101015 8 min

Knowledge As System: A Logic Of Epistemology

Joe Brenner, Lausanne


Despite the remarkable achievements of science in general and systems science in particular, there seems to be no adequate epistemological framework for development of a more responsible, ethical approach to their application. Potentially unifying theories proposed in the late 20 th Century, such as dynamic structuralism (catastrophe theory), have been shown to have fundamental limitations. To a certain extent, systems theory and 2 nd Order Cybernetics have become uncoupled from von Bertalanffy’s original vision of a “science of wholeness”[1].

At the same time, 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. The possibility of a relation between these two situations suggests that a new view of logic may be called for. Newer ampliative adaptive and paraconsistent logics provide a better picture of some changes, but they refer primarily to abstract semantic domains and do not give a satisfactory picture of the dynamics of real-world systems and processes, in particular of knowing, the knower and the known.

In the paper, I propose a transconsistent logic (TCL) as a needed extension of logic to reality. I explore the relation between this logic and real systems and an epistemology that not only incorporates a concept of temporality, but also reflects the underlying physical/metaphysical organization of the world into systems. In this approach, the traditional boundaries between disciplines – logic, epistemology, ontology, ethics, and phenomenology – do not disappear, but they become more permeable. Recognition of the complex contradictorial aspects of knowing may be useful in avoiding simplistic, binary models implying Manichean world-views.

A Transconsistent Logic of Energy

Based on the quantum mechanics of Planck, Pauli and Heisenberg, developmental biology and cosmology, Stéphane Lupasco[2] (Bucharest, 1900 – Paris, 1988) proposed that the characteristics of energy - extensive and intensive; continuous and discontinuous; entropic (tendency toward identity or homogeneity – 2 nd Law of Thermodynamics) and negentropic (tendency toward diversity or heterogeneity – Pauli Exclusion Principle) - could be formalized as a structural logical principle of dynamic opposition, an antagonistic duality inherent in the nature of energy and accordingly of phenomena, including information, propositions and judgments, etc.

The key Lupasco postulate is that every 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 disappearing completely. The point of equilibrium - semi-actualization and semi-potentialization - is one of maximum antagonism or “contradiction” from which a T-state (T for “tiers inclus”, included third term) emerges, resolving the contradiction (or “counter-action”), as proposed by Nicolescu[3], at a higher level of reality.

The logic that describes this picture of reality is a logic of an included middle, consisting of axioms or rules for determining the state of the three dynamic terms involved in a phenomenon (“dynamic” in its physical sense, related to real rather than to formal change, e.g., the facility of changing rules or conclusions.) In this formalism, the reciprocally determined values of the degree of actualization A, potentialization P and T-state T replace the truth values in standard truth tables, permitting a non-truth-functional semantics. The term “transconsistent” is preferred for this logic since all three axioms of classical logic are modified, and contradiction is handled differently than in paraconsistent logic. TCL contains the law 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[4].

The objection can be raised against TCL that it is not a logic, as it fails to have the required formal structure. However, Béziau[5] has shown that the essence of logic is not its formality, mathematical or other, and one is best off in speaking about logic tout court.

Opposing aspects of phenomena that are generally considered independent can be understood as being in the dynamic relationship suggested, namely, as one is actualized, the other is potentialized. Problems due to the assumption of an absolute independence or separation between terms (e.g., local/ global, part/whole, set/member of set, rational/irrational, etc.) can be approached from this standpoint.

The Logical Origin of Systems in Energy

Stéphane Lupasco formulated a conception of the formation of systems via a set of dynamic constitutive relations: (1) a relation of antagonism (attraction – repulsion); (2) a relation of contradiction or essential difference of type (homogeneous – heterogeneous). Systems require the energy involved in these dynamic relations in order to exist. Since all their constituents and elements, according to the equivalence of mass, energy and information, must consist of energy, systems instantiate the indicated dialectical characteristics. These notions provide another perspective on the phenomenon of feedback in complex systems. As an antagonistic energetic duality, each element is a system, and all more complex systems are generated by such by their subsequent interactions of the same kind, leading to systems of systems, systems of systems of systems, etc., transfinitely, resulting in “systemogenesis” or emergence, especially, at the biological, mental and social levels.

A Metaphysics of Knowledge

In the TCL approach to knowledge, the primary elements subject to the above systems relations are the knower and the known. The existence of a knower and a known implies both an internal and external reality, and the hypothesis is made that the knower does not know himself in the act of knowing (one can’t know two things at once). A counterfactual argument then shows that the known is neither totally identical nor totally other than the knower. The dualities are contradictory: for one to be (mostly) actual, the other must be (mostly) potential. The two are not both actual at once, but as one is actualized, the other is potentialized.

Knowledge of Knowledge and Intuition
In the paper, I discuss some consequences of this theory: the contradictorial relation between knowledge and the knowledge of knowledge, and between knowledge-as-such and intuition, both being considered as accessible to logical analysis, and I show that these considerations provide a method for ending the infinite epistemic regress.

This view of the grounding of epistemology in science supports the idea of naturalized epistemology as discussed in the comprehensive review article by Feldman[6]. Regarding the original discussion by Quine of the foundations of science[7], our approach suggests that his reduction of epistemology to psychology was not as radical as generally considered. Epistemology and natural science are reciprocally “contained”, and TCL can support the development of a formal dynamic epistemology of experience.


I propose a ternary, transconsistent logic of reality (TCL) whose principles enable its functional integration with current advances in physical science and establishes a framework for looking at their epistemological connections with complex natural systems. TCL assigns domains of application of binary and ternary logic to systems in computational and non-computational contexts respectively. Of the latter, human cognitive systems involving knowledge, reasoning and meaning are the most important examples. Knowledge and knowing are considered as systems of systems that share the same underlying metaphysics as systems in general. Such application of TCL requires a shift from the current focus on the axioms and formalism of both classical and neo-classical propositional and mathematical logic as the criteria of a valid logical approach. Consideration of the contradictorial aspects of knowledge, as a supplement to existing methods of inquiry, could provide useful insights for the development of a new transdisciplinary scientific, philosophical and social agenda.

{{[1] Von Bertalanffy, General Systems Theory. New York: George Braziller, (revised edition), 1969

[2] Lupasco, Le principe d’antagonisme et la logique de l’énergie. Paris: Editions du Rocher, 1987 (1951)

[3] Nicolescu, Nous, la particule et le monde. Paris: Editions du Rocher, 2002 (1985)

[4] Kirshbaum, Introduction to Complex Systems, calresco.org, 2002

[5] Béziau, “What is a Logic?”, paper for publication, 2004

[6] Feldman, “Naturalized Epistemology”, The Stanford Encyclopedia of Philosophy (Fall 2001 Edition), Edward N. Zalta (ed.), URL = plato.stanford.edu

[7] Quine, Ontological Relativity and Other Essays. New York: Columbia University Press, 1969, Chapter 3, “Epistemology Naturalized”}}

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