriate emendations of concepts such as complementarity3 can be made that have increased explanatory power.

6.3 Epistemology and the Logic of Religion

In addition to the natural sciences and humanities, the domain of transdisciplinarity includes religious beliefs, studies and perspectives. Their relevance to a discussion of the unity of knowledge is that the term religion defines or refers to a knowledge that is different in two respects from both scientific and other commonsense knowledge: its object – a divinity - and the validity of the related process of knowing, that is, faith or belief. I will assume that the key aspects of religious experience are 1) the sacredness of natural existence and; 2) belief in a Supreme Being that may or may not be identical to Nature, or is an additional property of Nature. Further, however, that this belief is not limited to a mental process, but can involve all the physical and mental components of the whole person.

The usual intellectual framework provides little basis for either 1) the sacred or 2) the reality to the believer of his or her belief in that sacred and accordingly of its validity for that individual. Further, the non-believer remains an outside observer, separated from the believer as a consequence of the latter’s mental and physical behavior in this regard.

It is unlikely, given the evolutionary form of development of religion by different ethnic groups that any consensus could be reached on the nature of the sacred starting from their respective conceptions of divinity. Lupasco suggests that peoples with relatively rigid forms of social organization, such as the Hindu and some meso-American caste systems, that instantiate identity, develop religious systems involving multiple divinities. Nomadic societies tend to be more egalitarian, perhaps because equality enables more flexible responses to external challenges, and to this diversity would correspond a tendency toward monotheism as the contradictorial identity. Further application of this approach to the conflicts between Protestants and Catholics is possible, but will not be attempted here.

6.3.1 The Sacred and the Real

The approach to the definition of the sacred proposed by Nicolescu in his Manifesto of Transdisciplinarity (Nicolescu 2001) is that what is sacred in the world is what is irreducibly real. This definition is in principle acceptable to everyone, but leads inevitably to disagreement as to what is to be considered real. In view of the lack of consensus among philosophers on this question, it would appear that we have acquired thereby few additional tools for an analysis of religion.

In the non-reductionist realism of the logic in reality, the existence of two broad groups of people, believers and non-believers is taken as the given and used as follows. Believers are those who believe that what appears to be real is not, in the sense that a non-apparent divinity is an ultimate ‘more real’ reality. Non-believers, as realists, believe the opposite, that not only is there an underlying reality to what we perceive that is nonetheless independent of us, but that the reality of the believers is an illusion, and any evidence offered of the reality of the divinity is irrational.

Anti-realists, who deny that what we perceive is independent of our thoughts, theories, etc., can be members of both groups. Logic in reality cuts the debate between realists and anti-realists by pointing to a contradictorial relationship between appearance and reality. To the former, the world is real with the appearance of unreality, due to the limitations of our senses, while to the latter, the world is unreal, with the appearance of reality. In any individual, these aspects are both present but follow the principle of dynamic opposition. Here, this means that when the world seems to be defined by human perception or belief, its physical reality is absent from the forefront of the mind, that is potentialized, but this reality can be rapidly actualized by the banana peel we slip on.

This argument, however, is not acceptable to the religious believer since he will still insist on his ‘alternate reality’ as more fundamental. In my view, the dialectical relation between appearance and reality provides a common language for discussion of belief by both believers and non-believers. Transdisciplinary logic preserves, across the believer/non-believer gap, the necessary attitude of mutual respect. Later, I will describe the dynamics of belief, and belief that belief is true, and show that application of the principles of LIR ends any infinite regress.

6.3.2 Transcendental Perception

The epistemology of the logic of transdisciplinarity describes the dynamics of religious feeling without “denaturing” it, that is, as a transcendental perception by the believer that is at the same time immanent to him or her. I am not a religious believer, in the common acceptation of ‘religious’, but I believe that this statement should be acceptable to one. It is no more (and no less) than a description of the fact that, with very few exceptions, no-one is in a state of transcendent religious experience all of the time. Thus when one set of perceptions is actualized, the other is potentialized. The known exceptions (saints, prophets and so on) might be considered as capable of instantiating an emergent state (T-state), an included middle between immanence and transcendence.

