I first encountered the term included middle in Nicolescu's book Manifesto of Transdisciplinarity (2002), a difficult book that I'm still not ready to discuss. According to Joseph E. Brenner in his essay The Logic of Transdisciplinarity (from Nicolescu's book Transdisciplinarity: Theory and Practice, 2008), "the logic of the included middle [was] developed by the Franc-Romanian philosopher Stèphane Lupasco (1900-1988) and extended by Nicolescu … [as a] needed replacement of the neoclassical logical framework that underlies current individual, social, and scientific paradigms" (155). As I understand it, the developments of quantum physics which sees light as both a particle and a wave at the same time establishes the need for a new logic to complement and transcend the old, classical logic, which Nicolescu (In Vitro and In Vivo Knowledge in Transdisciplinarity: Theory and Practice) says was "founded on three axioms:
- The axiom of identity: A is A.
- The axiom of noncontradiction: A is not non-A.
- The axiom of the excluded middle: There exists no third term T ("T" from "third") which is at the same time A and non-A" (6).
According to this fundamental way of constructing Reality, light can either be a particle or a wave, but it can not be both at the same time. Quantum physics, however, said that light was both particle and wave and at the same time. Something had to give. Lupasco and Nicolescu decided that logic would give, and so they developed the logic of the included middle, and I think it is this included middle that Mending Wall captures for me.
The wall in the poem is, of course, the boundary between the narrator's farm and the neighbor's farm. It is also the boundary between the narrator's dislike of walls and the neighbor's like of them. According to the old logic then, traceable all the way back to Aristotle, the narrator's farm is the narrator's farm, it is not the neighbor's farm, and there is no middle ground that is both narrator's farm and neighbor's farm. This logic makes great sense at the level of common, everyday Reality. It puts everything in its place and keeps it there. Most of us act on this common, classical logic everyday.
But when we shift levels of Reality, then the limitations of this logic become obvious. Nicolescu says that natural science has discovered at least three different levels of Reality—"the macrophysical level, the microphysical level, and the cyber-space-time"—with a break in the laws and concepts applicable to each level. These levels exist simultaneously and through engagement with one another, and the contradictions at one level (A vs. non-A) become non-contradictory at another level. I do not have the skill with mathematics or formal logic to describe this for you, but I think the poem gives me a way of visualizing this concept. At the everyday scale, or Level B, of reality, the wall creates a boundary between the narrator's farm and the neighbor's farm such that each is itself and not the other and there is no middle zone that they both occupy. There is indeed a boundary between the two at Level B of Reality, and a person can step over that boundary. Or not. This defines our day-to-day existence at Level B.
However, if I stand at the boundary and rise upward to the level of the macrophysical, to Level A, then the two farms become smaller and smaller until they become two dots and then one dot and then nothing. No boundary. Likewise, if I fall downward to the level of the microphysical, to Level C, then the two farms become larger and larger until they become molecules, atoms, and strings of vibrating energy. Again, no boundary, at least not between two farms. Thus, the contradiction at one level of reality is a non-contradiction at another level. It is not resolved, as it would be in a Hegelian dialectic, because the contradiction continues to exist on Level B at the same time that it does not exist at Levels A and C. There is no resolution, only a certain tension among the various points of view. The wall both is and is not at the same time. Turn your head one way, and it is. Turn your head the other way, and it is not. The wall is both actual and potential at the same time. Your knowledge of its state depends on your position relative to the wall.
Well, I think this is one way to think about the included middle. It's one way to think about boundaries.