Logic of the Excluded Middle and the Inclued Middle
Discernement and Wisdom
A non-exhaustive line of inquiry, connected to the search for a unified theory of the universe
This page is not meant to be exhaustive. It aims to open a line of reflection: to understand how the logic of the excluded middle, the notion of the included middle, and the notion of a hidden third can be articulated within a relational approach to the real—and how this articulation resonates both with certain intuitions of contemporary physics and with my own approach grounded in causal analysis.
Page Summary
- Classical logic: an indispensable foundation
- My gradual discovery of the included middle
- Quantum physics: included middle and relational mediation
- The driving principle as a real hidden third
- Reality and the real: levels of intelligibility
- Rational, rationalizable, and transdisciplinarity
- Convergence with my causal approach
- Discernment, wisdom, and responsibility
- Conceptual postulate and system of thought
- Illustration the feminine and masculine roles - Basarab Nicolescu
1. Classical logic: an indispensable foundation
In Aristotle’s logic, three fundamental principles are distinguished: the principle of identity (everything that is, by the very fact that it is, is one), the principle of non-contradiction (one cannot affirm and deny the same thing, of the same reality, under the same respect), and the principle of the excluded middle (between A and not-A, there is no third possibility).
These principles ground all rigorous thinking. At the level of local, determined, and measurable phenomena, they remain indispensable: without this logic, no coherent scientific approach is possible.
2. My gradual discovery of the included middle
I had once heard of the included middle without attaching much importance to it, thinking it sought to weaken a well-established logic. Only recently, while listening to talks by Basarab Nicolescu, did I grasp the importance of this principle—precisely because it does not oppose the excluded middle: it operates at another level.
In other words, the logic of the excluded middle remains fully valid for local states. The included middle concerns the mediation through which oppositions can be understood within a deeper unity, without confusing the planes.
3. Quantum physics: included middle and relational mediation
In quantum physics, entanglement shows that one cannot always consider a particle independently of another. The state of A may be a function of the state of B. Locally, a measurement yields a determined result: the logic of the excluded middle remains valid. But globally, A and B form a system whose coherence cannot be reduced to a mere juxtaposition of isolated elements.
In this configuration, one can say that the A–B relation plays the role of an included third for A: to understand A, one must sometimes consider B. However, this relational mediation raises a deeper question: what grounds the unity of the system? This is where, for me, the notion of a hidden third comes in.
4. The driving principle as a real hidden third
In my perspective, the driving principle plays precisely the role of a real hidden third: it grounds the coherence of relations without reducing to a mechanical force or to an object among others.
I can then specify the articulation as I understand it:
- B, when considered in its relational aspect, can constitute an included middle for A : (A, in some of its characteristics, may depend on its relation to B).
- But B can play this role only thanks to a hidden third that grounds the unity and coherence of the system.
- This hidden third corresponds, in my approach, to the driving principle acting immanently and through interrelation, according to the determination of the elements.
The included middle thus belongs to the plane of observable relations; the hidden third belongs to the fundamental ontological plane. The included middle manifests in dependencies; the hidden third is their condition.
5. Reality and the real: levels of intelligibility
This articulation resonates with an important distinction proposed by Basarab Nicolescu between reality and the real. Reality refers to what resists our representations, our models, and our constructions: it is the domain that can be objectified and tested. The real refers to the ultimate depth of what is, which can never be exhausted by our descriptions.
Nicolescu is not satisfied with a conception in which the real would be merely “veiled” and therefore fundamentally inaccessible. For him, the real is structured: there are levels of reality separated by breaks in laws, yet these levels remain interdependent. A mediation is therefore needed to think the relations between levels without confusing them: this is precisely the role of the included middle, and, more deeply, of the hidden third.
6. Rational, rationalizable, and transdisciplinarity
In this perspective, transdisciplinarity does not mean mixing disciplines, but letting a methodology of discernment emerge— one capable of articulating levels of intelligibility without confusion.
A crucial distinction then appears: that between the rational and the rationalizable. Not everything that is rational is entirely rationalizable. Authentic rationality must leave room for mystery, not in order to abandon rigor, but in order to avoid intellectual excess.
Excessive specialization, when it makes us lose a deep perception of things, can lead to a loss of meaning, to formal drifts, and, ultimately, to forms of destruction of the human being through power and knowledge without wisdom.
7. Convergence with my causal approach
For my part, I arrived at a similar architecture by another path: a causal analysis inspired by Aristotle, pushed to its end regarding the question of efficient causality in the physical world. This approach led me to recognize that a local event is not self-sufficient: it is inscribed within a broader relational coherence.
The driving principle grounds this coherence: it unifies without reducing, orients without constraining, and makes possible the articulation between the excluded middle (local rigor) and the included middle (relational mediation), on the foundation of the hidden third (ontological unity).
8. Discernment, wisdom, and responsibility
Without the excluded middle, thought dissolves. Without the included middle, it becomes rigid. Without the hidden third, it loses its orientation. Discernment consists in knowing at which level one is situated; wisdom consists in not absolutizing one level at the expense of the others.
Authentic knowledge maintains harmony between understanding, power, and wisdom: it respects mystery without renouncing rigor, and remains at the service of the human being rather than at the service of blind mastery.
9. Conceptual postulate and system of thought
Finally, I can add an important remark: the notion of a conceptual postulate. In my work, I was led to formulate a foundational postulate from which it becomes possible to build a coherent system of thought. I developed this idea in an still embryonic way in my book In Search of the Theory of the Universe and my book Conceptual Foundations and Theory.
A conceptual postulate is neither an arbitrary hypothesis nor a mere provisional model: it aims at an overall coherence by articulating causal analysis, scientific facts, and philosophical requirements. It allows, for example, the organization of fundamental concepts (space, time, mass, inertia, causality, relation, actualization) into an intelligible whole—without claiming to exhaust the real.
This approach can be understood as an element of transdisciplinary methodology: it respects the autonomy of disciplines while seeking a principle of articulation capable of avoiding both reductionism and mere juxtaposition. It thus maintains the balance between the rational, the rationalizable, and mystery—condition of a knowledge that is both rigorous and respectful of reality in all its dimensions.
10. Illustration the femine and masculine roles : Basarab Nicolescu
The Feminine: Specific Role (Fr)