6.4 Social Science

For comparison with the transdisciplinary approach of Nicolescu in the area of social science, I will refer to the also broadly humanist view of transdisciplinarity of Aerts (2001). In his realistic model of society, starting from his extensions of the formalisms of quantum mechanics to complex macroscopic phenomena, Aerts seeks ways of closing the gap between free market dynamics and the “state’s correction dynamics”, in order to maximize the contribution of both. His “third way” depends on “introducing the cultural entities considered fundamental to our Western humanist culture into the dynamics of society”, to make the latter “more fundamentally grounded”.

Aerts’ concepts of actuality and potentiality are not the same as those of Lupasco, but Aerts uses them to develop a realistic model of society as a basis for eventual solutions to the “two fundamental problems with which humanity is confronted in relation to sustainable development.” The first is the incapacity of human talent to control and steer the actual complex world society, to which Aerts proposes some rather idealistic solutions, and the second, to repeat, is the “confusion and misunderstanding that exists in our actual society about the fundamental contradiction between potency and variety versus efficiency and yield.” Aerts’ third way, would tend to eliminate the “apparently irreconcilable duality between socialist and liberal political movements. A simple shift to the center, to a centralist (identifying) organization is not the basis for a better society because

“It leaves too little space for variety and therefore neglects potential. It is a fundamental law that a robust society can only be built when variety and potential are allowed to develop properly. This profound truth is too little understood. This is mainly because it is in conflict with several aspects of society which in our era are overvalued at the expense of variety and potential, namely, ‘efficiency’ and ‘profitability’.”

In Lupasco’s terms, the source of the overvaluation of the latter is yet another expression of the prevailing paradigm of logical identity.

Aerts’ description of his “third way” is compatible with the principle of dynamic opposition and the logic of/in reality. The third way should maintain a variety of political choice and society should be allowed to “evolve in a natural way towards an amalgam of political, economic and cultural niches that exist alongside each other and interact. Duality should evolve towards plurality, and it is only when the third way refers to this sort of plurality that it as a good evolution.” The word amalgam is perhaps unfortunate, as too static, especially as Aerts’ next sentence explicitly mentions the kind of antagonisms that in the LIR view, really exist and are operative: “We must also watch out for the forces that have only an eye to efficiency and yield, not because they are in themselves negative values – they are not – but because they repeatedly endanger variety and potential.” This is equivalent to my position, as is also Aerts’ comment that both likeness and difference should be fostered because they are both fundamental values of reality. If we follow LIR theory, this phrase can be changed to “fundamental logical values of reality”. In a Darwinian survival situation, such as one of constant competition, “stabilizing forces originate in the hidden potency of all the people participating.” In my terms, it is the potential for an emergent resolution of the contradictions involved that may be actualized. (One may still question whether it is a state of peaceful cooperation that corresponds to the deep nature of reality.) In any event, it is in this broad humanist view of transdisciplinarity, the importance of its reflection on the fundamental nature of reality and its objective of increasing the awareness of it that we see a relation to the transdisciplinarity of Lupasco and Nicolescu.

6.5 The Logic of the Development of Transdisciplinarity

As noted, transdisciplinarity is about what lies between and beyond the disciplines, and one of those things is the transdisciplinary logic that links them dynamically. But apart from the application of transdisciplinary logic to various disciplines, what can one say about its application to transdisciplinarity itself as a scientific and social phenomenon? In other words, does transdisciplinarity, considered as a developmental process, follow some kind of logic?

According to the tenets of LIR, all processes do so, but I believe that the origins of the transdisciplinary movement illustrate some aspects of this in a particularly useful way. For example, the career of Stéphane Lupasco was one of continual conflict with the academic establishment in France, which eventually rejected him as not fitting into any one of its convenient boxes – logician, epistemologist, etc. On the other hand, the importance of his central ideas, which I have summarized very briefly here, were intuitively accepted by many other members of the French intelligentsia – artists, writers, poets as well as the physicist Nicolescu and the critical observer of the changes in society René Berger. The founding of the International Center for Transdisciplinary Research and Study was an emergent consequence of the oppositions between the different disciplines practiced by these people, a T-state that includes, without their disappearance, its own sources.

