20-12-2020
Prologue
We are used to think in terms of classical Aristotelian logic. Much of the problems in thought arises because of the inherent limitation of Aristotelian logic of the excluded middle.
The Romanian-French philosopher and logician Stephan Lupasco (1900 -1 988) developed a new system of non-Aristotelian logic of the Included Middle, inspired by quantum physics wherein logical paradox is one of its main features (e.g. the wave-particle duality).
Lupasco’s logic includes classical Aristotelian logic as a special case, which can be used when we deal with simple and consistent situations in gross reality, which is similar in the way in which Einsteinian physics includes Newtonian physics as a special case approximation for the local universe.
Stephan Lupasco’s Logic of the Included Middle
A. Fundamental Postulate
The key postulate, as 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 logic is the Logic of the Included Middle, which consists 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 change rather than to formal change, e.g. of conclusions).
B. Classical Aristotelian Axioms
The three fundamental axioms of classical Aristotelian logic, in one version, are the following:
1. The axiom of identity: A is A.
2. The axiom of non-contradiction: A is not non-A.
3. The axiom of the excluded middle: there exists no third term ‘T’ (‘T’ from third) that is at the same time A and non-A.
Based on his quantum worldview, Lupasco rewrote the three major axioms of classical logic as follows:
C. The Philosophical Logic of Stéphane Lupasco
1. (Physical) Non-Identity: There is no A at a given time that is identical to A at another time.
2. 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, but never to the limit of 100%.
3. Included Middle: An included or additional third element or ‘T-state’ exists (‘T’ for ‘tiers inclus’, included third) [at a contiguously higher level of reality or complexity].
The evolution of real processes is therefore asymptotically toward a non-contradiction of identity or toward contradiction.
The mid-point of semi-actualization and semi-potentialization of both is a point of maximum contradiction, a ‘T-state’ resolving the contradiction (or ‘counter-action’) at a higher level of reality or complexity.
Lupasco’s Logic of the Included Middle is a valid multivalent logic, with the indicated terms. At a single level of reality, the second and third axioms are essentially equivalent.
The 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 resolved.
A paradigm example is the unification in the quanton (T) of the apparently contradictory elements of particle (A) and wave (non-A).
In contrast to the Hegelian triad, the three terms here coexist at the same moment of time. The Logic of the Included Middle does not abolish that of the excluded middle, which remains valid for simple, consistent situations. However, the former is the privileged logic of complexity, of the real mental, social and political world.
The Logic of the Included Middle is capable of describing the coherence between levels of reality. A given T-state (which operates the unification of A and non-A) is associated with another couple of contradictory terms at its higher level (A1 , non-A1 ), which are in turn resolved at another level by T1 .
The action of the Logic of the Included Middle induces an open structure of the set of all possible levels of reality, similar to that defined by Gödel for formal systems.
In relating and dealing with the phenomenal world, which is binary through and through, I use Lupasco’s logic, when thinking, so that I can look at the world of duality from the perspective of the Included Middle on a higher and more complex level of reality and consciousness (conception/perception), but when deciding (to decide = to cut off/to kill the alternative), I commit to what I consider to be the better hypothesis out of the binary alternative from the perspective of the Included Middle.
To commit to what I consider to be the better hypothesis is not the same as to believe or to be convinced. With new information and observation accumulating relative to the same level of reality or complexity, I may continue to recommit (commit again) to the same hypothesis or recommit (commit anew) to the other alternative or a new (modified) hypothesis.
Therefore, while I am committed, I am not attached, to my hypothesis. Because commitment has a thought-power, people may think that I am convinced, but I am not convinced of anything or I do not believe (in) anything. My views and opinions concerning the binary phenomenal world are all hypotheses that are in constant and continual modification and revision.
This commitment constitutes what is called trust.