In my view, this is an example of the essence of the logic in transdisciplinarity as something that is inseparable from experience, that is, the experience of the people involved with it, and from the method of analysis used for its understanding. As Lupasco said, logic, method and experience are one, not one in some reduced and inert identity, but one in which all the individual approaches interact and support one another. These approaches, to be specific, are the more scientific one of the logic, which looks at the interactions and changes as real entities; the set of experiences of the players in which subjectivity is more actualized; and the methodological framework for looking at all the processes from a more formal standpoint.

There is no conflation here. Individual scientific and philosophical disciplines retain their specificity and their methodology. Nevertheless, some of the traditional boundaries, for example between ontology, epistemology and metaphysics, while not disappearing, become more permeable, Specific characteristic points of view, that one usually associates with, say, ontology as a set of categories of reality, turn out to be not that different - logically - from the metaphysical standpoint of a study of everything that is, once the in my view artificial absolute separation between categories is removed.

Finally, however, this logical analysis of transdisciplinarity does not exhaust the content of the concept, nor its relation to the unity of science. By definition, it should not and could not. Other papers have indicated some of the many other points of view that are possible. There is also, in transdisciplinarity, a degree of self-reference that should also be discussed. What I have tried to do here is simply give an initial idea of the broad range of application of the principles that are at the heart of the logic first created by Lupasco. My hope is that some of you may perceive some of them as relevant to your own work.

7. THE UNITY OF SCIENCE

As noted, transdisciplinarity is about what lies between and beyond the disciplines, and one of those things is the transdisciplinary logic that links them dynamically. Thus the existence of something like a transdisciplinary logic speaks directly to the question of the unity of science.

If all the sciences, their other properties notwithstanding, have in a common a logic, this logically contributes to the content of that unity. As examples, it suffices to take as widely different disciplines as chemistry and psychology, the latter being one of the group often referred to as the ‘special sciences’, precisely due to the differences they display vs. the physical or natural sciences, as if psychology were not natural.

What one finds, however, even at a level of reality where the feedback loops and internal systems of representation associated with higher ones are not present, there exist structures that correspond to the basic elements of antagonism. In organic chemistry, for example, there are energy fields, bonding orbitals that bond atoms to one another; anti-bonding orbitals that correspond to repulsive forces; and non-bonding orbitals that are neither attractive nor repulsive, but contribute to the properties of the organic molecule as a whole. When two molecules react, they do so either after absorbing sufficient energy to reach a ‘transition state’ at which neither the original unchanged reactants or the future reaction products are present,

The conversion of either chemical and psychological entities to new ones, in my view, requires passing in both cases from states in which actualities and potentialities are real energetic states in interaction to states in which these properties, or some of them, are physically and logically, in my sense of logic, inversed.

The reason there is perhaps no ‘logic of psychology’ per se is doubtlessly to be found in the characteristics of standard logic. Given its limitations to essentially abstract entities, it is not surprising that no specific logic of psychology exists that has been generally accepted. Since the subject matter of psychology to a very large extent deals with pathological, non-“normal” states of mind, the implied irrational nature of the terms suggests that no logic would be applicable to psychological data. LIR provides a transdisciplinary way of naturalizing psychology and the related discipline of phenomenology, that is, making more scientific, some of the first person and other subjective or better subjective-objective data that constitute it.

8. THE UNITY OF KNOWLEDGE

The unity of knowledge has been proposed by Nicolescu as the finality of his conception of transdisciplinarity, based on the logic of Lupasco. In the last thirty-odd years, and especially since the advent of the computer, there have been several encyclopedic projects in the spirit of Diderot and others, such as critical theory, whose primary reference is the social sciences are cited as “unifying” concepts. Other recent, purportedly global views of science, logic and society could be mentioned such as the “New Kind of Science” of Stephen Wolfram and the “Consilience” of the biologist E. O. Wilson (Wilson 2000)

Julie Thompson Klein provided an entry for the Encyclopedia of Life Support Systems (EOLSS) (Klein 2002), released in the context of the International Conference on Sustainable Development, held in South Africa in July 2002. The title of her text was “Unity of Knowledge and Transdisciplinarity: Contexts of Definition, Theory and the New Discourse of Problem Solving.” Klein is particularly interested in the latter subject and offers a coherent program for the involvement of “actors” or “stakeholders” from all segments of society.

In a Section entitled “The Relational Pluralism of Transdisciplinarity”, she writes that along with changes in relational learning fostered by “reconfigurations of disciplines, new ways of thinking, new fields and pedagogies”, a comparable relational pluralism is evident in descriptions of knowledge:

“Once described as a foundation or linear structure, knowledge today is depicted as a network, a web and a dynamic system. The metaphor of unity, with its accompanying implications of universality and certainty, has been replaced by metaphors of plurality and relationality in a complex world. Images of boundary crossing and cross-fertilization supersede older images of disciplinary depth and compartmentalization. Isolated modes of work are supplanted by affiliations, coalitions and alliances. And, older values of control, mastery and expertise are reformulated in rhetorical figures of dialogue, process, interaction and negotiation. This body of images echoes in more specific descriptions of transdisciplinarity.”

There are several comments to be made about this citation, but the one of most relevance here has to do with the questioning of the concept of the unity of science and/or knowledge. The unity of knowledge, also in Nicolescu’s conception, should not be taken to imply a new, closed ideology. As discussed by Nicolescu, the operation of logic in reality is a guarantee of the openness of knowledge. I will not go further here into Klein’s position. I only wish to point out that the concept of unity requires definition, and may in any case not be universally perceived, especially in areas closer to the social than to the natural sciences, as automatically desirable. Participants and others should take perhaps this into account.

The EOLSS body of knowledge, according to the mission presented on the indicated website, is

“inspired by a vision that includes the following paradigm: The sciences should be at the service of humanity as a whole, and should contribute to providing everyone with a deeper understanding of nature and society, a better quality of life and a sustainable and healthy environment for present and future generations.”

Sponsored by UNESCO, the EOLSS, which is intended to be the “largest on-line encyclopedia”, will be “a source of knowledge for sustainable development and global security to lead to fulfillment of human needs through simultaneous socio-economic and technological progress and conservation of the Earth’s natural systems.” The organizers recognize that “Knowledge is dynamic. It grows and evolves according to the needs of human society. In the past, different civilizations categorized knowledge to suit the cultural paradigm of their times.” They wish to “build on the best of our culture to engender a new attitude towards the quality and sustainability of life on earth. Above all we need to foster a culture of peace.”

I agree that there must be fundamental changes in education to create the “desire for environmental protection and respect for human dignity and rights, as the two are mutually empowering”, and avoiding the fostering of a culture characterized by narrow vested interests, intolerance, and violence.” The EOLSS will undoubtedly contribute to solidarity between workers in environmental areas and the public. One should, however, be careful to avoid, in this effort, the reproduction, here also, of the prevailing logical, Manichean paradigm of identity, without recognition of the fundamentally contradictory nature of social dynamics. In a phrase, “metaphors” of both unity and plurality are required.

8.1 Consilience, Gödel and the Unity of Knowledge

Wilson (Wilson 2000) re-introduced the term “consilience” to describe the unification of disciplines by cause-and-effect explanations (epigenetic rules). The current interdisciplinary discourse is seen as an instantiation of Whewell’s original Consilience of Inductions, “by which science can not only progress but can achieve a type of ‘unity’ in the face of complexity and postmodernism.”

In my view, such models cannot lead to a new comprehension of nature as long as binary logic and its idealized formulations of cause and effect are maintained. Wilson admits that: “the convergence of the great branches of learning is mostly an empirical process, light on formal logic and theory in its initial stages.” Nicolescu proposed the unity of knowledge as the finality of transdisciplinarity, and it is the logical aspects of transdisciplinarity that support this.

The unity of knowledge should thus not be taken to imply a new, closed ideology. The unity of science and the unity of knowledge are objectives to be achieved in specific respects for the common good, inspired by a vision that knowledge should be at the service of humanity as a whole. By giving adequate ontological value to uncertainty and Gödelian inconsistency and incompleteness, logic in reality supports the transdisciplinary concept of an open hierarchy of knowledge that avoids all dogmatism or fundamentalism.

In the absence of any perceived need or reason in science to extend Gödel’s principles outside mathematics, the extensions made or proposed have been largely informal. For example, in his definitive presentation of Lupasco’s contribution to logic and metaphysics, Nicolescu (Nicolescu 2002) states that physicists have neglected Gödel’s theorems and they have been without impact on science despite the fact that physical theories use mathematics and therefore are subject to the conclusions of those theorems.

The Gödel theorems and logic – as written – do not apply to physical or mental emergent phenomena, but LIR views the principle involved, the duality of consistency and completeness, axiomatically, as another instantiation of the fundamental duality of the universe. This is a leap that Gödel, who was fundamentally conservative, did not make. He rejected, correctly in my view, the more idealist implications of many-world pictures of reality, but did not make the extension of his own ideas to it. The current logical and ontological development undertaken in LIR provides a bridge between prior definitions of the principle of dynamic opposition and Gödelian dualism.

The relation between consistency (or absence of internal contradiction) and completeness, in mathematics, is between two abstract entities. For any application in physics or other science, what must be recognized is that a similar relation of opposition or dynamic interaction exists in the physical domain between real elements, which can in addition have emergence of new phenomena as a consequence.

The reason that this desirable result has not taken place is due to the absence of a (transdisciplinary) bridge between the original definition by Lupasco of the principle of dynamic opposition and Gödelian dualism. The current demonstration of the logical and ontological development undertaken in LIR illuminates Gödelian dualism as another expression of the fundamental dynamic opposition at the heart of energy and phenomena.

This paper will not discuss the merits of the other views, but look for something more transdisciplinary in the terms of the Conference themselves - “unity” and “knowledge”.

8.2 The Unity of Knowledge

It should be clear that the unity of knowledge in question is not an identity. All the knowledge subsumed in the various disciplines is not identical. But, as a product of the human mind, it cannot be totally diverse in the sense of lacking something in common that is not unique to a discipline. But nothing requires that this be a datum of knowledge. The LIR view is that the unity in question is a Unity* that emerges as an included middle from both unity and the diversity that are properties of the disciplines, but is itself not separated from them. It is exists, and should be perceived as existing, at the same time as the elements from which it is derived, but not reducible to them. The still intensely argued question of the necessity and utility of philosophical vs. physicalist reduction between theories loses much of its pertinence in my theory, but this aspect will not be discussed further here as it is quite ‘technical’.

At the same time, neither disciplines nor individual theories lose their identity and specificity. They do not need to be conflated in this Unity*.

8.3 The Unity of Knowledge

The logic in and of reality (LIR) describes a dialectical basis for perception and action leading to consciousness, and a contradictorial view of consciousness that leads to a new dynamic view of epistemology in the sense of both what we know, how we know, and how we know that we know. Let us assume that what we know includes different disciplines. Let us assume also that how we know includes both the usually accepted concept of firm knowledge or what Lupasco called knowledge-as-such, something clearly actual, and other vaguer, generally (but not always) weaker ways we can call intuition or belief as discussed above. Standard epistemology quickly leads to the well-known paradoxes of knowledge and justification of belief, that is, that we may think we know something, but that is, for any observer, simply a belief that we know.

LIR cuts through these debates by relaxing the absolute separation of classical logic between the essential properties of both objects and relations. It is not necessary as in noneism to say that non-existent objects of belief have no mode of being. I focus on the processes of generation of such objects in the minds of their author or reader, for example. Such actualizations define its real aspects, accompanied by their not yet actualized potentialities, which may or may not ever be actualized. The non-existent emergent entity that the processes represent, better, are, e.g., Zeus, is thus both real and non-real, existent and non-existent. The mind moves back and forth between these properties of beliefs and LIR explicates and formalizes such movement. The dialectical relation between appearance and reality provides a common language for discussion of belief by both believers and non-believers.

The LIR description of the dynamics of belief is in terms of a movement of alternating actualization and potentialization between processes at two-levels - a belief and a belief that that belief is true, and application of its principles can be shown to end the lurking infinite regress. The reason is that LIR accepts the reality of both knowledge and intuition as being two forms of thought related dialectically in the same way as knowledge and knowledge-of-knowledge. When one is actualized, the other is potentialized, but never completely; there is always a part of real knowledge in intuition and vice versa. In addition, however, the two-levels of knowledge and knowledge-of-knowledge exhaust essentially completely the available configuration space. Little or no information is added by postulating additional iterations – knowledge-of-knowledge-of knowledge, and one observes that such iterations stop, or stop themselves, in real life. Thus a belief, in my view, does not imply a requirement for an infinite regress of beliefs that the preceding beliefs are true.

Regarding the origin of intentionality, I believe the only honest answer is similar to that of the weak anthropic principle of reality: consciousness (Emmeche 2003) is an emergent higher order pattern that has both causal powers and a qualitative phenomenal aspect. In LIR, this dual aspect concept receives a natural explanation. A physical model is provided of the locus of intentionality in the dynamic interpretation of experience, experience of experience and their on-going, continuous and contradictorial oppositions. No independent entities of the kind postulated in the various forms of representationalism are required, due to the interactive relation between internal and external aspects of phenomena. It is the alternating actualizations and potentializations derived from the initial inputs that are our ideas, images, beliefs, etc. Logic in reality does not attempt to give a complete understanding of the origin of individual consciousness. It appears to be an irreducible aspect of the universe as we know it.

9. FREE WILL

I will finish this overview of the operation of the principles of my system by discussing a subject - the existence of free will that is generally considered to lie outside the purview of logic. The debate over the existence of free will is, as you know, closely related to the question of determinism vs. indeterminism. Many of the arguments are, however, more or less sophisticated equivalents of the following two models:

- Free will exists. - Determinism is true.

- Free will is incompatible with determinism.

- Therefore, determinism is false. - Therefore, free will does not exist.

I will show briefly how LIR can be used to cut through such arguments. A highly simplified outline of the standard theory of free will is as follows (Kane 1998): people who believe that free will exists believe that the choices they make are not determined by some other agency, including the totality of their own origins and past experience. Such people are further divided into two groups: incompatibilists, who support a view that free will exists and is incompatible with determinism, and compatibilists, who say that free will, or the most important or desirable aspects of it, is compatible with a generally determined universe. Free will also requires analysis as a self-referential phenomenological datum, that is, our view of ourselves as intelligently exercising free will at the same time as having reasons for making the choices we make.

The major problems with the above views are the following: 1) incompatibilists have to show that the universe is not deterministic; 2) compatibilists, who accept determinism, must explain the basis for the feeling and/or appearance of freedom. Further, compatibilists would seem to have no obvious basis for individual moral responsibility, whose existence most human beings would like to establish and live by. In other words, if all one’s choices are totally predetermined, it would appear that one would lack responsibility for one’s actions.

In my opinion, if the problems are given in the above terms, they are insoluble. Another formulation is essentially the same: “Free will is defined as the power of agents to be the ultimate creators and sustainers of their own ends and purposes.” In this theory, although most of our actions can be said to be ‘determined’ in the general sense, by past experience, heredity, or in the worst case by external constraints, every individual will have been, at some earlier point in his lifetime, the locus of some non-determined events or free choices. On the other hand, if phenomenological or folk-psychological descriptions of free will, as efforts made by agents, are eliminated or reduced to a mechanistic, physico-chemical descriptions of mental activity, at least as far as physics and chemistry are usually constituted, then free will would be written out of the world picture. But then, so would also consciousness and intentionality.

The LIR position is that free will as defined initially does not exist; the universe at all levels of reality is characterized by the appearance and reality of both determinacy and indeterminacy. Mental activity at the unconscious level is constituted by a physics and chemistry that also involves potentialities and is related thereby to activity at the higher, conscious level, and free agency as such does not survive the analysis. There remains, however, the need to find some basis for the sense of individual moral responsibility that some people, at least, still feel. I see free will as a particularly strong and lasting intuition, one that inverts the usual relation between intuition and knowledge-as-such. The phenomenon of free will instantiates several processes explicable by a logic that is transdisciplinary across cognitive science, philosophy and morality:

Apparent free will exists, but only as an appearance in the conscious mind of an individual in opposition to and because of her unconscious knowledge of her lack of total ‘freedom’, that is, isolation from other individuals. The issue of compatibility is therefore a false problem; individual responsibility for one’s actions does exist, but its source does not lie in free will, or the absence of it.

We are in the presence of a reciprocal mutual instantiation of appearance and reality that corresponds to the contradictorial, LIR interpretation: appearance and reality can never both be fully actualized at the same time.

If we as knowers are not totally external to what is known by us, not completely different from it, then I conclude that there are other knowers that are part of our known and vice versa.

The source of our dignity is in ourselves as knowers, but if we avoid the error of solipsism, the origin of the sense of moral responsibility can only come from the relation to other knowers, in other words, all human beings, and by extension, other beings. A contrario, one cannot find responsibility in oneself as an isolated agent. Since we are both ‘not-other’ and ‘other’ in the two-tier structure of LIR, a self-interest argument for morality holds.

The LIR position is thus that, paradoxically, two or more human individuals are entities that are logically non-separable. The categorial feature of non-separability in the LIR ontology provides a logical basis for altruism. In other words, since will possesses both deterministic and indeterministic aspects, which interact, the deterministic aspects do not preclude individual moral responsibility. An individual is no more isolated logically, psychologically and morally than he or she is economically. It is because our will is not free that we must try to insure the viability of the environment and behave in an ethical manner.

CONCLUSION

The principles of the ternary, transdisciplinary logic of and in reality enable the functional integration of the contradictorial aspects of phenomena with current advances in science, and offer a supplement to existing methods of inquiry. The LIR framework assigns domains of application of binary and ternary logic to philosophy and real systems in computational and complex non-computational contexts respectively, the latter including evolution, developmental biology and the mental phenomena of knowledge, reasoning and meaning. Such applications of LIR require a shift from the current focus on the axioms and formalism of both classical and non-classical propositional and mathematical logic as the criteria of a valid logical approach. Universal Logic, as the preferred framework for propositional and predicate logics and Gödel’s systems for logic and mathematics (Hintikka 2000) may be considered as special cases to which a broader theory involving a fundamental dialectical principle of dynamic opposition may reduce.

The logic of transdisciplinarity is a system that is directly relevant to reality, not only to human thought and reasoning, but also to other complex biological and social processes, defined categorically as instantiations of dualities that are non-separable. Accordingly, this logic may have an important role as a framework that is a synthetic complement to the analytic strategies of the standard natural sciences and humanities in complex non-computational contexts including evolution, developmental biology and the mental phenomena of knowledge, reasoning and meaning. It offers a transdisciplinary meta-philosophical perspective that integrates the insights of quantum mechanics and uses them to avoid the on-going problems associated with the standard bivalent approaches based in classical conceptions of logic. The principles of the logic of transdisciplinarity do not guarantee the unity of knowledge, but their presence and applicability in all domains of knowledge suggest that they may be useful tools in defining the transdisciplinary agenda.

Aerts, D. (2001), “Transdisciplinary and Integrative Sciences: Humanity’s Mind and Potential”, published as Aerts, D., “Transdisciplinary and integrative sciences in sustainable development”, in the Encyclopedia of Life Support Systems. Oxford: Baldwin House

1 For reasons that are themselves explicable in my approach, attempts are still being made to save classical principles in quantum, category and probability theories, among others.

2 This axiom has been designated as a ‘law of the included middle’ and the original Lupasco logic as a ‘logic of the included middle’, LIM. This term does differentiate it from both the classical logic of the excluded middle and intuitionist logic, in which the law of the excluded middle does not hold. However, since a T-state is ‘included’ only in the sense of being positioned conceptually between opposing elements, I have tended to avoid this locution that carries, incorrectly of course, the idea of two things occupying the same space at the same time.

3 “Somehow” is another expression that is widely (and shamelessly) used in the literature as an admission of ignorance. My theory does not claim to explain the detailed behavior of all phenomena, but it does take explanation down to (at least) one lower level of basic physics.